Panik nggak karena sebentar lagi UTBK? Gapapa, normal kok. Jaga kesehatan, berdoa dan jangan lupa perbanyak latihan soal. Kali ini latihan bareng-bareng soal TPS Kuantitatif yuk!
—
Topik: Pengetahuan Kuantitatif
Sunbtopik: Bilangan
1. Bentuk sederhana dari – adalah…
Jawaban: E
Pembahasan:
Perhatikan perhitungan berikut!
Kemudian, ingat bahwa pada pengurangan bilangan kuadrat berlaku persamaan berikut
Dengan demikian, diperoleh hasil perhitungan sebagai berikut.
Dengan demikian, bentuk sederhana dari adalah
Jadi, jawaban yang tepat adalah E.
Topik: Pengetahuan Kuantitatif
Subtopik: Geometri
2. Sebuah bak mandi berbentuk balok berisi air dengan tinggi air adalah dari tinggi bak mandi. Jika ditambahkan 20 liter air ke dalam bak mandi, maka tinggi air saat ini adalah dari tinggi bak mandi. Volume bak mandi tersebut adalah … liter.
- 100
- 110
- 115
- 120
- 130
Jawaban: D
Pembahasan:
Misalkan luas alas bak mandi adalah dan tinggi bak mandi adalah
Maka Volume bak mandi yang berbentuk balok adalah
Karena tinggi air pada mulanya adalah dari tinggi bak mandi, maka volume air pada mulanya,
Kemudian ditambahkan 20 liter air ke dalam bak mandi sehingga tinggi air saat ini adalah dari tinggi bak mandi. Tinggi air saat ini adalah
Karena Volume bak mandi adalah
maka volume bak mandi adalah 120 liter.
Jadi, jawaban yang tepat adalah D.
Topik: Pengetahuan Kuantitatif
Subtopik: Bilangan
3. Lani, Rista, dan Ipul berlatih bulu tangkis. Lani berlatih setiap 4 hari sekali, Rista berlatih setiap 6 hari sekali, dan Ipul berlatih setiap 12 hari sekali. Jika ketiganya terakhir kali berlatih bulu tangkis bersama-sama pada hari Rabu, mereka akan berlatih bulu tangkis bersama-sama lagi pada hari ….
- Senin
- Selasa
- Rabu
- Kamis
- Jumat
Jawaban: A
Pembahasan:
Dari soal tersebut, diketahui bahwa Lani, Rista, dan Ipul terakhir kali berlatih bersama-sama pada hari Rabu.
Kemudian, waktu yang dibutuhkan mereka untuk belajar bulu tangkis bersama lagi dapat diketahui dengan menentukan KPK dari 4, 6, dan 12.
Faktorisasi dari 4 adalah
Faktorisasi dari 6 adalah 2×3
Faktorisasi dari 12 adalah
Dengan demikian, KPK dari 4, 6, dan 12 adalah
Karena mereka akan bertemu kembali 12 hari setelah hari Rabu, maka ketiganya akan berlatih bulu tangkis bersama lagi pada hari Senin.
Jadi, jawaban yang tepat adalah A.
Topik: Pengetahuan Kuantitatif
Sunbtopik: Statistika dan Peluang
4. Nilai rata-rata ulangan Bahasa Inggris 25 siswa di suatu kelas adalah 75,2. Setelah ada satu orang siswa baru yang mengikuti ulangan susulan, nilai rata-rata ulangan Bahasa Inggris di kelas tersebut menjadi 75,4. Berdasarkan informasi tersebut, diperoleh data sebagai berikut.
- Jumlah keseluruhan nilai sebelum siswa susulan adalah 1.881.
- Nilai Bahasa Inggris siswa yang baru adalah 80,4.
- Selisih antara jumlah keseluruhan nilai sebelum dan setelah susulan adalah 81,4.
- Jumlah seluruh nilai siswa setelah ulangan susulan adalah 1.960,4.
- 1, 2, dan 3 SAJA yang benar.
- 1 dan 3 SAJA yang benar.
- 2 dan 4 SAJA yang benar.
- HANYA 4 yang benar.
- SEMUA pilihan benar.
Jawaban: C
Pembahasan:
Dari soal diketahui jumlah siswa ada 25 orang, dan rata-rata nilainya 75,2. Dengan demikian, jumlah keseluruhan nilai adalah sebagai berikut.
25×75,2=1.880
Setelah ditambah satu orang siswa yang mengikuti ulangan susulan, rata-rata nilainya menjadi 75,4. Jumlah keseluruhan nilai yang baru adalah sebagai berikut.
26×75,4=1.960,4
Oleh karena itu, dapat diketahui bahwa nilai ulangan Bahasa Inggris siswa yang mengikuti ulangan susulan adalah sebagai berikut.
=jumlah nilai 26 siswa-jumlah nilai 25 siswa
=1960,4 -1.880= 80,4
Berdasarkan penjelasan tersebut, pernyataan yang tepat adalah nomor 2 dan 4.
Jadi, jawaban yang tepat adalah C.
Topik: Pengetahuan Kuantitatif
Subtopik: Bilangan
5. Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 8, 12, and 16 hours, respectively. What is the ratio of the time it takes printer X to do the job working alone at its rate, to the time it takes printers Y and Z to do the job working together at their individual rates?
