Soal Latihan Olimpiade Matematika

<div dir="ltr" style="text-align: left;" trbidi="on"><div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">Soal Latihan Olimpiade Matematika. Olimpiade Matematika adalah suatu perlombaan yang menggunakan materi matematik sebagai bahan perlombaan. Kegiatan ini diadakan untuk mengetahui sejauh mana tingkat pemahaman tentang matematika, penalaran dan komunikasi matematika untuk memecahkan masalah Matematika. Peserta olimpiade matematika ini biasanya berasal dari siswa sekolah dasar dan menengah. Baik siswa sekolah menengah pertama maupun sekolah menengah atas. Biasanya pemenang dari kegiatan olimpiade matematika ini selain mendapat hadiah, juga akan diikutsertakan dalam kegiatan serupa pada tingkat yang lebih tinggi. Olimpiade matematika ini pada dasarnya sama dengan berbagia macam kegiatan lomba lain. Hanya saja, materi yang diujikan bagi siswa adalah dengan memecahkan masalah yang berhubungan dengan materi dalam pelajaran matematika. Berikut ini contoh soal Olimpiade Matematika Tahun 2010, walaupun sudah jadul tidak ada salahnya mempelajari soal ini.</span><br /><span style="font-family: Georgia, 'Times New Roman', serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;"><b>Soal Eksplorasi</b></span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">1. A numberworm is made up of sixteen squares numbered consecutively from 1 to 16. It can be fit into a 4 x 4 grid so that two consecutive squares share a side, one possibility is given on the left below.  </span></div><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 1em; text-align: justify; width: 120px;"><tbody><tr><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5 </span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4 </span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">1</span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3 </span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">11</span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">12</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">16 </span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">14</span></div></div></div></td><td style="background-color: #f8f8f8;" width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">13</span></div></div></div></td></tr></tbody></table><div style="text-align: justify;"><span style="font-family: Georgia, 'Times New Roman', serif;">Find as many as possible ways to fit a numberworm onto the grid on the right</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 1em; text-align: justify; width: 560px;"><tbody><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">1</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">16</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></td><td rowspan="4" width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">1</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">16</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">14</span></div></td><td rowspan="4" width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">1</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">16</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">13</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">12</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">12</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">12</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">13 </span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">14</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">11</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">14</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">13</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></td></tr><tr><td colspan="14" width="560"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">1</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">16</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">14</span></div></td><td rowspan="4" width="40"><div style="text-align: center;"></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">1</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">16</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">14 </span></div></td><td rowspan="4" width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">1</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">16</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">14</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">13</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">13</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">12</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">13</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></td><td width="40"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">12</span></div></div></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">12 </span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4 </span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></td></tr></tbody></table></div><div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">2. Ada dua orang pria yaitu Budi dan Coki serta dua orang wanita yaitu Ani dan Diana. Keempat orang itu ada sepasang suami-istri dan dua orang yang belum menikah. Pasangan yang menikah mengeluarkan pernyataan yang benar dan dua orang yang belum menikah mengeluarkan pernyataan yang salah. Pernyataan mereka sebagai berikut.</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Pria pendek :"Saya tidak menikah dengan Diana"</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Pria tinggi    :"Saya Coki".</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Wanita pendek :"Coki lebih pendek dibanding Budi".</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Wanita tinggi :"Yang menikah adalah pria yang tinggi dengan wanita yang pendek".</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Dari keempat pernyataan tersebut di atas, kita dapat menentukan nama masing-masing beserta ciri-cirinya. Lengkapilah tabel di bawah ini dengan nama dan statuspernikahan (menikah atau tidak menikah).</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 1em; text-align: justify; width: 600px;"><tbody><tr><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Nama</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Status Pernikahan</span></div></td></tr><tr><td width="200"><div style="text-align: center;"><div style="text-align: left;"><span style="font-family: Georgia, 'Times New Roman', serif;">Pria Pendek</span></div></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td></tr><tr><td width="200"><div style="text-align: center;"><div style="text-align: left;"><span style="font-family: Georgia, 'Times New Roman', serif;">Pria Tinggi</span></div></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td></tr><tr><td width="200"><div style="text-align: center;"><div style="text-align: left;"><span style="font-family: Georgia, 'Times New Roman', serif;">Wanita Pendek</span></div></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td></tr><tr><td width="200"><div style="text-align: center;"><div style="text-align: left;"><span style="font-family: Georgia, 'Times New Roman', serif;">Wanita Tinggi</span></div></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td></tr></tbody></table><span style="font-family: Georgia, Times New Roman, serif;">Jawab :</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 1em; text-align: justify; width: 600px;"><tbody><tr><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Nama</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Status Pernikahan</span></div></td></tr><tr><td width="200"><div style="text-align: left;"><span style="font-family: Georgia, 'Times New Roman', serif;">Pria Pendek</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Coki (3)</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">Menikah (4)</span></div></td></tr><tr><td width="200"><div style="text-align: left;"><span style="font-family: Georgia, 'Times New Roman', serif;">Pria Tinggi</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Ani (3)</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">Tidak Menikah (4)</span></div></td></tr><tr><td width="200"><div style="text-align: left;"><span style="font-family: Georgia, 'Times New Roman', serif;">Wanita Pendek</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Budi (5)</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">Menikah (2)</span></div></td></tr><tr><td width="200"><div style="text-align: left;"><span style="font-family: Georgia, 'Times New Roman', serif;">Wanita Tinggi</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Diana (5)</span></div></td><td width="200"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Tidak Menikah (1)</span></div></td></tr></tbody></table><ul><li><span style="font-family: Georgia, 'Times New Roman', serif;">(1). Pernyataan 2 dan 3 bertentangan. Salah satu pasti salah. Dengan demikian pria tinggi tidak menikah dengan wanita pendek. Akibatnya pernyataan 4 salah. Jadi Wanita tinggi tidak menikah.