Artikel ini memberikan latihan soal TPS UTBK 2020 untuk topik Pengetahuan Kuantitatif dengan Bahasa Inggris
—
Psst, sudah tahu belum jika di soal TPS Pengetahuan Kuantitatif akan ada soal yang berbahasa Inggris? Nggak usah panik, konsepnya sama kok dengan soal lainnya, hanya saja mengguakan bahasa Inggris. Waktu pelaksaan UTBK 2020 sudah tinggal sedikit lagi. Ayo, terus latih keterampilan berhitung kamu pada soal berbahasa Inggris dengan latihan soal TPS UTBK Pengetahuan Kuantitatif berikut ini.
Soal 1
In the xy-plane, (1, 1) is a solution to the system of inequalities above.
Which is the correct relation between quantities P and Q must be true?
- P > Q.
- Q > P.
- P = Q.
- The information provided is not enough.
JAWABAN : A
PEMBAHASAN :
Dikatakan bahwa (1, 1) is a solution to the system of inequalities above.
Artinya, (1, 1) memenuhi sistem pertidaksamaan yang diberikan.
Jadi, dari sistem pertidaksamaan tersebut, dapat disubstitusikan Oleh karena itu didapat
dan
Perhatikan bahwa
Oleh karena itu,
Jadi, Q < P atau P > Q.
Dengan demikian, jawaban yang tepat adalah A.
SOAL 2
A rectangle was altered by increasing its length bypercent and decreasing its width by 20 percent. If these alterations decreased the area of the rectangle by 8 percent, what is the value of ?
- 8
- 9
- 12
- 15
- 28
JAWABAN : D
PEMBAHASAN :
Diketahui terdapat “rectangle” atau persegi panjang.
Misalkan panjangnya adalah dan lebarnya adalah
Luas dari persegi panjang ini adalah
Kemudian dikatakan bahwa “A rectangle was altered by increasing its length bypercent and decreasing its width by 20 percent” yang berarti persegi panjang tersebut diubah dengan meningkatkan panjangnya sebesarpersen dan menurunkan lebarnya sebesar 20 persen.
Dalam hal ini, persegi panjang memiliki panjang baru yang ukurannya adalahpersen lebih panjang dari panjang sebelumnya. Jadi, dapat dituliskan
Kemudian lebar barunya memiliki ukuran 20 persen lebih pendek dari lebar sebelumnya. Jadi, dapat dituliskan
Selanjutnya, dikatakan pula bahwa “These alterations decreased the area of the rectangle by 8 percent” yang berarti perubahan ini menurunkan luas persegi panjang sebesar 8 persen. Oleh karena itu, dapat dituliskan
Luas barunya dapat dihitung dengan
Oleh karena itu, didapat
Oleh karena itu, didapat nilai = 15.
Jadi, jawaban yang tepat adalah D.
SOAL 3
A certain package requires 6 centimeters of tape to be closed securely. What is the maximum number of packages of this type that can be secured with 5 meters of tape?
- 75
- 80
- 83
- 84
- 85
JAWABAN : C
PEMBAHASAN :
Diketahui bahwa “A certain gift requires 6 centimeters of tape to be closed securely” yang berarti sebuah paket membutuhkan 6 cm selotip untuk dapat tertutup dengan aman.
Kemudian ditanyakan “What is the maximum number of packages of this type that can be secured with 5 meters of tape?” yang menanyakan maksimum banyaknya paket dengan tipe ini yang dapat tertutup dengan aman oleh 5 meter selotip.
Karena satu paket membutuhkan 6 cm selotip, maka x paket akan membutuhkan 6x cm selotip.
Akan dicari nilai x maksimum sehingga panjang selotip yang dibutuhkan tidak lebih dari 5 meter atau 500 cm. Akibatnya 6x kurang dari atau sama dengan 500. Oleh karena itu,
Karena banyak paket pasti merupakan bilangan bulat non-negatif, maka banyak paket maksimum yang dapat tertutup dengan aman adalah 83 buah paket.