- 411
- 76
- 1522
- 2215
- 114
Jawaban: B
Pembahasan:
Dari soal tersebut, diperoleh informasi sebagai berikut.
Printer X dapat melakukan pekerjaan selama 8 jam, artinya printer X dapat melakukan bagian dalam satu jam.
Printer Y dapat melakukan pekerjaan selama 12 jam, artinya printer Y dapat melakukan bagian dalam satu jam.
Printer Z dapat melakukan pekerjaan selama 16 jam, artinya printer Z dapat melakukan bagian dalam satu jam.
Ketika printer Y dan Z digunakan bersamaan dalam 1 jam, maka pekerjaan yang dapat mereka selesaikan adalah sebagai berikut.
Jadi, printer Y dan Z membutuhkan jam untuk menyelesaikan suatu pekerjaan secara bersama-sama.
Kemudian, karena printer X dapat melakukan pekerjaan selama 8 jam, maka rasio waktu yang diperlukan oleh printer X untuk dapat menyelesaikan suatu pekerjaan dibandingkan dengan waktu yang dibutuhkan jika printer Y dan Z bekerja bersama adalah sebagai berikut.
Jadi, jawaban yang tepat adalah B.
Topik: Pengetahuan Kuantitatif
Subtopik: Statistika dan Peluang.
6. Four identical cars and eight identical bicycles are each randomly given to 12 different people. Each of the twelve receives either a car, or a bicycle, but not both. Ann and Elsa are two of these people. The probability that Ann and Elsa got the different prizes is ….
Jawaban: C
Pembahasan:
Dari soal tersebut, diperoleh informasi bahwa terdapat 12 hadiah undian yang terdiri dari 4 mobil dan 8 sepeda. Kemudian dua orang, yaitu Ann dan Elsa, adalah dua pemenang undian tersebut.
Kemudian, yang ditanyakan adalah peluang mereka mendapatkan hadiah yang berbeda.
Dalam hal ini, terdapat dua kemungkinan sebagai berikut.
- Ann mendapat mobil dan Elsa mendapat sepeda.
- Ann mendapat sepeda dan Elsa mendapat mobil.
Kemungkinan pertama, peluang Ann mendapat mobil dan Elsa mendapat sepeda adalah sebagai berikut.
Kemungkinan kedua, peluang Ann mendapat sepeda dan Elsa mendapat mobil adalah sebagai berikut.
Dengan demikian, peluang Ann dan Elsa mendapat hadiah yang berbeda adalah sebagai berikut.
Jadi, jawaban yang tepat adalah C.
Topik: Pengetahuan Kuantitatif
Subtopik: Aljabar
7. Diketahui himpunan Y = {r,a,s,i,g,u.} Dari himpunan-himpunan berikut ini, manakah yang merupakan himpunan bagian dari Y ?
- M = {g, u, r, i}
- N = {s, i, a, r}
- O = {a, u, r, i}
- P = {o, u, r, i}
- 1, 2, dan 3 SAJA yang benar.
- 1 dan 3 SAJA yang benar.
- 2 dan 4 SAJA yang benar.
- HANYA 4 yang benar.
- SEMUA pilihan benar.
Jawaban: A
Pembahasan:
Ingat bahwa himpunan A dikatakan sebagai himpunan bagian dari himpunan B, jika semua anggota himpunan A merupakan anggota himpunan B.
Pada soal yang semua anggota himpunannya merupakan anggota himpunan Y adalah himpunan M, N, dan O.
Dengan demikian, yang merupakan himpunan bagian dari himpunan Y adalah pernyataan 1, pernyataan 2, dan pernyataan 3.
Jadi, jawaban yang tepat adalah A.
Topik: Pengetahuan Kuantitatif
Subtopik: Aljabar
8. Diketahui bahwa
Manakah pernyataan berikut yang benar?
- 1, 2, dan 3 SAJA yang benar.
- 1 dan 3 SAJA yang benar.
- 2 dan 4 SAJA yang benar.
- HANYA 4 yang benar.
- SEMUA pilihan benar.
Jawaban: C
Pembahasan:
Perhatikan perhitungan berikut!
Kemudian,
Eliminasi persamaan (i) dan (ii)
Substitusikan ke persamaan (i)
Dengan demikian, diperoleh Kemudian, periksa setiap pernyataan.
Pernyataan 1 salah, seharusnya .
Pernyataan 2 benar, karena
dan
Dengan demikian, didapat bahwa
Pernyataan 3 salah, karena adalah bilangan genap.
Pernyataan 4 benar, karena 6 dan -3 keduanya habis dibagi 3.
Oleh karena itu, pernyataan yang benar adalah pernyataan 2 dan 4.
Jadi, jawaban yang tepat adalah C.
9. .. , … , 71 , 79 , 158, 153, 161.
Which numbers are possibly correct to fill in the blanks?
- 38
- 33
- 76
- 66
- 1, 2, and 3 ONLY
- 1 and 3 ONLY
- 2 and 4 ONLY
- 4 ONLY
- 1, 2, 3, and 4
Jawaban: B
Pembahasan:
Misal bagian kosong pertama adalah A dan bagian kosong kedua adalah B
Perhatikan pola barisan berikut!