</span></li><li><span style="font-family: Georgia, 'Times New Roman', serif;">(2). Karena wanita tinggi tidak menikah maka wanita pendek menikah.</span></li><li><span style="font-family: Georgia, 'Times New Roman', serif;">(3). Karena wanita pendek menikah, dia mengeluarkan pernyataan yang benar. Dengan demikian Coki adalah pria pendek dan Budi adalah pria tinggi. Selain itu didapat kesimpulan bahwa Pria tinggi mengeluarkan pernyataan yang salah.</span></li><li><span style="font-family: Georgia, 'Times New Roman', serif;">(4). Karena pria tinggi (Budi) mengeluarkan pernyataan salah, dia tidak menikah dan Coki menikah.</span></li><li><span style="font-family: Georgia, 'Times New Roman', serif;">(5) Karena Coki tidak menikah dengan Diana, maka Coki menikah dengan Ani</span></li></ul><span style="font-family: Georgia, Times New Roman, serif;">3. Sembilan bilangan asli berbeda yang masing-masing kurang dari 21 diletakkan pada tabel 3 x 3 dengan ketentuan sebagai berikut. Pada setiap baris, kolom, atau diagonal berlaku “bilangan yang berada di tengah sama dengan rata-rata dari dua yang lain.” Jika bilangan 10 dan 15 menduduki posisi sebagaimana pada tabel di bawah ini, tuliskan sebanyak mungkin susunan yang memenuhi ketentuan di atas.</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 1em; text-align: justify; width: 120px;"><tbody><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></td></tr></tbody></table></div></div><div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">Jawaban :</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 1em; text-align: justify; width: 600px;"><tbody><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">12</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">19</span></div></td><td rowspan="3" width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">17</span></div></td><td rowspan="3" width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">9</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">13</span></div></td><td rowspan="3" width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">8</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">11</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">3</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">17</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">4</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">16</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">6</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">14</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">7</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">13</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">1</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">8</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">3</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">9</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">7</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">9</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">12</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">15</span></div></td></tr><tr><td colspan="15" width="600"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">3</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">1</span></div></td><td rowspan="3" width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">4</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">3</span></div></td><td rowspan="3" width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">6</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">7</span></div></td><td rowspan="3" width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">5</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">7</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">9</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">12</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">8</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">9</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">9</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">8</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">10</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">12</span></div></td></tr><tr><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">19</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">17</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">17</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">16</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">13</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">14</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">15</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">11</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">13</span></div></td><td width="40"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">15</span></div></td></tr></tbody></table><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">4. Sisi dari setiap dadu masing-masing diberi angka 1, 2, 3, 4, 5 dan 6. Angka 1 berseberangan dengan 6, angka 2 berseberangan dengan angka 5, dan angka 3 berseberangan dengan 4. Beberapa dadu akan disusun (bukan ditumpuk keatas) menjadi sebuah rangkaian dengan cara merekatkan satu sisi sebuah dadu dengan satu sisi dadu yang lain. Hanya dua buah sisi dengan angka sama yang boleh direkatkan. Dengan cara demikian, sisi-sisi yang direkatkan dan sisi bagian bawah menjadi tidak nampak (tidak terlihat). </span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">a. Jika kita menyusun dua buah dadu, berapa nilai terbesar yang mungkin didapat  </span><span style="font-family: Georgia, 'Times New Roman', serif;">dari jumlah angka-angka yang tampak? </span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">b. Jika kita menyusun tiga buah dadu, berapa nilai terbesar yang mungkin didapat  </span><span style="font-family: Georgia, 'Times New Roman', serif;">dari jumlah angka-angka yang tampak? </span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">c. Jika kita menyusun enam buah dadu, berapa nilai terbesar yang mungkin  </span><span style="font-family: Georgia, 'Times New Roman', serif;">didapat dari jumlah angka-angka yang tampak? </span></div><div style="text-align: justify;"></div><div style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOE16wR0-kRHtbMtbQ_nFpzKk8HlXuy2qvw1DrcLCgMGs5ElWXIkx2BCjpEVQr_Ba4gZt8tnK5SXE3L_1Us8_ZBlfTz2l-gGCQi0a2Ux1HwA4MdmN0O0faKsX2ftLng6SzFoxzGY1yyHSq/s1600/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOE16wR0-kRHtbMtbQ_nFpzKk8HlXuy2qvw1DrcLCgMGs5ElWXIkx2BCjpEVQr_Ba4gZt8tnK5SXE3L_1Us8_ZBlfTz2l-gGCQi0a2Ux1HwA4MdmN0O0faKsX2ftLng6SzFoxzGY1yyHSq/s1600/4.png" /></span></a></div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">5. Tuliskan sebanyak mungkin bilangan asli yang memenuhi semua empat sifat berikut:</span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">a. Terdiri atas empat digit yang semuanya berbeda</span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">b. Tidak memuat digit 0</span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">c. Jumlah keempat digitnya habis dibagi 4</span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">d. Hasil kali dua digit pertama sama dengan hasil kali dua digit terakhir </span><br /><span style="font-family: Georgia, Times New Roman, serif;">Tabel berikut memperlihatkan bilangan yang memenuhi syarat (i), (ii), dan (iv).