Jadi, jawaban yang tepat adalah C.
SOAL 4
In 2020 the population of City A and City B were equal. From 2018 to 2020, the population of City A decreased by 15% and the population of City B increased by 25%. If the population of City A was 340.000 in 2018, what was the population of City B in 2018?
- 231.200
- 300.000
- 312.800
- 385.300
- 500.000
JAWABAN :
PEMBAHASAN :
Diketahui bahwa “In 2020 the population of City A and City B were equal” yang berarti pada tahun 2020, populasi kota A dan kota B sama. Dapat dituliskan bahwa
Kemudian diketahui pula bahwa “From 2018 to 2020, the population of City A decreased by 15% and the population of City B increased by 25%” yang berarti dari tahun 2018 ke tahun 2020, populasi kota A turun sebesar 15% dan populasi kota B naik sebesar 25%. Oleh karena itu, dapat dituliskan
dan
Karena maka
Diketahui pula bahwa “the population of City A was 340.000 in 2018” yang berarti populasi kota A adalah 340.000 pada tahun 2018. Maka,
Jadi,
Oleh karena itu, populasi di kota B pada tahun 2018 adalah 231.200.
Jadi, jawaban yang tepat adalah A.
SOAL 5
The function f is defined above. If p is a negative integer and q is a positive integer, which of the following could represent the graph of -plane?
A.
B.
C.
D.
E.
JAWABAN : D
PEMBAHASAN :
Perhatikan bahwa fungsi f didefinisikan sebagai berikut
Terbentuk suatu fungsi kuadrat.
Diketahui bahwa “p is a negative integer and q is a positive integer”.
Hal ini berarti p adalah bilangan bulat negatif dan q adalah bilangan bulat positif.
Kemudian ditanyakan “which of the following could represent the graph of -plane” yang berarti “mana yang dapat merepresentasikan grafik atau bidang koordinat Kartesius”.
Ingat bahwa pada fungsi kuadrat
Jika a bernilai positif, maka grafik fungsi terbuka ke atas. Sebaliknya, jika a bernilai negatif, maka grafik fungsi terbuka ke bawah.
Kemudian, jika a dan b sama-sama positif atau sama-sama negatif, maka sumbu simetri berada di sebelah kiri sumbu-y. Selain itu, jika dan berbeda tanda, maka sumbu simetri berada di sebelah kanan sumbu-y.
Selanjutnya, titik c mewakili titik potong grafik fungsi dengan sumbu-y, yaitu pada titik (0,c). Jika c bernilai positif, maka grafik fungsi berpotongan dengan sumbu-y positif dan jika c bernilai negatif, maka grafik fungsi berpotongan dengan sumbu-y negatif.
Perhatikan kembali fungsi f, yaitu
Didapat
Karena a = 1 bernilai positif, maka grafik fungsi f terbuka ke atas.
Kemudian, b = p – q. Karena p adalah bilangan bulat negatif dan q adalah bilangan bulat positif, maka b = p – q adalah bilangan bulat negatif.
Karena a positif, namun b negatif, maka sumbu simetri dari grafik fungsi berada di sebelah kanan sumbu-y.
Selanjutnya, c = -pq. Karena p adalah bilangan bulat negatif dan q adalah bilangan bulat positif, maka c = -pq adalah bilangan bulat positif.
Oleh karena itu, grafik fungsi f berpotongan dengan sumbu-y positif.
Kemudian ingat nilai diskriminan
Jika D > 0, maka grafik memotong sumbu-x di dua titik.
Jika D = 0, maka grafik menyinggung sumbu-x.
Jika D < 0, maka grafik tidak berpotongan dengan sumbu-x.
Sejauh ini, telah didapat informasi sebagai berikut.
- Grafik fungsi f terbuka ke atas.