Terdapat tiga pola dalam penyusunan deret angka ini, yaitu perkalian 2, pengurangan 5, dan penjumlahan 8.
Dengan demikian, pola untuk A dan B adalah sebagai berikut.
Dari pola tersebut, diperoleh hasil perhitungan sebagai berikut.
dan
Jadi, bilangan pertama dan kedua yang tepat untuk mengisi tempat kosong tersebut adalah 38 dan 76.
Dengan demikian, pernyataan yang tepat adalah 1 dan 3.
Jadi, jawaban yang tepat adalah B.
Topik: Pengetahuan Kuantitatif
Subtopik: Statistika dan Peluang
10. Dua buah dadu dilempar secara bersamaan.
Manakah hubungan yang tepat antara P dan Q berikut berdasarkan informasi yang diberikan?
-
P > Q.
-
Q > P.
-
P = Q.
- Informasi yang diberikan tidak cukup untuk memutuskan salah satu dari tiga pilihan di atas.
Jawaban: B
Pembahasan:
Dua buah dadu dilempar secara bersamaan, maka jumlah ruang sampelnya adalah
Kejadian mata dadu kembar yang mungkin adalah {(1, 1, 2, 2, 3, 3, 4, 4, 5, 5, (6, 6)}, banyaknya kejadian adalah
Peluang muncul mata dadu kembar dapat ditentukan melalui perhitungan berikut.
Penyebut P dan Q disamakan menjadi 18, maka didapat nilai P.
Hubungan antara P dan Q yang tepat adalah P<Q atau dapat dituliskan menjadi Q>P.
Jadi, jawaban yang tepat adalah pilihan B.
Yeaaay! Akhirnya semua latihan soal UTBK SBMPTN 2021 telah dibagikan oleh tim Ruangguru untuk kamu. Coba cek blog Ruangbaca deh, mungkin ada artikel latihan soal yang belum dibaca. Kalau masih kurang, ada tryout gratis di ruanguji lho!
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<h1 class="content-title">
Latihan Soal UTBK SBMPTN 2021: Pengetahuan Kuantitatif </h1>
<div class="content-meta">
<p class="content-author"><a href="https://www.ruangguru.com/blog/author/salsabila-nanda" class="">Salsabila Nanda</a> </p>
<p class="content-info"><span>March 31, 2021 • </span> <span>7 minutes read</span></p>
<br />
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<div class="content-body">
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Latihan_Soal_-_Pengetahuan_Kuantitatif-01.jpg" alt="Latihan_Soal_-_Pengetahuan_Kuantitatif-01" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<blockquote>
<p style="text-align: justify; font-size: 16px;">Panik nggak karena sebentar lagi UTBK? Gapapa, normal kok. Jaga kesehatan, berdoa dan jangan lupa perbanyak latihan soal. Kali ini latihan bareng-bareng soal TPS Kuantitatif yuk!</p>
</blockquote>
<p style="text-align: center;">—</p>
<p><span id="more-5161"></span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<p><strong>Topik: Pengetahuan Kuantitatif </strong><strong><br /></strong><strong>Sunbtopik: Bilangan</strong></p>
<p style="font-weight: normal;">1. Bentuk sederhana dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/utbk%20kuantitatif%201a.jpg" alt="utbk kuantitatif 1a" width="61" loading="lazy" style="width: 61px;"> –<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/utbk%20kuantitatif%201b.jpg" alt="utbk kuantitatif 1b" width="79" loading="lazy" style="width: 79px;"> adalah…</p>
<p style="font-weight: normal;"><span style="font-weight: bolder;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1b.jpg" alt="1b" width="130" loading="lazy" style="width: 130px;"></span></p>
<p style="text-align: justify;"><strong>Jawaban: E</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Perhatikan perhitungan berikut!</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1cc.jpg" alt="1cc" width="553" loading="lazy" style="width: 553px;"></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1d.jpg" alt="1d" width="457" loading="lazy" style="width: 457px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Kemudian, ingat bahwa pada pengurangan bilangan kuadrat berlaku persamaan berikut</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1h.jpg" alt="1h" width="161" loading="lazy" style="width: 161px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Dengan demikian, diperoleh hasil perhitungan sebagai berikut.</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1f.jpg" alt="1f" width="370" loading="lazy" style="width: 370px; margin-left: auto; margin-right: auto; display: block;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1g.jpg" alt="1g" width="287" loading="lazy" style="width: 287px; margin-left: auto; margin-right: auto; display: block;"></p>
<p>Dengan demikian, bentuk sederhana dari <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1i.jpg" alt="1i" width="148" loading="lazy" style="width: 148px;"> adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1j.jpg" alt="1j" width="98" loading="lazy" style="width: 98px;"></p>
<p><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah E.</span></strong> </p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></p>
<p><strong>Topik: Pengetahuan Kuantitatif </strong><strong><br /></strong><strong>Subtopik: Geometri</strong></p>