</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 1em; text-align: justify; width: 600px;"><tbody><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">Dua Digit Pertama</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">Dua Digit Terakhir</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">Dua Digit Pertama</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">Dua Digit Terakhir</span></div></td></tr><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">16</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">23,32</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">43</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">26,62</span></div></td></tr><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">18</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">24,42</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">46</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">38,83</span></div></td></tr><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">23</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">16,61</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">62</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">34,43</span></div></td></tr><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">24</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">18,81</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">63</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">29,92</span></div></td></tr><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">26</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">34,43</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">64</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">38,83</span></div></td></tr><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">29</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">36,63</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">81</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">24,42</span></div></td></tr><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">32</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">16,61</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">83</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">46,64</span></div></td></tr><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">34</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">26,62</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">92</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">36,63</span></div></td></tr><tr><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">36</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">46,64</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">-</span></div></td><td width="150"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">-</span></div></td></tr></tbody></table><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">Dengan memeriksa, bilangan yang juga memenuhi syarat ketiga (sehingga ia memenuhi keempat syarat yang diminta) adalah 1623, 1632, 2316, 2361, 2936, 2963, 3216, 3261, 3629, 3692, 6329, 6392, 9236, dan 9263.</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">6. Setiap kerangka kubus mempunyai 12 rusuk. Apabila kita menghimpitkan dua kerangka kubus yang berukuran sama dan setiap dua rusuk yang berimpitan dianggap satu rusuk maka didapat sebuah bangun balok yang mempunyai 20 rusuk. Dengan aturan seperti di atas maka :</span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">a. Apabila 8 buah kerangka kubus yang berukuran sama disusun berjajar memanjang membentuk bangun balok, ada berapa rusuk pada bangun balok yang terbentuk?</span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">b. Apabila 8 buah kerangka kubus yang berukuran sama disusun sehingga membentuk bangun kubus , ada berapa rusuk pada bangun tersebut?</span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">c. Apabila 125 buah kerangka kubus yang berukuran sama disusun berjajar memanjang, ada berapa rusuk pada bangun balok tersebut?</span></div><div style="text-align: justify;"><span style="font-family: Georgia, Times New Roman, serif;">d. Apabila 125 buah kerangka kubus yang berukuran sama disusun sehingga membentuk bangun kubus, ada berapa rusuk pada bangun tersebut?</span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7KKHsZ049StEbbi24hty3KPnq9vDAQ9oimIVYt-Iq2A_V4hVTEZNVBgArU66u9aE6HaNrS606Cb1FzHns2t0C4JtFoaD3rYipsy3AEuMb_d0-Odp8C9EuC1Etb7y4bHeYJvCrgWa4bqxv/s1600/6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7KKHsZ049StEbbi24hty3KPnq9vDAQ9oimIVYt-Iq2A_V4hVTEZNVBgArU66u9aE6HaNrS606Cb1FzHns2t0C4JtFoaD3rYipsy3AEuMb_d0-Odp8C9EuC1Etb7y4bHeYJvCrgWa4bqxv/s1600/6.png" /></span></a></div><span style="font-family: Georgia, Times New Roman, serif;">a. (8×12)-(7×4) = 68</span><br /><span style="font-family: Georgia, Times New Roman, serif;">b. (2×12)-(1×4) =20 (2×20)-(1×7) =33 (2×33)-(1×12) = 54</span><br /><span style="font-family: Georgia, Times New Roman, serif;">c. (125×12)-(124×4) = 1004</span><br /><span style="font-family: Georgia, Times New Roman, serif;">d.(5×12)-(4×4) = 44 (5×44)-(4×16) = 156 (5×156)-(4×60)=540</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;"><b>Soal Isian Singkat</b></span><br /><span style="font-family: Georgia, Times New Roman, serif;">7. Sepuluh anak kelas VI berangkat berkemah dengan membawa bekal yang cukup untuk 9 hari. Dalam perjalanan, 5 anak lain bergabung untuk ikut berkemah, tetapi mereka tidak membawa bekal. Bekal semula yang mereka bawa tersebut cukup untuk ....hari.</span><br /><span style="font-family: Georgia, 'Times New Roman', serif;">10 x 9 = 15 x 6 = 6 hari</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">8. Banyaknya pasangan segitiga yang kongruen (sama dan sebangun) dari gambar jajargenjang di samping ini adalah ...</span><br /><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAnI0-HaFjQBUKTXSUct8-TcYDBMAkiKA2sgK5XYW4q8KjGuNVGqHwLTXp3H-VPhyphenhyphenaM3PWhzj4b5J4CeI_pbzcgrILBn4uQ_9ikWti3Ud4ie8nmkoVnHi16Tei8JIYWu9CyPteW87dqP7O/s1600/23.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAnI0-HaFjQBUKTXSUct8-TcYDBMAkiKA2sgK5XYW4q8KjGuNVGqHwLTXp3H-VPhyphenhyphenaM3PWhzj4b5J4CeI_pbzcgrILBn4uQ_9ikWti3Ud4ie8nmkoVnHi16Tei8JIYWu9CyPteW87dqP7O/s1600/23.png" /></a></span></div><br /><span style="font-family: Georgia, Times New Roman, serif;">Jawab :</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Satu segitiga : 3 Dua segitiga : 1; </span><span style="font-family: Georgia, 'Times New Roman', serif;">Tiga segitiga : 2; </span><span style="font-family: Georgia, 'Times New Roman', serif;">Total 6 pasang</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">9. The remainder of (3457689 x 9876543 x 7777</span><span style="font-family: Georgia, 'Times New Roman', serif;"> ) : 5 is 4</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">10. Sebuah kotak berisi bola merah dan bola putih dengan 80% di antaranya adalah  </span><span style="font-family: Georgia, 'Times New Roman', serif;">bola merah. Mula-mula diambil 35 bola merah dan 5 bola putih dari kotak tersebut. </span><span style="font-family: Georgia, 'Times New Roman', serif;">Sisanya dibagi menjadi beberapa kelompok, masing-masing terdiri atas 7 bola. </span><span style="font-family: Georgia, 'Times New Roman', serif;">Pada setiap kelompok terdapat 5 bola merah. Pada awalnya paling sedikit terdapat</span><span style="font-family: Georgia, 'Times New Roman', serif;"> bola dalam kotak tersebut.</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 0px; text-align: justify; width: 500px;"><tbody><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">No </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">#Bola Merah</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">#Bola Putih</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Rasio</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">Apakah Rasionya 4 : 1 ?