- Sumbu simetri dari grafik fungsi berada di sebelah kanan sumbu-y.
- Grafik fungsi f berpotongan dengan sumbu-y positif.
- Grafik fungsi f bisa berpotongan, bersinggungan, atau tidak berpotongan dengan sumbu-x.
Jadi, didapat kemungkinan grafik fungsi f ketika berpotongan dengan sumbu-x sebagai berikut.
Ingat bahwa grafik fungsi f tetap berpotongan dengan sumbu-y positif.
Selanjutnya, didapat kemungkinan grafik fungsi f ketika bersinggungan dengan sumbu-x sebagai berikut.
Kemudian, didapat kemungkinan grafik fungsi f ketika tidak berpotongan dengan sumbu-x sebagai berikut.
Dari kelima pilihan pada soal, pilihan yang tepat adalah D.
SOAL 6
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?
JAWABAN : B
PEMBAHASAN :
Printer Y dapat melakukan pekerjaan selama 12 jam, artinya printer Y dapat melakukan pekerjaan dalam satu jam. Printer Z dapat melakukan pekerjaan selama 16 jam, artinya printer Z dapat melakukan pekerjaan dalam satu jam. Ketika bersama, printer Y dan Z dapat melakukan pekerjaan sebanyak dalam satu jam. Artinya printer Y dan Z membutuhkan jam untuk menyelesaikan pekerjaan.
Printer X dapat melakukan pekerjaan selama 8 jam, maka rasio dari waktu yang diperlukan printer X untuk dapat menyelesaikan pekerjaan dibandingkan wakty yang dibutuhkan jika printer Y dan Z bekerja bersama adalah
Jadi, jawaban yang tepat adalah B.
SOAL 7
Each employee of a certain company is in either Department P or Q, and there are more than thrice as many employees in Department P as in Department Q. The average salary is $20,000 for the employees in Department P and $10,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees of the company?
(1) $17,600
(2) $16,500
(3) $18,400
(4) $15,300
- (1), (2), and (3) ONLY.
- (1) and (3) ONLY.
- (2) and (4) ONLY.
- (4) ONLY.
- (1), (2), (3), and (4).
JAWABAN : B
PEMBAHASAN :
Perhatikan bahwa salah satu strategi menjawab pernyataan semacam ini adalah menemukan kemungkinan nilai paling kecil dan paling besar.
Jelas bahwa gaji rata-rata berada diantara $10,000 dan $20,000 dan semua pilihan jawabannya berada pada interval tersebut.
Diketahui bahwa banyaknya karyawan di departemen P adalah lebih dari 3 kali banyaknya karyawan di Departemen Q. Kemudian, gaji karyawan di Departemen P lebih besar dibandingkan dengan gaji karyawan di departemen Q. Maka batas bawah rata-rata gaji semua karyawan adalah
Misalkan rerata gaji semua karyawan di perusahaan tersebut adalah
Jadi, berdasarkan pilihan yang ada, maka kemungkinan rata-rata gaji semua karyawan di perusahaan tersebut adalah $17,600 dan $18,400.
Jadi, jawaban yang tepat adalah B.
SOAL 8
Determine whether the data provided by the statements is sufficient to answer the following question.
If the length of a rectangle is 1 greater than the width of the rectangle, what is the perimeter of the rectangle?
(1) The length of the diagonal of the rectangle is 5.
(2) The area of the rectangular region is 12.
- Statement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.
- Statement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
JAWABAN :
PEMBAHASAN :
Diketahui bahwa “the length of a rectangle is 1 greater than the width of the rectangle”. Hal ini berarti panjang dari persegi panjang adalah 1 lebihnya dari lebar persegi panjang tersebut. Misalkan panjangnya adalah p dan lebarnya adalah maka
Kemudian ditanyakan “what is the perimeter of the rectangle?” yang menanyakan keliling persegi panjang.