<p>2. Sebuah bak mandi berbentuk balok berisi air dengan tinggi air adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2a.jpg" alt="2a" width="20" loading="lazy" style="width: 20px;"> dari tinggi bak mandi. Jika ditambahkan 20 liter air ke dalam bak mandi, maka tinggi air saat ini adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2b.jpg" alt="2b" width="19" loading="lazy" style="width: 19px;"> dari tinggi bak mandi. Volume bak mandi tersebut adalah … liter.<strong><img decoding="async" src="https://lh5.googleusercontent.com/GeQjSU9SyLM8r2cxx8WiN66N7x-dS2VHQfhHjvrYHr--CsvpqbH6OV1bE-Y2PkpUlJ7IFzqJVmAxLqBEWIT48dpdaCDaJ50v9TSBloXuoMUtGwFiQ4ya102kqt8qYgjdt4Zm3g8" width="8" height="5" loading="lazy"></strong> </p>
<ol style="list-style-type: upper-alpha;">
<li aria-level="1">100</li>
<li aria-level="1">110</li>
<li aria-level="1">115</li>
<li aria-level="1">120</li>
<li aria-level="1">130</li>
</ol>
<p> </p>
<p style="text-align: justify;"><strong>Jawaban: D</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify; font-weight: normal;">Misalkan luas alas bak mandi adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2c.jpg" alt="2c" width="26" loading="lazy" style="width: 26px;"> dan tinggi bak mandi adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2d.jpg" alt="2d" width="16" loading="lazy" style="width: 16px;"></p>
<p>Maka Volume bak mandi yang berbentuk balok adalah</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2e.jpg" alt="2e" width="87" loading="lazy" style="width: 87px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Karena tinggi air pada mulanya adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2a.jpg" alt="2a" width="20" loading="lazy" style="width: 20px;"> dari tinggi bak mandi, maka volume air pada mulanya,</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2f.jpg" alt="2f" width="439" loading="lazy" style="width: 439px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Kemudian ditambahkan 20 liter air ke dalam bak mandi sehingga tinggi air saat ini adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2b.jpg" alt="2b" width="19" loading="lazy" style="width: 19px;"> dari tinggi bak mandi. Tinggi air saat ini adalah<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2b.jpg" alt="2b" width="19" loading="lazy" style="width: 19px;"><em><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2d.jpg" alt="2d" width="16" loading="lazy" style="width: 16px;"></em></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2h.jpg" alt="2h" width="399" loading="lazy" style="width: 399px; margin-left: auto; margin-right: auto; display: block;"></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2i.jpg" alt="2i" width="324" loading="lazy" style="width: 324px; margin-left: auto; margin-right: auto; display: block;"></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2j.jpg" alt="2j" width="260" loading="lazy" style="width: 260px; margin-left: auto; margin-right: auto; display: block;"></p>
<p>Karena Volume bak mandi adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2e.jpg" alt="2e" width="87" loading="lazy" style="width: 87px; margin-left: auto; margin-right: auto; display: block;"></p>
<p>maka volume bak mandi adalah 120 liter.</p>
<p><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah D.</span></strong></p>
<p><strong><span style="text-decoration: underline;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></strong></p>
<p><strong>Topik: Pengetahuan Kuantitatif</strong><strong><br /></strong><strong>Subtopik: Bilangan</strong></p>
<p>3. Lani, Rista, dan Ipul berlatih bulu tangkis. Lani berlatih setiap 4 hari sekali, Rista berlatih setiap 6 hari sekali, dan Ipul berlatih setiap 12 hari sekali. Jika ketiganya terakhir kali berlatih bulu tangkis bersama-sama pada hari Rabu, mereka akan berlatih bulu tangkis bersama-sama lagi pada hari …. <strong><img decoding="async" src="https://lh3.googleusercontent.com/v25or7S0M-tC7dRHnHXZoKIcb20APimAHtR6dXZG1haliyJH5-xczuFGZK6ryY5eqjTgGVy0PdsqIr9Gg3GOA55O9xIyMeOspjvmhoOYdyNGSUte9bkI0mxpH4DkTrOXtz4avP8" width="4" height="5" loading="lazy"></strong> </p>
<ol style="list-style-type: upper-alpha;">
<li aria-level="1">Senin</li>
<li aria-level="1">Selasa</li>
<li aria-level="1">Rabu</li>
<li aria-level="1">Kamis</li>
<li aria-level="1">Jumat</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban: A</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Dari soal tersebut, diketahui bahwa Lani, Rista, dan Ipul terakhir kali berlatih bersama-sama pada hari Rabu.</p>
<p style="text-align: justify;">Kemudian, waktu yang dibutuhkan mereka untuk belajar bulu tangkis bersama lagi dapat diketahui dengan menentukan KPK dari 4, 6, dan 12.</p>
<p style="text-align: justify;">Faktorisasi dari 4 adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/3a.jpg" alt="3a" width="23" loading="lazy" style="width: 23px;"></p>
<p>Faktorisasi dari 6 adalah 2×3</p>
<p>Faktorisasi dari 12 adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/3b.jpg" alt="3b" width="37" loading="lazy" style="width: 37px;"></p>
<p>Dengan demikian, KPK dari 4, 6, dan 12 adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/3c.jpg" alt="3c" width="74" loading="lazy" style="width: 74px;"></p>