</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Diambil </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">35</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Sisa 1 klpk </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+5</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+2</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">40 : 7</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">x</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Sisa 2 klpk</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+10</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+4</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">45 : 9</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">x</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Sisa 3 klpk</span><span style="font-family: Georgia, 'Times New Roman', serif;"> </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+15</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+6</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">50 : 11</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">x</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Sisa 4 klpk</span><span style="font-family: Georgia, 'Times New Roman', serif;"> </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+20</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+8</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">55 : 13</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">x</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Sisa 5 klpk</span><span style="font-family: Georgia, 'Times New Roman', serif;"> </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+25</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">+10</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">60 : 15</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">√</span></div></div></div></td></tr></tbody></table><span style="font-family: Georgia, Times New Roman, serif;">Jadi isi kotak semula 60 + 15 = 75 bola</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">11. Pada gambar di samping, tiga lingkaran yang terletak pada titik-titik sudut suatu </span><span style="font-family: Georgia, 'Times New Roman', serif;">segitiga disebut lingkaran-lingkaran serumpun. Setiap kali Fikry menambahkan </span><span style="font-family: Georgia, 'Times New Roman', serif;">bilangan 1 pada suatu lingkaran, ia harus menambahkan pula bilangan 1 pada dua </span><span style="font-family: Georgia, 'Times New Roman', serif;">lingkaran lain yang serumpun dengan lingkaran tersebut. Setelah beberapa kali </span><span style="font-family: Georgia, 'Times New Roman', serif;">penambahan bilangan 1, diperoleh susunan bilangan seperti tampak pada gambar </span><span style="font-family: Georgia, 'Times New Roman', serif;">tersebut. Jika pada awalnya semua lingkaran tersebut berisi bilangan 0, maka nilai</span><span style="font-family: Georgia, 'Times New Roman', serif;"> adalah . </span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKf_jYoHAv_6IhZbtKxW9S8Hqg1GeoVpVaRVqH5dz5iyCBYlS7VueRQAcZGXef7XJ8vrsJPSJ5JzwQ26SC8ikQf8ig_z7XGwWzyiDhs7HBAJsSNsx78IN8x1YkNt7dO4_GN1dMFTHTjmNn/s1600/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKf_jYoHAv_6IhZbtKxW9S8Hqg1GeoVpVaRVqH5dz5iyCBYlS7VueRQAcZGXef7XJ8vrsJPSJ5JzwQ26SC8ikQf8ig_z7XGwWzyiDhs7HBAJsSNsx78IN8x1YkNt7dO4_GN1dMFTHTjmNn/s1600/5.png" /></a></div><div><div><span style="font-family: Georgia, Times New Roman, serif;">Nilai a = 2</span></div><div><div style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4n0svfjGW0r5P1oz2tDaA2zbhqdJ5goOKwt-qxeZ7EkWR1w7VAmj-LaYRvG85bubqm37YC457Z0yGogMkD9_A5CkwgKBuJC5tjD_RBiY5DCKv69XnTD01M9C83qWiYsJZ-BBPuu5uO0Nr/s1600/6a.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4n0svfjGW0r5P1oz2tDaA2zbhqdJ5goOKwt-qxeZ7EkWR1w7VAmj-LaYRvG85bubqm37YC457Z0yGogMkD9_A5CkwgKBuJC5tjD_RBiY5DCKv69XnTD01M9C83qWiYsJZ-BBPuu5uO0Nr/s1600/6a.png" /></a><span style="font-family: Georgia, Times New Roman, serif;">6. Sisi-sisi dari 6 kubus masing-masing diberi angka 1, 2, 3, 4, 5 dan 6. Angka </span><span style="font-family: Georgia, Times New Roman, serif;">1 </span><span style="font-family: Georgia, 'Times New Roman', serif;">berseberangan dengan 6, angka 2 berseberangan dengan angka 5, dan angka 3 </span><span style="font-family: Georgia, Times New Roman, serif;">berseberangan dengan 4. Selanjutnya kubus-kubus satuan tersebut disusun </span><span style="font-family: Georgia, 'Times New Roman', serif;">susunan sebagai berikut. </span><span style="font-family: Georgia, 'Times New Roman', serif;">Jumlah terbesar yang mungkin dari angka-angka pada 21 sisi yang tampak (sisi-sisi </span><span style="font-family: Georgia, 'Times New Roman', serif;">atas, samping, depan, dan belakang) pada susunan kubus tersebut adalah . </span></div></div></div><div class="separator" style="clear: both; text-align: center;"></div><div><div><span style="font-family: Georgia, Times New Roman, serif;">Jawab: 89</span><br /><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj15LSlctl_BjlUtQ03jSwfArt2-nDzOF0ClaN87DlFr02KJIDVUOprdfHX952JKS-yuAKTZ7rgmox2Rrw_QMzxROAh-7espfOOVd8Rt9QJaBnTE34VVZYEe8eQiI6Tp0YPm9GV2BTV61pa/s1600/6a.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj15LSlctl_BjlUtQ03jSwfArt2-nDzOF0ClaN87DlFr02KJIDVUOprdfHX952JKS-yuAKTZ7rgmox2Rrw_QMzxROAh-7espfOOVd8Rt9QJaBnTE34VVZYEe8eQiI6Tp0YPm9GV2BTV61pa/s1600/6a.png" /></a></span></div><span style="font-family: Georgia, Times New Roman, serif;">Penjelasan :</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Kubus A satu sisi tidak tampak.</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jumlah terbesar = (2+3+4+5+6) = 20</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Kubus B dan F dua sisi tidak tampak</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jumlah terbesar = 2(3+4+5+6) = 36</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Kubus C dan D</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jumlah terbesar = 2(13) = 26</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Kubus E</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jumlah terbesar = 7</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jumlah keseluruhan = 20+36+26+7=89</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">12. Banyaknya segitiga berbeda yang ukuran ketiga sisinya merupakan bilangan asli </span><span style="font-family: Georgia, 'Times New Roman', serif;">dan ukuran sisi terpanjangnya 10 adalah .... </span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jawab: 30</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Penjelasan</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Misalkan a adalah ukuran sisi terpanjang segitiga itu. Berlaku b, c =a dan a < b + c.</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Berikut adalah kemungkinan ukuran sisi-sisi segitiga tersebut.</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 0px; text-align: justify; width: 450px;"><tbody><tr><td style="background-color: #f8f8f8;" width="150"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Sisi Terpanjang </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Sisi Kedua</span></div></div></div></td><td style="background-color: #f8f8f8;" width="200"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Sisi Terpendek</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="150"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></div></div></td><td style="background-color: #f8f8f8;" width="200"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">ada 10 macam (1 - 10)</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="150"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></div></div></td><td style="background-color: #f8f8f8;" width="200"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">ada 8 macam (2 - 9)</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="150"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10 </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></div></div></td><td style="background-color: #f8f8f8;" width="200"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">ada 6 macam (3 - 8)</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="150"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></div></div></td><td style="background-color: #f8f8f8;" width="200"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">ada 4 macam (4 - 7)</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="150"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10 </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></div></div></td><td style="background-color: #f8f8f8;" width="200"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">ada 2 macam (5 - 6)</span></div></div></div></td></tr></tbody></table><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">13. Joko