Perhatikan pernyataan (1).
“The length of the diagonal of the rectangle is 5.”
Hal ini berarti panjang diagonal persegi panjang adalah 5.
Ingat bahwa panjang diagonal persegi panjang (d), dapat dihitung sebagai berikut
Karena lebar persegi panjang tidak mungkin bernilai negatif, maka
Jadi,
Keliling dari persegi panjang tersebut adalah
Jadi, dari pernyataan (1) dapat diketahui keliling dari persegi panjang.
Selanjutnya, perhatikan pernyataan (1).
“The area of the rectangular region is 12.”
Hal ini berarti luas persegi panjang adalah 12.
Ingat bahwa luas persegi panjang (L), dapat dihitung sebagai berikut
Karena lebar persegi panjang tidak mungkin bernilai negatif, maka
Jadi,
Keliling dari persegi panjang tersebut adalah
Jadi, dari pernyataan (2) dapat diketahui keliling dari persegi panjang.
Oleh karena itu, baik pernyataan (1) maupun pernyataan (2) masing-masing cukup untuk menjawab pertanyaan.
Jadi, jawaban yang tepat adalah D.
Tenang, nggak usah takut dengan soal-soal TPS Pengetahuan Kuantitatif berbahasa Inggris. Dengan rajin berlatih kamu bisa lancar dalam mengerjakan soal matematika dalam bahasa Inggris. Masih banyak juga lho latihan soal TPS UTBK 2020 di ruangbelajar!
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<h1 class="content-title">
Latihan Soal TPS UTBK 2020 Pengetahuan Kuantitatif Bahasa Inggris </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/shabrina-alfari" class="">Shabrina Alfari</a> </p>
<p class="content-info"><span>June 30, 2020 • </span> <span>9 minutes read</span></p>
<br />
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<div class="content-body">
<p style="background-color: #ffffff; font-family: 'Source Sans Pro', sans-serif; margin: 0px 0px 1em;"><em><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Pojok_Kampus_-_Latihan_Soal_Kuantitatif_bahasa_Inggris_(Low).jpg" width="820" style="width: 820px;" alt="latihan soal tps utbk pengetahuan kuantitatif"></em></p>
<p style="background-color: #ffffff; font-family: 'Source Sans Pro', sans-serif; margin: 0px 0px 1em;"><em>Artikel ini memberikan latihan soal<span> </span><strong style="font-weight: 600;">TPS UTBK 2020</strong><span> </span>untuk topik Pengetahuan Kuantitatif dengan Bahasa Inggris</em></p>
<p><span id="more-6547"></span></p>
<p style="background-color: #ffffff; font-family: 'Source Sans Pro', sans-serif; margin: 0px 0px 1em; text-align: center;"><em>—</em></p>
<p style="text-align: justify;"><em>Psst</em>, sudah tahu belum jika di soal <strong>TPS</strong> Pengetahuan Kuantitatif akan ada soal yang berbahasa Inggris? <span style="font-style: italic;">Nggak</span> usah panik, konsepnya sama <span style="font-style: italic;">kok</span> dengan soal lainnya, hanya saja mengguakan bahasa Inggris. <strong>Waktu pelaksaan UTBK 2020</strong> sudah tinggal sedikit lagi. Ayo, terus latih keterampilan berhitung kamu pada soal berbahasa Inggris dengan <a href="/latihan-soal-tps-utbk-2020-pemahaman-bacaan" rel="noopener" target="_blank" style="font-weight: bold;">latihan soal TPS UTBK</a> Pengetahuan Kuantitatif berikut ini.</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM" width="1709" style="width: 1709px;"></p>
<p style="text-align: justify;"><strong>Soal 1</strong></p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/fgf.jpg" alt="fgf" width="91" style="width: 91px; display: block; margin-left: auto; margin-right: auto;"></p>
<p style="text-align: justify;"><span>In the xy-plane, (1, 1) is a solution to the system of inequalities above.</span></p>
<p style="text-align: justify;"><span>Which is the correct relation between quantities P and Q must be true?</span></p>
<p><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/fgrh.jpg" alt="fgrh" width="165" style="width: 165px; display: block; margin-left: auto; margin-right: auto;"></span></p>
<ol style="list-style-type: upper-alpha;">