<p style="text-align: justify;">Karena mereka akan bertemu kembali 12 hari setelah hari Rabu, maka ketiganya akan berlatih bulu tangkis bersama lagi pada hari <strong>Senin.</strong><img decoding="async" src="https://lh5.googleusercontent.com/pOA_BFfZq5mFKwBWqo77A-UnMaZPtI26N2JESvc3r5SZzihQIKB5XqleryUiOGEL0y5zfZqZx4_8xiN8Tpk-VtkMm9FlZCFp4dGA_BTVRqVETrzp2hY3acctEysBilWKc1nc2Tc" width="8" height="5" loading="lazy"> </p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah A.</span></strong><img decoding="async" src="https://lh3.googleusercontent.com/v25or7S0M-tC7dRHnHXZoKIcb20APimAHtR6dXZG1haliyJH5-xczuFGZK6ryY5eqjTgGVy0PdsqIr9Gg3GOA55O9xIyMeOspjvmhoOYdyNGSUte9bkI0mxpH4DkTrOXtz4avP8" width="4" height="5" loading="lazy"><strong> </strong></p>
<p><strong><span style="text-decoration: underline;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></strong></p>
<p><strong>Topik: Pengetahuan Kuantitatif </strong><strong><br /></strong><strong>Sunbtopik: Statistika dan Peluang</strong></p>
<p style="text-align: justify;">4. Nilai rata-rata ulangan Bahasa Inggris 25 siswa di suatu kelas adalah 75,2. Setelah ada satu orang siswa baru yang mengikuti ulangan susulan, nilai rata-rata ulangan Bahasa Inggris di kelas tersebut menjadi 75,4. Berdasarkan informasi tersebut, diperoleh data sebagai berikut.</p>
<ol>
<li aria-level="1">Jumlah keseluruhan nilai sebelum siswa susulan adalah 1.881.</li>
<li aria-level="1">Nilai Bahasa Inggris siswa yang baru adalah 80,4.</li>
<li aria-level="1">Selisih antara jumlah keseluruhan nilai sebelum dan setelah susulan adalah 81,4.</li>
<li aria-level="1">Jumlah seluruh nilai siswa setelah ulangan susulan adalah 1.960,4. </li>
</ol>
<ol style="list-style-type: upper-alpha;">
<li aria-level="1">1, 2, dan 3 SAJA yang benar.</li>
<li aria-level="1">1 dan 3 SAJA yang benar.</li>
<li aria-level="1">2 dan 4 SAJA yang benar.</li>
<li aria-level="1">HANYA 4 yang benar.</li>
<li aria-level="1">SEMUA pilihan benar.</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Dari soal diketahui jumlah siswa ada 25 orang, dan rata-rata nilainya 75,2. Dengan demikian, jumlah keseluruhan nilai adalah sebagai berikut.</p>
<p style="text-align: center;">25×75,2=1.880 </p>
<p style="text-align: justify;">Setelah ditambah satu orang siswa yang mengikuti ulangan susulan, rata-rata nilainya menjadi 75,4. Jumlah keseluruhan nilai yang baru adalah sebagai berikut.</p>
<p style="text-align: center;">26×75,4=1.960,4 </p>
<p style="text-align: justify;">Oleh karena itu, dapat diketahui bahwa nilai ulangan Bahasa Inggris siswa yang mengikuti ulangan susulan adalah sebagai berikut.</p>
<p style="text-align: center;">=jumlah nilai 26 siswa-jumlah nilai 25 siswa</p>
<p style="text-align: center;">=1960,4 -1.880= 80,4</p>
<p style="text-align: justify;">Berdasarkan penjelasan tersebut, pernyataan yang tepat adalah nomor <strong>2 dan 4</strong>.<img decoding="async" src="https://lh3.googleusercontent.com/uZ6OEyTw--Ad-plG4RBxdpu4OppXlVW7oh7NGsacpaTMJbT3H6hJFJcVwjp_rYc5EatZZPQSrsXLrgFQD3i_-NtjF9GiAP7Ugi7BvRoF6rpJ8KQbjSWa2gmLqRfuSUFyV5K-GLw" width="16" height="5" loading="lazy"> </p>
<p><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah C.</span></strong><img decoding="async" src="https://lh5.googleusercontent.com/pOA_BFfZq5mFKwBWqo77A-UnMaZPtI26N2JESvc3r5SZzihQIKB5XqleryUiOGEL0y5zfZqZx4_8xiN8Tpk-VtkMm9FlZCFp4dGA_BTVRqVETrzp2hY3acctEysBilWKc1nc2Tc" width="8" height="5" loading="lazy"></p>
<p><strong><span style="text-decoration: underline;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></strong></p>
<p><strong>Topik: Pengetahuan Kuantitatif </strong><strong><br /></strong><strong>Subtopik: Bilangan</strong></p>
<p style="text-align: justify;">5. Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 8, 12, and 16 hours, respectively. What is the ratio of the time it takes printer X to do the job working alone at its rate, to the time it takes printers Y and Z to do the job working together at their individual rates?</p>
<ol style="list-style-type: upper-alpha;">
<li aria-level="1">411</li>
<li aria-level="1">76</li>
<li aria-level="1">1522</li>
<li aria-level="1">2215</li>
<li aria-level="1">114</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban: B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Dari soal tersebut, diperoleh informasi sebagai berikut.</p>
<p style="text-align: justify;">Printer X dapat melakukan pekerjaan selama 8 jam, artinya printer X dapat melakukan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5a.jpg" alt="5a" width="17" loading="lazy" style="width: 17px;"> bagian dalam satu jam.</p>
<p style="text-align: justify;">Printer Y dapat melakukan pekerjaan selama 12 jam, artinya printer Y dapat melakukan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5b.jpg" alt="5b" width="19" loading="lazy" style="width: 19px;"> bagian dalam satu jam.</p>
<p style="text-align: justify;">Printer Z dapat melakukan pekerjaan selama 16 jam, artinya printer Z dapat melakukan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5c.jpg" alt="5c" width="21" loading="lazy" style="width: 21px;"> bagian dalam satu jam.</p>