dan Badrun berdiri pada suatu antrian. Pada antrian tersebut, perbandingan </span><span style="font-family: Georgia, 'Times New Roman', serif;">antara banyaknya orang di depan dan di belakang Joko adalah 1 ∶ </span><span class="Apple-tab-span" style="font-family: Georgia, 'Times New Roman', serif; white-space: pre;"> </span><span style="font-family: Georgia, 'Times New Roman', serif;">3. Sedangkan </span><span style="font-family: Georgia, 'Times New Roman', serif;">perbandingan antara banyaknya orang di depan dan di belakang Badrun adalah </span><span style="font-family: Georgia, 'Times New Roman', serif;">2∶</span><span style="font-family: Georgia, 'Times New Roman', serif;">5. Paling sedikit banyaknya orang pada antrian tersebut adalah . </span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jawab: 29 orang</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Penjelasan :</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 0px; text-align: justify; width: 600px;"><tbody><tr><td colspan="3" style="background-color: #f8f8f8;" width="300"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Antrian Joko</span></div></div></div></td><td colspan="3" style="background-color: #f8f8f8;" width="300"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Antrian Badrun </span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Depan</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Belakang</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Jml Antrian</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Depan</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Belakang</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Jml Antrian</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">1</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">13</span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">20</span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">29</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">12</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">17</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">10</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">25</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">36</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">15</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">21</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">-</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">-</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">-</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">18</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">25</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">-</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">-</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">-</span></div></div></div></td></tr><tr><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7 </span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">21</span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">29</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">-</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">-</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">-</span></div></div></div></td></tr></tbody></table></div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">14. Saat ini, usia Hasan sama dengan 7 kali usia Yenny. Dua tahun lalu, usia Hasan </span><span style="font-family: Georgia, 'Times New Roman', serif;">sama dengan 9 kali usia Yenny. Usia Hasan saat ini adalah...</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jawab: 56 tahun</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Penjelasan</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Kemungkinan usia Hasan dan Usia Yenny disajikan pada tabel berikut.</span><br /><div><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 0px; text-align: justify; width: 600px;"><tbody><tr><td colspan="3" width="300"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Dua Tahun Lalu</span></div></div></div></td><td colspan="3" width="300"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Saat Ini</span></div></div></div></td></tr><tr><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Usia Hasan</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Usia Yeny</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Perbandingan</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Usia Hasan</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Usia Yeny</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Perbandingan</span></div></div></div></td></tr><tr><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">1</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9 : 1</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">11</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">11 : 3</span></div></div></div></td></tr><tr><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">18</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9 : 1</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">20</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5 : 1</span></div></div></div></td></tr><tr><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">27</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9 : 1</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">29</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">29 : 5</span></div></div></div></td></tr><tr><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">36</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">4</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9 : 1</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">38</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">19 : 3</span></div></div></div></td></tr><tr><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">45</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9 : 1</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">47</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">47 : 7</span></div></div></div></td></tr><tr><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">54</span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">6</span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9 : 1</span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">56<br /></span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">8</span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7 : 1</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">63</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">7</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9 : 1</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">65</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">9</span></div></div></div></td><td width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">65 : 9</span></div></div></div></td></tr></tbody></table></div><div><span style="font-family: Georgia, Times New Roman, serif;">Dari Tabel di atas dapat diketahui bahwa usia Hasan dan Yenny saat ini berturut-turut adalah 56 </span><span style="font-family: Georgia, 'Times New Roman', serif;">tahun dan 8 tahun.</span><br /><span style="font-family: Georgia, 'Times New Roman', serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">15. The measure of an angle of an isosceles triangle is four times of the others. The </span><span style="font-family: Georgia, 'Times New Roman', serif;">smallest possible measure of this angle is . . .°. </span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jawab : 20</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Misalkan dua buah sudut tersebut adalah x dan 4x.</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jika sudut yang ketiga adalah x , maka jumlah ketiganya adalah x +  x +  4x = 6x . Akibatnya</span><br /><span style="font-family: Georgia, Times New Roman, serif;">6 x 180</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, Times New Roman, serif;"> atau </span><span style="font-family: Georgia, 'Times New Roman', serif;">x= 30</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, 'Times New Roman', serif;">, yang memberikan sudut-sudut segitiga </span><span style="font-family: Georgia, 'Times New Roman', serif;">30</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, 'Times New Roman', serif;">, </span><span style="font-family: Georgia, 'Times New Roman', serif;">30</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, 'Times New Roman', serif;">, dan </span><span style="font-family: Georgia, 'Times New Roman', serif;">120</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, 'Times New Roman', serif;">.