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> P > Q.</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> Q > P.</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> P = Q.</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> The information provided is not enough.</span></li>
</ol>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>JAWABAN : A</strong></p>
<p style="text-align: justify;"><strong>PEMBAHASAN :</strong></p>
<p style="text-align: justify;">Dikatakan bahwa <span>(1, 1) is a solution to the system of inequalities above.</span></p>
<p style="text-align: justify;"><span>Artinya, (1, 1) memenuhi sistem pertidaksamaan yang diberikan.</span></p>
<p style="text-align: justify;"><span>Jadi, dari sistem pertidaksamaan tersebut, dapat disubstitusikan</span><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/sdgsg.jpg" alt="sdgsg" width="107" style="width: 107px;"></span><span> Oleh karena itu didapat</span></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/nn.jpg" alt="nn" width="92" style="width: 92px;"></p>
<p style="text-align: justify;"><span>dan</span></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/nbn.jpg" alt="nbn" width="77" style="width: 77px;"></p>
<p style="text-align: justify;"><span>Perhatikan bahwa</span></p>
<p style="text-align: justify;"><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/ndgsrg.jpg" alt="ndgsrg" width="104" style="width: 104px;"></span></p>
<p style="text-align: justify;"><span>Oleh karena itu, </span><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/fsr.jpg" alt="fsr" width="56" style="width: 56px;"></span></p>
<p style="text-align: justify;"><span>Jadi, Q < P atau P > Q.</span></p>
<p style="text-align: justify;"><strong><u><span>Dengan demikian, jawaban yang tepat adalah A.</span></u></strong></p>
<p style="text-align: justify;"><strong><u><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM" width="1709" style="width: 1709px;"></span></u></strong></p>
<p style="text-align: justify;"><strong><span>SOAL 2</span></strong></p>
<p style="text-align: justify;"><span>A rectangle was altered by increasing its length by<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/4-1.jpg" alt="4-1" width="16" style="width: 16px;"></span><span>percent and decreasing its width by 20 percent. If these alterations decreased the area of the rectangle by 8 percent, what is the value of </span><span>?</span></p>
<ol style="list-style-type: upper-alpha;">
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 8</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 9</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 12</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 15</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 28</span></li>
</ol>
<p style="text-align: justify;"> </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;">Diketahui terdapat “rectangle” atau persegi panjang.</p>
<p style="text-align: justify;">Misalkan panjangnya adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/2-3.jpg" alt="2-3" width="18" style="width: 18px;">dan lebarnya adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1-4.jpg" alt="1-4" width="19" style="width: 19px;"></p>
<p style="text-align: justify;">Luas dari persegi panjang ini adalah</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/3-1.jpg" alt="3-1" width="106" style="width: 106px;"></p>
<p style="text-align: justify;">Kemudian dikatakan bahwa “<span>A rectangle was altered by increasing its length by<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/4-1.jpg" alt="4-1" width="16" style="width: 16px;"></span><span>percent and decreasing its width by 20 percent” yang berarti persegi panjang tersebut diubah dengan meningkatkan panjangnya sebesar<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/4-1.jpg" alt="4-1" width="16" style="width: 16px;"></span><span>persen dan menurunkan lebarnya sebesar 20 persen.</span></p>
<p style="text-align: justify;"><span>Dalam hal ini, persegi panjang memiliki panjang baru yang ukurannya adalah<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/4-1.jpg" alt="4-1" width="16" style="width: 16px;"></span><span>persen lebih panjang dari panjang sebelumnya. Jadi, dapat dituliskan</span></p>