<p style="text-align: justify;">Ketika printer Y dan Z digunakan bersamaan dalam 1 jam, maka pekerjaan yang dapat mereka selesaikan adalah sebagai berikut.</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5d.jpg" alt="5d" width="159" loading="lazy" style="width: 159px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Jadi, printer Y dan Z membutuhkan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5e.jpg" alt="5e" width="27" loading="lazy" style="width: 27px;"> jam untuk menyelesaikan suatu pekerjaan secara bersama-sama. </p>
<p style="text-align: justify;">Kemudian, karena printer X dapat melakukan pekerjaan selama 8 jam, maka rasio waktu yang diperlukan oleh printer X untuk dapat menyelesaikan suatu pekerjaan dibandingkan dengan waktu yang dibutuhkan jika printer Y dan Z bekerja bersama adalah sebagai berikut.</p>
<p style="text-align: center;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5f.jpg" alt="5f" width="156" loading="lazy" style="width: 156px;"></p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah B.</span></strong></p>
<p><strong><span style="text-decoration: underline;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></strong></p>
<p><strong>Topik: Pengetahuan Kuantitatif </strong><strong><br /></strong><strong>Subtopik: Statistika dan Peluang</strong><span style="background-color: transparent; font-size: 1rem;">.</span></p>
<p style="text-align: justify;"><span style="background-color: transparent; font-size: 1rem;">6. Four identical cars and eight identical bicycles are each randomly given to 12 different people. Each of the twelve receives either a car, or a bicycle, but not both. Ann and Elsa are two of these people. The probability that Ann and Elsa got the different prizes is ….</span></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Mar-30-2021-01-01-27-20-PM.png" loading="lazy"></p>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Dari soal tersebut, diperoleh informasi bahwa terdapat 12 hadiah undian yang terdiri dari 4 mobil dan 8 sepeda. Kemudian dua orang, yaitu Ann dan Elsa, adalah dua pemenang undian tersebut.</p>
<p style="text-align: justify;">Kemudian, yang ditanyakan adalah peluang mereka mendapatkan hadiah yang berbeda.</p>
<p style="text-align: justify;">Dalam hal ini, terdapat dua kemungkinan sebagai berikut.</p>
<ol>
<li>Ann mendapat mobil dan Elsa mendapat sepeda.</li>
<li>Ann mendapat sepeda dan Elsa mendapat mobil.</li>
</ol>
<p style="text-align: justify;"><strong>Kemungkinan pertama,</strong> peluang Ann mendapat mobil dan Elsa mendapat sepeda adalah sebagai berikut.</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/6b.jpg" alt="6b" width="147" loading="lazy" style="width: 147px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;"><strong>Kemungkinan kedua, </strong>peluang Ann mendapat sepeda dan Elsa mendapat mobil adalah sebagai berikut.</p>
<p style="text-align: center;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/6c.jpg" alt="6c" width="154" loading="lazy" style="width: 154px;"></p>
<p style="text-align: justify;">Dengan demikian, peluang Ann dan Elsa mendapat hadiah yang berbeda adalah sebagai berikut.</p>
<p style="text-align: center;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/6d.jpg" alt="6d" width="92" loading="lazy" style="width: 92px;"></p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah C.</span></strong></p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></strong></p>
<p><strong>Topik: Pengetahuan Kuantitatif</strong><strong><br /></strong><strong>Subtopik: Aljabar</strong></p>
<p>7. Diketahui himpunan Y = {<em>r,a,s,i,g,u.</em>} Dari himpunan-himpunan berikut ini, manakah yang merupakan himpunan bagian dari Y ?</p>
<ol>
<li aria-level="1"><em>M = {g, u, r, i}</em></li>
<li aria-level="1"><em>N = {s, i, a, r}</em></li>
<li aria-level="1"><em>O = {a, u, r, i}</em></li>
<li aria-level="1"><em>P = {o, u, r, i}</em></li>
</ol>
<ol style="list-style-type: upper-alpha;">
<li aria-level="1">1, 2, dan 3 SAJA yang benar.</li>
<li aria-level="1">1 dan 3 SAJA yang benar.</li>
<li aria-level="1">2 dan 4 SAJA yang benar.</li>
<li aria-level="1">HANYA 4 yang benar.</li>
<li aria-level="1">SEMUA pilihan benar.</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban: A</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Ingat bahwa himpunan A dikatakan sebagai himpunan bagian dari himpunan B, jika semua anggota himpunan A merupakan anggota himpunan B.</p>
<p style="text-align: justify;">Pada soal yang semua anggota himpunannya merupakan anggota himpunan Y adalah himpunan M, N, dan O.</p>
<p style="text-align: justify;">Dengan demikian, yang merupakan himpunan bagian dari himpunan Y adalah pernyataan 1, pernyataan 2, dan pernyataan 3.</p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah A.</span></strong></p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></strong></p>
<p><strong>Topik: Pengetahuan Kuantitatif</strong><strong><br /></strong><strong>Subtopik: Aljabar</strong></p>
<p>8. Diketahui bahwa <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8a.jpg" alt="8a" width="181" loading="lazy" style="width: 181px;"></p>