</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Sedangkan jika sudut yang ketiga adalah 4x, maka jumlah ketiganya adalah x+ 4x + 4x =9x .</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Akibatnya 9x 180</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, Times New Roman, serif;"> atau x = 20</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, Times New Roman, serif;">, yang memberikan sudut-sudut segitiga 20</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, Times New Roman, serif;">, 80</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, Times New Roman, serif;">, dan 80</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, Times New Roman, serif;">.</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jadi, nilai terkecil yang mungkin bagi sudut segitiga tersebut adalah 20</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, Times New Roman, serif;"> sedangkan nilai </span><span style="font-family: Georgia, Times New Roman, serif;">terbesarnya adalah 120</span><span style="font-family: Georgia, 'Times New Roman', serif;">°</span><span style="font-family: Georgia, Times New Roman, serif;">.</span></div><div><div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">16. Sebuah kotak memuat 20 bola kuning, 9 bola merah, dan 6 bola biru. Paling sedikit </span><span style="font-family: Georgia, 'Times New Roman', serif;">bola yang harus diambil dari kotak tersebut untuk memastikan terambil sedikitnya 2 </span><span style="font-family: Georgia, 'Times New Roman', serif;">bola dari masing-masing warna adalah...</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jawab: 31</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jika hanya mengambil 30 bola, mungkin terjadi yang terpilih adalah 20 bola kuning, 9 bola merah, </span><span style="font-family: Georgia, 'Times New Roman', serif;">dan 1 bola biru. Jadi, banyaknya bola yang harus diambil paling sedikit adalah 31 bola.</span></div><div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">17. Dua belas segitiga sama sisi disusun seperti pada gambar di bawah. </span><span style="font-family: Georgia, 'Times New Roman', serif;">Banyaknya segiempat pada gambar tersebut adalah . </span></div></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQwmO42ixMzCt9slXnF6hsq-UjK__sgStjL7IEA76Fval_lZMBue_6hyphenhyphenFf1B3a1wkjzsCzuAVCGZepYOzeY6HIkSFfJPe1wrTBjC_bIO80cFekpgtc9wgl4FmgBDBvf-92auB11NjHGa-x/s1600/12.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQwmO42ixMzCt9slXnF6hsq-UjK__sgStjL7IEA76Fval_lZMBue_6hyphenhyphenFf1B3a1wkjzsCzuAVCGZepYOzeY6HIkSFfJPe1wrTBjC_bIO80cFekpgtc9wgl4FmgBDBvf-92auB11NjHGa-x/s1600/12.png" /></a></div><div><div><span style="font-family: Georgia, Times New Roman, serif;">Jawab :</span><br /><ul><li><span style="font-family: Georgia, Times New Roman, serif;">Dua buah segitiga yang berdekatan akan membentuk belah ketupat. Banyaknya belah </span><span style="font-family: Georgia, 'Times New Roman', serif;">ketupat ini adalah 11.</span></li><li><span style="font-family: Georgia, Times New Roman, serif;">Tiga buah segitiga yang berdekatan akan membentuk trapesium sama kaki. Banyaknya </span><span style="font-family: Georgia, 'Times New Roman', serif;">trapesium ini adalah 10.</span></li><li><span style="font-family: Georgia, Times New Roman, serif;">Perhatikan juga, bahwa jajargenjang yang dibentuk oleh empat buah segitiga berdekatan </span><span style="font-family: Georgia, 'Times New Roman', serif;">ada 4.</span></li><li><span style="font-family: Georgia, 'Times New Roman', serif;">Lima buah atau lebih segitiga tidak membentuk segiempat.</span></li><li><span style="font-family: Georgia, Times New Roman, serif;">Jadi, banyaknya segiempat yang terdaat pada gambar tersebut adalah 25, terdiri dari 11 </span><span style="font-family: Georgia, 'Times New Roman', serif;">belahketupat, 10 trapesium, dan 4 jajargenjang.</span></li></ul><span style="font-family: Georgia, Times New Roman, serif;">18. Pada tahun 2009 perbandingan banyaknya rusa jantan dan rusa betina di suatu </span><span style="font-family: Georgia, 'Times New Roman', serif;">kebun binatang adalah 2 : </span><span style="font-family: Georgia, 'Times New Roman', serif;">3. Pada tahun 2010 banyaknya rusa jantan bertambah 9 </span><span style="font-family: Georgia, 'Times New Roman', serif;">ekor dan banyaknya rusa betina berkurang 4 ekor, sehingga perbandingannya </span><span style="font-family: Georgia, 'Times New Roman', serif;">menjadi 3 : </span><span class="Apple-tab-span" style="font-family: Georgia, 'Times New Roman', serif; white-space: pre;"> </span><span style="font-family: Georgia, 'Times New Roman', serif;">2. Banyaknya rusa jantan pada tahun 2010 di kebun binatang tersebut </span><span style="font-family: Georgia, 'Times New Roman', serif;">adalah...</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jawab: 21</span><br /><span style="font-family: Georgia, 'Times New Roman', serif;"> </span> <span style="font-family: Georgia, Times New Roman, serif;">Penjelasan</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 0px; text-align: justify; width: 500px;"><tbody><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Tahun </span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Jantan</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Betina</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">Jantan</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">Betina</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2009</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3 </span><span style="text-align: left;">→</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">12</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">18</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2010</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">J + 9</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">B - 4 </span><span style="text-align: left;">→</span></div></div></div></td><td style="background-color: gold;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">21</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">14</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2010</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">2 </span><span style="text-align: left;">→</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">3</span></div></div></div></td><td style="background-color: #f8f8f8;" width="100"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">2</span></div></div></div></td></tr></tbody></table><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">19. Eleven students have a math test with the average score 65. The difference </span><span style="font-family: Georgia, 'Times New Roman', serif;">between the highest and the lowest scores is 20. If the highest and the lowest </span><span style="font-family: Georgia, 'Times New Roman', serif;">scores are ignored then the average is 63. The highest score is . . . . </span><span style="font-family: Georgia, 'Times New Roman', serif;"> </span><br /><span style="font-family: Georgia, 'Times New Roman', serif;">Jawab: Jumlah nilai dari 11 anak: 11 x 65 = 715</span><br /><span style="font-family: Georgia, 'Times New Roman', serif;">Jumlah nilai 9 anak = 9 x 63 = 567</span><br /><span style="font-family: Georgia, 'Times New Roman', serif;">Misalkan x adalah nilai siswa tertinggi, maka x + (x - 20) = 715 - 567 - 148</span></div><div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">20. Diketahui susunan lima angka 1 2 3 4 5. Sebuah tanda tambah (+) dan sebuah </span><span style="font-family: Georgia, 'Times New Roman', serif;">tanda kurang (–) disisipkan di antara dua angka yang berdekatan sehingga jika </span><span style="font-family: Georgia, 'Times New Roman', serif;">dihitung menghasilkan suatu bilangan dengan nilai tertentu. Berikut dua contoh </span><span style="font-family: Georgia, 'Times New Roman', serif;">penempatan tanda: </span></div><div><span style="font-family: Georgia, Times New Roman, serif;">a. 1<span style="white-space: pre;"> + </span>234<span style="white-space: pre;"> </span>– 5 = 230<span class="Apple-tab-span" style="white-space: pre;"> </span></span></div><div><span style="font-family: Georgia, Times New Roman, serif;">b. 12<span style="white-space: pre;"> </span>–<span style="white-space: pre;"> </span>3<span class="Apple-tab-span" style="white-space: pre;"> + </span>45 = 54 </span></div><div><span style="font-family: Georgia, Times New Roman, serif;">Selisih bilangan terbesar dengan bilangan terkecil yang mungkin dihasilkan dengan  </span><span style="font-family: Georgia, 'Times New Roman', serif;">cara tersebut adalah...