<p style="text-align: justify;"><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/5-1.jpg" alt="5-1" width="151" style="width: 151px;"></span></p>
<p style="text-align: justify;">Kemudian lebar barunya memiliki ukuran 20 persen lebih pendek dari lebar sebelumnya. Jadi, dapat dituliskan</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/6-Jun-26-2020-06-35-38-18-AM.jpg" alt="6-Jun-26-2020-06-35-38-18-AM" width="153" style="width: 153px;"></p>
<p style="text-align: justify;">Selanjutnya, dikatakan pula bahwa “<span>These alterations decreased the area of the rectangle by 8 percent” yang berarti perubahan ini menurunkan luas persegi panjang sebesar 8 persen. Oleh karena itu, dapat dituliskan</span></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/7-1.jpg" alt="7-1" width="163" style="width: 163px;"></p>
<p style="text-align: justify;">Luas barunya dapat dihitung dengan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/8-1.jpg" alt="8-1" width="155" style="width: 155px;"></p>
<p style="text-align: justify;">Oleh karena itu, didapat</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/9-1.jpg" alt="9-1" width="231" style="width: 231px;"></p>
<p style="text-align: justify;">Oleh karena itu, didapat nilai <span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/4-1.jpg" alt="4-1" width="16" style="width: 16px;">= 15</span>.</p>
<p style="text-align: justify;"><strong><u>Jadi, jawaban yang tepat adalah D.</u></strong></p>
<p style="text-align: justify;"><strong><u><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM" width="1709" style="width: 1709px;"></span></u></strong></p>
<p style="text-align: justify;"><strong><span>SOAL 3</span></strong></p>
<p style="text-align: justify;"><span>A certain package requires 6 centimeters of tape to be closed securely. What is the maximum number of packages of this type that can be secured with 5 meters of tape?</span></p>
<ol style="list-style-type: upper-alpha;">
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 75</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 80</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 83</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 84</span></li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> 85</span></li>
</ol>
<p style="text-align: justify;"> </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;">Diketahui bahwa “<span>A certain gift requires 6 centimeters of tape to be closed securely” yang berarti sebuah paket membutuhkan 6 cm selotip untuk dapat tertutup dengan aman.</span></p>
<p style="text-align: justify;">Kemudian ditanyakan “<span>What is the maximum number of packages of this type that can be secured with 5 meters of tape?” yang menanyakan maksimum banyaknya paket dengan tipe ini yang dapat tertutup dengan aman oleh 5 meter selotip.</span></p>
<p style="text-align: justify;"><span>Karena satu paket membutuhkan 6 cm selotip, maka<em> x </em></span><span>paket akan membutuhkan 6<em>x</em></span><span> cm selotip.</span></p>
<p style="text-align: justify;"><span>Akan dicari nilai <em>x</em></span><span> maksimum sehingga panjang selotip yang dibutuhkan tidak lebih dari 5 meter atau 500 cm. Akibatnya 6<em>x</em></span><span> kurang dari atau sama dengan 500. Oleh karena itu,</span></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/10-1.jpg" alt="10-1" width="96" style="width: 96px;"></p>
<p style="text-align: justify;"><span>Karena banyak paket pasti merupakan bilangan bulat non-negatif, maka banyak paket maksimum yang dapat tertutup dengan aman adalah 83 buah paket.</span></p>
<p style="text-align: justify;"><strong><u><span>Jadi, jawaban yang tepat adalah C.</span></u></strong></p>
<p style="text-align: justify;"><strong><u><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM" width="1709" style="width: 1709px;"></span></u></strong></p>
<p style="text-align: justify;"><strong><span>SOAL 4</span></strong></p>