<p style="text-align: justify;">Manakah pernyataan berikut yang benar?</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8b.jpg" alt="8b" width="234" loading="lazy" style="width: 234px;"></p>
<ol style="list-style-type: upper-alpha;">
<li aria-level="1">1, 2, dan 3 SAJA yang benar.</li>
<li aria-level="1">1 dan 3 SAJA yang benar.</li>
<li aria-level="1">2 dan 4 SAJA yang benar.</li>
<li aria-level="1">HANYA 4 yang benar.</li>
<li aria-level="1">SEMUA pilihan benar.</li>
</ol>
<p style="text-align: justify;"><strong>Jawaban: C</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Perhatikan perhitungan berikut!</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8c.jpg" alt="8c" width="389" loading="lazy" style="width: 389px; margin-left: auto; margin-right: auto; display: block;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8d.jpg" alt="8d" width="242" loading="lazy" style="width: 242px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Kemudian,</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8e.jpg" alt="8e" width="393" loading="lazy" style="width: 393px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8e-1.jpg" alt="8e-1" width="393" loading="lazy" style="width: 393px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Eliminasi persamaan (i) dan (ii)</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8g.jpg" alt="8g" width="238" loading="lazy" style="width: 238px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Substitusikan <img decoding="async" src="https://lh3.googleusercontent.com/DHSHwbkYhxzjJbDujj-NEzCJDIR48hvJa13B60ejpIxS2S_KhlHpfUPNlgOwkJ4pN_GWptmjo4eyO-WLpaeP_TLaS3--renwPejOrimPZ0Z2ACpGVTqcxPedcSPlFntmuMUXsqY" width="47" height="13" loading="lazy"> ke persamaan (i)</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8h.jpg" alt="8h" width="268" loading="lazy" style="width: 268px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Dengan demikian, diperoleh <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8i.jpg" alt="8i" width="119" loading="lazy" style="width: 119px;"> Kemudian, periksa setiap pernyataan.</p>
<p style="text-align: justify;">Pernyataan 1 salah, seharusnya <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8j.jpg" alt="8j" width="38" loading="lazy" style="width: 38px;">.</p>
<p style="text-align: justify;">Pernyataan 2 benar, karena <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8k.jpg" alt="8k" width="146" loading="lazy" style="width: 146px;"></p>
<p style="text-align: justify;">dan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8l.jpg" alt="8l" width="124" loading="lazy" style="width: 124px;"><span style="text-decoration: underline;"></span></p>
<p style="text-align: justify;">Dengan demikian, didapat bahwa <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8m.jpg" alt="8m" width="73" loading="lazy" style="width: 73px;"> </p>
<p style="text-align: justify;">Pernyataan 3 salah, karena <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8n.jpg" alt="8n" width="19" loading="lazy" style="width: 19px;"> adalah bilangan genap.</p>
<p style="text-align: justify;">Pernyataan 4 benar, karena 6 dan -3 keduanya habis dibagi 3.</p>
<p style="text-align: justify;">Oleh karena itu, pernyataan yang benar adalah pernyataan 2 dan 4.<img decoding="async" src="https://lh3.googleusercontent.com/v25or7S0M-tC7dRHnHXZoKIcb20APimAHtR6dXZG1haliyJH5-xczuFGZK6ryY5eqjTgGVy0PdsqIr9Gg3GOA55O9xIyMeOspjvmhoOYdyNGSUte9bkI0mxpH4DkTrOXtz4avP8" width="4" height="5" loading="lazy"><img decoding="async" src="https://lh4.googleusercontent.com/wqjGU0nNdLTQlPzYQso0m516BBjhEas16VXlOQf1bv-987mWl8-vS4dzHwzrpXv6HvzR8Z9WjJ4Wr2XhTWEeOmGo-0vWkgzR0iTsmMDv8CC-CfjtNcJLFzVd4UfxLqTVpuaxCOg" width="12" height="5" loading="lazy"> </p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah C.</span></strong><img decoding="async" src="https://lh5.googleusercontent.com/pOA_BFfZq5mFKwBWqo77A-UnMaZPtI26N2JESvc3r5SZzihQIKB5XqleryUiOGEL0y5zfZqZx4_8xiN8Tpk-VtkMm9FlZCFp4dGA_BTVRqVETrzp2hY3acctEysBilWKc1nc2Tc" width="8" height="5" loading="lazy"> </p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></strong></p>
<p>9. .. , … , 71 , 79 , 158, 153, 161.</p>
<p style="text-align: justify;">Which numbers are possibly correct to fill in the blanks?<strong><img decoding="async" src="https://lh5.googleusercontent.com/1EoYbspDR6syjeCK_wyDpJOVF-O4b-KqUS1vO2nDaNu73VB7W4A1PwBZAXz6Hbc5nVf28ctRq4bSSbwTPtUxHZWADuCfWOC3C_tuzl4oTgBU57ZxZcysFdZibqp_-NVCuvzRnoU" width="16" height="5" loading="lazy"></strong> </p>
<ol>
<li aria-level="1">38</li>
<li aria-level="1">33</li>
<li aria-level="1">76</li>
<li aria-level="1">66</li>
</ol>
<ol style="list-style-type: upper-alpha;">
<li aria-level="1">1, 2, and 3 ONLY</li>
<li aria-level="1">1 and 3 ONLY</li>
<li aria-level="1">2 and 4 ONLY</li>
<li aria-level="1">4 ONLY</li>
<li aria-level="1">1, 2, 3, and 4</li>
</ol>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Jawaban: B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p>Misal bagian kosong pertama adalah A dan bagian kosong kedua adalah B</p>