</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jawab : 686</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Penjelasan</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Perhatikan bahwa, bilangan terbesar yang dapat dihasilkan adalah 1 - 2 + 345 = 344. Sedangkan </span><span style="font-family: Georgia, 'Times New Roman', serif;">bilangan terkecilnya adalah 1 + 2 - 345 = -342. Dengan demikian, selisih antara bilangan terbesar </span><span style="font-family: Georgia, 'Times New Roman', serif;">dan bilangan terkecil yang mungkin adalah 344 -(-342) = 686.</span></div><div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">21. Empat lingkaran dengan perbandingan jari-jari 8 ∶ 4 ∶ 2 ∶ 1 bersinggungan pada </span><span style="font-family: Georgia, 'Times New Roman', serif;">suatu titik, seperti pada gambar di bawah. Perbandingan ukuran luas daerah yang </span><span style="font-family: Georgia, 'Times New Roman', serif;">diarsir dengan luas daerah yang tidak diarsir adalah...</span></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBWkySAJYirLSW2FnQ9xNH6UGqqjpncwhZ34pnIymt2RB7nzDYJ6HOO0uXPLgR5r9awIiNlLv0rTQd0fMGeP6e0MOkB-qH8cyKeq4qO_I-ZVdyOLXbnDo2i3uqM4pHRBdCutYSNqZjLfdB/s1600/16.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBWkySAJYirLSW2FnQ9xNH6UGqqjpncwhZ34pnIymt2RB7nzDYJ6HOO0uXPLgR5r9awIiNlLv0rTQd0fMGeP6e0MOkB-qH8cyKeq4qO_I-ZVdyOLXbnDo2i3uqM4pHRBdCutYSNqZjLfdB/s1600/16.png" /></a></div><div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzVOvfOol7Jy9qIp251B9KYJiXKfg9e-B6xpUCGHJOUxD0kvY3hPhGJElGIMrYnPZlhtb00G9qt4M_MsTCGM28KGez9RLIgych1CUPHDekj_aqMD3DSusjxneuR1K4kSeXHeKHQ5nSbXgM/s1600/asd.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzVOvfOol7Jy9qIp251B9KYJiXKfg9e-B6xpUCGHJOUxD0kvY3hPhGJElGIMrYnPZlhtb00G9qt4M_MsTCGM28KGez9RLIgych1CUPHDekj_aqMD3DSusjxneuR1K4kSeXHeKHQ5nSbXgM/s1600/asd.png" /></a></div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">22. Banyaknya penduduk Desa Suka Maju adalah 250 orang dengan rincian sebagai </span><span style="font-family: Georgia, 'Times New Roman', serif;">berikut. </span></div><div><span style="font-family: Georgia, Times New Roman, serif;">Sebanyak 85% penduduk berusia di atas 15 tahun. </span></div><div><span style="font-family: Georgia, Times New Roman, serif;">Sebanyak 45% penduduk berusia di bawah 25 tahun. </span></div><div><span style="font-family: Georgia, Times New Roman, serif;">Sebanyak 25% penduduk berusia di atas 50 tahun. </span></div><div><span style="font-family: Georgia, Times New Roman, serif;">Banyaknya penduduk desa tersebut yang berusia di atas 15 tahun dan tidak lebih </span><span style="font-family: Georgia, 'Times New Roman', serif;">dari 50 tahun adalah ....orang. </span><br /><span style="font-family: Georgia, 'Times New Roman', serif;">60% x 250 orang = 150 orang</span></div><div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">23. Pada trapesium di bawah ini, 12 cm, 6 cm, dan sudut 45°. </span><span style="font-family: Georgia, 'Times New Roman', serif;">Jika luas trapesium adalah 45 cm2</span><span style="font-family: Georgia, 'Times New Roman', serif;">, maka panjang adalah ... cm. </span></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHQUhCHo2VQvmfJbvrsTgkKhNvQTDPCv4XG-lEiDOYJMw-tb8R9O9Ew1BL8ajauzVWg1h5L6aLi664bhJ91ZPPDdcizd8z8i18_-fpt-aTqufEZGufWenMdma2pPCk4F4g9XhNUzG9tM4F/s1600/18.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHQUhCHo2VQvmfJbvrsTgkKhNvQTDPCv4XG-lEiDOYJMw-tb8R9O9Ew1BL8ajauzVWg1h5L6aLi664bhJ91ZPPDdcizd8z8i18_-fpt-aTqufEZGufWenMdma2pPCk4F4g9XhNUzG9tM4F/s1600/18.png" /></a></div><div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEQjehDFHSAxGB9epDyCyGGooFipuyrkRrq8bXf66Af3i-RvbpMvtoRDMZ5Zi_oDsgfe79a657e3Kjc0GKM8jQnFWXTLz5zQpLVqTwHASYGKfbjXoC4LgQtwCmo6X5Z2xdFRFYAqu7ORty/s1600/asde.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEQjehDFHSAxGB9epDyCyGGooFipuyrkRrq8bXf66Af3i-RvbpMvtoRDMZ5Zi_oDsgfe79a657e3Kjc0GKM8jQnFWXTLz5zQpLVqTwHASYGKfbjXoC4LgQtwCmo6X5Z2xdFRFYAqu7ORty/s1600/asde.png" /></a></div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">24. The sequences 1, 20, 39, 58, 77, and 17, 29, 41, 53, 65, 77, have 77 as a </span><span style="font-family: Georgia, 'Times New Roman', serif;">common term. The next common term of these sequences is...</span><br /><span style="font-family: Georgia, 'Times New Roman', serif;">Jawab : 77 + 19 x 12 = 305</span></div><div><span style="font-family: Georgia, Times New Roman, serif;">20. Rata-rata nilai matematika seluruh siswa kelas V adalah 9. Rata-rata nilai </span><span style="font-family: Georgia, 'Times New Roman', serif;">matematika siswa laki-laki di kelas tersebut adalah 8,8. Apabila di kelas tersebut di </span><span style="font-family: Georgia, 'Times New Roman', serif;">antaranya adalah siswa laki-laki, maka rata-rata nilai matematika siswa perempuan </span><span style="font-family: Georgia, 'Times New Roman', serif;">di kelas tersebut adalah .... </span></div><div><span style="font-family: Georgia, Times New Roman, serif;">Jawab: 36,6/4 =9,15</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Penjelasan: Seandainya di kelas tersebut ada 7 orang.</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Banyaknya siswa      = 7 dengan total nilai 7 x 9     = 63</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><u>Banyaknya laki-laki = 3 dengan total nilai 8,8 x 3 = 26,4</u></span><br /><span style="font-family: Georgia, Times New Roman, serif;">Banyaknya perpn     = 4 dengan total nilai              = 36,6</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Rata-rata nilai siswa perempuan = 36,6/4 = 9,15</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">25. Suatu bangun ruang mempunyai jaring-jaring seperti gambar di bawah ini. Banyak </span><span style="font-family: Georgia, 'Times New Roman', serif;">titik sudut bangun ruang tersebut adalah . </span></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWCkA2M4t7D5tUzQq2IvTGRuGof_-0VSXLUxZ52n3g-QPauWBNBIuFtt4I-cXVix-tN3wXNo6vdG95KeIXsdqM7eS7hICjh7MRzkfMiTmDs2bz71WsdKKxpMXVCOpd_r8owsnCPSyMWbrU/s1600/21.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWCkA2M4t7D5tUzQq2IvTGRuGof_-0VSXLUxZ52n3g-QPauWBNBIuFtt4I-cXVix-tN3wXNo6vdG95KeIXsdqM7eS7hICjh7MRzkfMiTmDs2bz71WsdKKxpMXVCOpd_r8owsnCPSyMWbrU/s1600/21.png" /></a></div><div><div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span><span style="font-family: Georgia, Times New Roman, serif;">Jawab : 20 (banyak segitiga ) x 3( banyak sisi tiap segitiga) : 5 = 12.</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Penjelasan</span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4Eu7Hddj4rdIayO8AFZuMg4yVeqywf0VEMQggUsmfx928P3dEQyixBVisvBjcvVGiJ1oNjSPOOpnq5i9kaTAQKayYU-MuwpN8iJXlUZVXSdTF5yBfYxuk2fD9ZB6h18XIWXNotZdIXSx0/s1600/17.