<p style="text-align: justify;"><span>In 2020 the population of City A and City B were equal. From 2018 to 2020, the population of City A decreased by 15% and the population of City B increased by 25%. If the population of City A was 340.000 in 2018, what was the population of City B in 2018?</span></p>
<ol style="list-style-type: upper-alpha;">
<li><span> 231.200</span></li>
<li><span> 300.000</span></li>
<li><span> 312.800</span></li>
<li><span> 385.300</span></li>
<li><span> 500.000</span></li>
</ol>
<p></p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>JAWABAN : </strong></p>
<p style="text-align: justify;"><strong>PEMBAHASAN :</strong></p>
<p style="text-align: justify;">Diketahui bahwa “<span>In 2020 the population of City A and City B were equal” yang berarti pada tahun 2020, populasi kota A dan kota B sama. Dapat dituliskan bahwa</span></p>
<p style="text-align: justify;"><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/11-1.jpg" alt="11-1" width="109" style="width: 109px;"></span></p>
<p style="text-align: justify;">Kemudian diketahui pula bahwa “<span>From 2018 to 2020, the population of City A decreased by 15% and the population of City B increased by 25%” yang berarti dari tahun 2018 ke tahun 2020, populasi kota A turun sebesar 15% dan populasi kota B naik sebesar 25%. Oleh karena itu, dapat dituliskan</span></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/12-1.jpg" alt="12-1" width="218" style="width: 218px;"></p>
<p style="text-align: justify;">dan</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/13-1.jpg" alt="13-1" width="214" style="width: 214px;"></p>
<p style="text-align: justify;">Karena <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/14-1.jpg" alt="14-1" width="103" style="width: 103px;"> maka</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/15-1.jpg" alt="15-1" width="177" style="width: 177px;"></p>
<p style="text-align: justify;">Diketahui pula bahwa “<span>the population of City A was 340.000 in 2018” yang berarti populasi kota A adalah 340.000 pada tahun 2018. Maka, </span><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/16-1.jpg" alt="16-1" width="127" style="width: 127px;"></span></p>
<p style="text-align: justify;">Jadi,</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/17-1.jpg" alt="17-1" width="200" style="width: 200px;"></p>
<p style="text-align: justify;">Oleh karena itu, populasi di kota B pada tahun 2018 adalah 231.200.</p>
<p style="text-align: justify;"><strong><u><span>Jadi, jawaban yang tepat adalah A.</span></u></strong></p>
<p style="text-align: justify;"><span> <strong><u><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM" width="1709" style="width: 1709px;"></u></strong></span></p>
<p style="text-align: justify;"><strong><span>SOAL 5</span></strong></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/18-1.jpg" alt="18-1" width="172" style="width: 172px;"></p>
<p style="text-align: justify;">The function <em>f</em> is defined above. If <i>p</i> is a negative integer and <em>q </em>is a positive integer, which of the following could represent the graph of <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/19-1.jpg" alt="19-1" width="129" style="width: 129px;">-plane?</p>
<p style="text-align: justify;">A. <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/20-1.jpg" alt="20-1" width="237" style="width: 237px;"></p>
<p style="text-align: justify;">B. <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/21-1.jpg" alt="21-1" width="231" style="width: 231px;"></p>
<p style="text-align: justify;">C. <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/22-1.jpg" alt="22-1" width="231" style="width: 231px;"></p>
<p style="text-align: justify;">D. <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/23-1.jpg" alt="23-1" width="249" style="width: 249px;"></p>