<p>Perhatikan pola barisan berikut!</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/9a.jpg" alt="9a" width="329" loading="lazy" style="width: 329px; margin-left: auto; margin-right: auto; display: block;"></p>
<p>Terdapat tiga pola dalam penyusunan deret angka ini, yaitu perkalian 2, pengurangan 5, dan penjumlahan 8.</p>
<p>Dengan demikian, pola untuk A dan B adalah sebagai berikut.</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/9b.jpg" alt="9b" width="263" loading="lazy" style="width: 263px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Dari pola tersebut, diperoleh hasil perhitungan sebagai berikut.</p>
<p style="text-align: center;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/9c.jpg" alt="9c" width="247" loading="lazy" style="width: 247px; margin-left: auto; margin-right: auto; display: block;"></p>
<p>dan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/9d.jpg" alt="9d" width="172" loading="lazy" style="width: 172px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Jadi, bilangan pertama dan kedua yang tepat untuk mengisi tempat kosong tersebut adalah 38 dan 76.</p>
<p style="text-align: justify;">Dengan demikian, pernyataan yang tepat adalah 1 dan 3.<img decoding="async" src="https://lh5.googleusercontent.com/1EoYbspDR6syjeCK_wyDpJOVF-O4b-KqUS1vO2nDaNu73VB7W4A1PwBZAXz6Hbc5nVf28ctRq4bSSbwTPtUxHZWADuCfWOC3C_tuzl4oTgBU57ZxZcysFdZibqp_-NVCuvzRnoU" width="16" height="5" loading="lazy"> </p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah B.</span></strong></p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></strong></p>
<p><strong>Topik: Pengetahuan Kuantitatif</strong><strong><br /></strong><strong>Subtopik: Statistika dan Peluang</strong></p>
<p>10. Dua buah dadu dilempar secara bersamaan.</p>
<p style="text-align: justify;">Manakah hubungan yang tepat antara P dan Q berikut berdasarkan informasi yang diberikan?</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/10a.jpg" alt="10a" width="349" loading="lazy" style="width: 349px; margin-left: auto; margin-right: auto; display: block;"></p>
<ol style="list-style-type: upper-alpha;">
<li aria-level="1"><em>P</em> > <em>Q</em>.</li>
<li aria-level="1"><em>Q</em> > <em>P</em>.</li>
<li aria-level="1"><em>P</em> = <em>Q</em>.</li>
<li aria-level="1">Informasi yang diberikan tidak cukup untuk memutuskan salah satu dari tiga pilihan di atas. </li>
</ol>
<p style="text-align: justify;"><strong>Jawaban: B</strong></p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Dua buah dadu dilempar secara bersamaan, maka jumlah ruang sampelnya adalah</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/10b.jpg" alt="10b" width="102" loading="lazy" style="width: 102px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Kejadian mata dadu kembar yang mungkin adalah {(1, 1, 2, 2, 3, 3, 4, 4, 5, 5, (6, 6)}, banyaknya kejadian adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/10c-1.jpg" alt="10c-1" width="58" loading="lazy" style="width: 58px;"></p>
<p>Peluang muncul mata dadu kembar dapat ditentukan melalui perhitungan berikut.</p>
<p> <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/10d.jpg" alt="10d" width="131" loading="lazy" style="width: 131px; margin-left: auto; margin-right: auto; display: block;"></p>
<p>Penyebut <em>P</em> dan <em>Q</em> disamakan menjadi 18, maka didapat nilai <em>P.</em></p>
<p style="text-align: center;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/10e.jpg" alt="10e" width="113" loading="lazy" style="width: 113px; margin-left: auto; margin-right: auto; display: block;"></p>
<p style="text-align: justify;">Hubungan antara <em>P</em> dan <em>Q</em> yang tepat adalah P<Q atau dapat dituliskan menjadi Q>P.</p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;">Jadi, jawaban yang tepat adalah pilihan B.</span></strong></p>
<p style="text-align: justify;"><strong><span style="text-decoration: underline;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Mar-30-2021-07-02-07-74-AM" width="820" loading="lazy" style="width: 820px; margin-left: auto; margin-right: auto; display: block;"></span></strong></p>
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<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
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</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
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<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
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<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
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</nav>
</div>
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</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
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</picture>
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</picture>
</a>
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</picture>
</a>
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</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>