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4Eu7Hddj4rdIayO8AFZuMg4yVeqywf0VEMQggUsmfx928P3dEQyixBVisvBjcvVGiJ1oNjSPOOpnq5i9kaTAQKayYU-MuwpN8iJXlUZVXSdTF5yBfYxuk2fD9ZB6h18XIWXNotZdIXSx0/s1600/17.png" /></a></div><span style="font-family: Georgia, Times New Roman, serif;"><br /></span> <span style="font-family: Georgia, Times New Roman, serif;">26. Bilangan 12 dapat dinyatakan sebagai hasil penjumlahan maupun hasil kali dari </span><span style="font-family: Georgia, 'Times New Roman', serif;">6 </span><span style="font-family: Georgia, 'Times New Roman', serif;">bilangan {1, 1, 1, 1, 2, 6} karena 1 + 1 + 1 + 1 + 2 +  6 = 12 dan 1+ </span><span style="font-family: Georgia, 'Times New Roman', serif;">1 +</span><span style="font-family: Georgia, 'Times New Roman', serif;">1 +</span><span style="font-family: Georgia, 'Times New Roman', serif;">1 +</span><span style="font-family: Georgia, 'Times New Roman', serif;"> 2 + </span><span style="font-family: Georgia, Times New Roman, serif;">6 = 12. Dengan kondisi seperti itu, kita sebut bahwa 12 dapat diuraikan menjadi 6 </span><span style="font-family: Georgia, 'Times New Roman', serif;">bilangan. Selain itu bilangan 12 juga dapat diuraikan menjadi 8 bilangan yaitu {</span><span style="font-family: Georgia, 'Times New Roman', serif;"> 1,1, 1, 1, 1, 2, 2, 3} karena 1+ 1 + 1 + 1 + 1 + 2 + 2 + 3 = 12 dan 1 +</span><span style="font-family: Georgia, 'Times New Roman', serif;">1 +</span><span style="font-family: Georgia, 'Times New Roman', serif;">1+ </span><span style="font-family: Georgia, 'Times New Roman', serif;">1 +</span><span style="font-family: Georgia, 'Times New Roman', serif;">1 + </span><span style="font-family: Georgia, 'Times New Roman', serif;">2 + </span><span style="font-family: Georgia, 'Times New Roman', serif;">2 + </span><span style="font-family: Georgia, 'Times New Roman', serif;">3 = 12. Dapat ditunjukkan bahwa bilangan 12 dapat diuraikan paling banyak </span><span style="font-family: Georgia, 'Times New Roman', serif;">menjadi 8 bilangan. Bilangan 2010 dapat diuraikan paling banyak menjadi. ...</span><span style="font-family: Georgia, 'Times New Roman', serif;">bilangan. </span><br /><span style="font-family: Georgia, Times New Roman, serif;">Jawab: 1937</span><br /><span style="font-family: Georgia, Times New Roman, serif;">Penjelasan</span><br /><ul><li><span style="font-family: Georgia, Times New Roman, serif;">Faktor prima dari 2010 adalah 2, 3, 5 dan 67. Hasil kali bilangan-bilangan ini adalah 2010, yaitu 2 </span><span style="font-family: Georgia, 'Times New Roman', serif;">x 3 x 5 x 67 = 2010 dan hasil penjumlahannya adalah (2 + 3 + 5 + 67) = 77.</span></li><li><span style="font-family: Georgia, Times New Roman, serif;">Bilangan-bilangan tersebut perlu ditambah bilangan 1 sebanyak (2010 – 77) = 1933 agar hasil </span><span style="font-family: Georgia, 'Times New Roman', serif;">penjumlahan seluruh bilangan tersebut adalah 2010; yaitu</span></li><li><span style="font-family: Georgia, 'Times New Roman', serif;">2 + 3 + 5 + 67 + 1 + 1 + …+ 1 = 2010.</span></li><li><span style="font-family: Georgia, Times New Roman, serif;">Demikian pula hasil kali seluruh bilangan tersebut adalah 2010; yaitu </span><span style="font-family: Georgia, 'Times New Roman', serif;">1 x 1 x 1 x …x 1 x 2 x 3 x 5 x 67 = 2010</span></li><li><span style="font-family: Georgia, 'Times New Roman', serif;">Jadi, bilangan-bilangan yang memenuhi ketentuan tersebut adalah {1, 1, 1, …,1, 2, 3, 5, 67}.</span></li><li><span style="font-family: Georgia, 'Times New Roman', serif;">Banyaknya bilangan tersebut adalah 4 + 1933 = 1937 bilangan.</span></li></ul><span style="font-family: Georgia, 'Times New Roman', serif;"></span></div><div><span style="font-family: Georgia, Times New Roman, serif;">27. In the following figure, the area of is 80 cm2</span><span style="font-family: Georgia, Times New Roman, serif;">. If, and divides </span><span style="font-family: Georgia, 'Times New Roman', serif;"> into two regions of the same area, then the length of is . . . cm.</span></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpBETUJWR9_eyLSy12nDxHfTsKrZ-egqXZoplRrMYcbTfEIdHMfAjC-OAFtWE-NBM8_iqzbleTHqaG_bifKUXHajQvOg7loB_0IcOmmXqIjY2OGw7br8yvos7XsLx6gARV38N7ppuzDM80/s1600/23.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpBETUJWR9_eyLSy12nDxHfTsKrZ-egqXZoplRrMYcbTfEIdHMfAjC-OAFtWE-NBM8_iqzbleTHqaG_bifKUXHajQvOg7loB_0IcOmmXqIjY2OGw7br8yvos7XsLx6gARV38N7ppuzDM80/s1600/23.png" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbUNkorMv77Y83jfDq-9SZq5KLQGklhd7AhUV6hQwaVkejKZd3G3XecTwRcbyYYWKoslxoSq8slEyPM5c5OVIC0N36Ty3S6XffR6yvI6uYuAW-UBoDQXM9fHIS9r6iOyt15ukE5ioGjvPr/s1600/22.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbUNkorMv77Y83jfDq-9SZq5KLQGklhd7AhUV6hQwaVkejKZd3G3XecTwRcbyYYWKoslxoSq8slEyPM5c5OVIC0N36Ty3S6XffR6yvI6uYuAW-UBoDQXM9fHIS9r6iOyt15ukE5ioGjvPr/s1600/22.png" /></a></div><span style="font-family: Georgia, Times New Roman, serif;">28. Misalkan 10000 = a x b x c, dengan a, b, dan c, adalah bilangan-bilangan asli yang tidak memiliki angka 0. Jika a, b dan c boleh sama, maka nilai terkecil yang mungkin dari a + b + c adalah...</span><br /><span style="font-family: Georgia, Times New Roman, serif;"><span style="white-space: pre;">Jawab : 66</span></span><br /><span style="font-family: Georgia, Times New Roman, serif;"><span class="Apple-tab-span" style="white-space: pre;">Perhatikan bahwa 10.000= 2⁴ x 5⁴. Karena a, b, dan c tidak memiliki angka 0</span></span><span style="font-family: Georgia, 'Times New Roman', serif;"> (oleh karena itu satuan dari bilangan-bilangan ini bukan 0), maka a, b, dan c tidak memiliki faktor 2, dan 5 sekaligus. Kemungkinan nilai a, b, dan c ditunjukan pada tabel di bawah ini :</span><br /><table border="1" cellpadding="1" cellspacing="0" style="background-color: #f8f8f8; border-collapse: collapse; border: 1px solid rgb(255, 153, 0); margin: 0em 0em 0em 0px; text-align: justify; width: 500px;"><tbody><tr><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">a</span></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">b</span></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">c</span></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">a + b + c</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">2</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">2x2x2=8</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">5x5x5x5 =625</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">635</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, Times New Roman, serif;">2x2=4</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">2x2=4</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">5x5x5x5 =625</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">635</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">2x2x2x2=16</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">5</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">5x5x5=125</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">146</span></div></div></div></td></tr><tr><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">2x2x2x2=16</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">5x5=25</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><div style="text-align: right;"><span style="font-family: Georgia, 'Times New Roman', serif;">5x5=25</span></div></div></div></div></td><td style="background-color: #f8f8f8;" width="125"><div style="text-align: center;"><div style="text-align: left;"><div style="text-align: center;"><span style="font-family: Georgia, 'Times New Roman', serif;">66</span></div></div></div></td></tr></tbody></table><span style="font-family: Georgia, Times New Roman, serif;">29. Bagian atas ∆ dilipat ke arah alas pada bagian seperti tampak pada gambar </span><span style="font-family: Georgia, 'Times New Roman', serif;">berikut. dan sejajar dengan panjang berturut-turut 10 cm dan 8 cm. Tinggi </span><span style="font-family: Georgia, 'Times New Roman', serif;">∆ adalah 15 cm. Luas daerah yang diarsir adalah.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisl-8wOWCzMM4Jvlx_05htoC9N_B7so9Mpi6arQhhkpHtdrOG7-41fu1IRXetwOxMBVYeSutgDNBoPQHHkqlRzzDLsADS3fRpsNPLHL4IoEboJBC5wo3UkShyphenhyphen2t-0Cn8tMRsj9MaiyD987/s1600/25.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisl-8wOWCzMM4Jvlx_05htoC9N_B7so9Mpi6arQhhkpHtdrOG7-41fu1IRXetwOxMBVYeSutgDNBoPQHHkqlRzzDLsADS3fRpsNPLHL4IoEboJBC5wo3UkShyphenhyphen2t-0Cn8tMRsj9MaiyD987/s1600/25.png" /></a></div></div></div></div></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiapVaSIcPpV8-r6-wHswv1gg4bXCiooFRAcEbvkpXxtDcaiSNa65LqaPGIbEANVeFF_Bxav_w9uFvnYJGURE1hc1GGVr4eU_OAEoMt9uYi-akqNAPs0uVDWFmRLY73G3iEBGq2C48zcjOV/s1600/25.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiapVaSIcPpV8-r6-wHswv1gg4bXCiooFRAcEbvkpXxtDcaiSNa65LqaPGIbEANVeFF_Bxav_w9uFvnYJGURE1hc1GGVr4eU_OAEoMt9uYi-akqNAPs0uVDWFmRLY73G3iEBGq2C48zcjOV/s1600/25.png" /></a></div></div>

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