<p style="text-align: justify;">E.<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/24-1.jpg" alt="24-1" width="222" style="width: 222px;"></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;">Perhatikan bahwa fungsi <em>f</em> didefinisikan sebagai berikut</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/25-1.jpg" alt="25-1" width="198" style="width: 198px;"></p>
<p style="text-align: justify;">Terbentuk suatu fungsi kuadrat.</p>
<p style="text-align: justify;">Diketahui bahwa “<em>p</em> is a negative integer and <em>q</em> is a positive integer”.</p>
<p style="text-align: justify;">Hal ini berarti <em>p </em>adalah bilangan bulat negatif dan <em>q</em> adalah bilangan bulat positif.</p>
<p style="text-align: justify;">Kemudian ditanyakan “which of the following could represent the graph of <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/19-1.jpg" alt="19-1" width="129" style="width: 129px;">-plane” yang berarti “mana yang dapat merepresentasikan grafik <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/26-1.jpg" alt="26-1" width="205" style="width: 205px;"> atau bidang koordinat Kartesius”.</p>
<p style="text-align: justify;">Ingat bahwa pada fungsi kuadrat</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/27-1.jpg" alt="27-1" width="153" style="width: 153px;"></p>
<p style="text-align: justify;">Jika <em>a</em> bernilai positif, maka grafik fungsi terbuka ke atas. Sebaliknya, jika <em>a </em>bernilai negatif, maka grafik fungsi terbuka ke bawah.</p>
<p style="text-align: justify;">Kemudian, jika <em>a</em> dan<em> b</em> sama-sama positif atau sama-sama negatif, maka sumbu simetri berada di sebelah kiri sumbu-y. Selain itu, jika dan berbeda tanda, maka sumbu simetri berada di sebelah kanan sumbu-y.</p>
<p style="text-align: justify;">Selanjutnya, titik <em>c</em> mewakili titik potong grafik fungsi dengan sumbu-y, yaitu pada titik (0,<em>c</em>). Jika <em>c </em>bernilai positif, maka grafik fungsi berpotongan dengan sumbu-y positif dan jika <em>c </em>bernilai negatif, maka grafik fungsi berpotongan dengan sumbu-y negatif.</p>
<p style="text-align: justify;">Perhatikan kembali fungsi <em>f</em>, yaitu <span style="font-family: 'Cambria Math','serif';"><br /></span></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/28-1.jpg" alt="28-1" width="202" style="width: 202px;"></p>
<p style="text-align: justify;">Didapat</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/29-1.jpg" alt="29-1" width="85" style="width: 85px;"></p>
<p style="text-align: justify;">Karena a = 1 bernilai positif, maka grafik fungsi<em> f</em> terbuka ke atas.</p>
<p style="text-align: justify;">Kemudian<em>, b = p – q</em>. Karena <em>p</em> adalah bilangan bulat negatif dan <em>q </em>adalah bilangan bulat positif, maka <em>b = p – q</em> adalah bilangan bulat negatif.</p>
<p style="text-align: justify;">Karena <em>a</em> positif, namun <em>b</em> negatif, maka sumbu simetri dari grafik fungsi berada di sebelah kanan sumbu-y.</p>
<p style="text-align: justify;">Selanjutnya, <em>c = -pq</em>. Karena <em>p </em>adalah bilangan bulat negatif dan <em>q </em>adalah bilangan bulat positif, maka <em>c = -pq </em>adalah bilangan bulat positif.</p>
<p style="text-align: justify;">Oleh karena itu, grafik fungsi <em>f</em> berpotongan dengan sumbu-y positif.</p>
<p style="text-align: justify;">Kemudian ingat nilai diskriminan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/30-1.jpg" alt="30-1" width="101" style="width: 101px;"></p>
<p style="text-align: justify;">Jika D > 0, maka grafik memotong sumbu-x di dua titik.</p>
<p style="text-align: justify;">Jika D = 0, maka grafik menyinggung sumbu-x.</p>
<p style="text-align: justify;">Jika D < 0, maka grafik tidak berpotongan dengan sumbu-x.</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/31-1.jpg" alt="31-1" width="708" style="width: 708px;"></p>
<p style="text-align: justify;">Sejauh ini, telah didapat informasi sebagai berikut.</p>
<ol>
<li style="text-align: justify;">Grafik fungsi <em>f</em> terbuka ke atas.</li>
<li style="text-align: justify;">Sumbu simetri dari grafik fungsi berada di sebelah kanan sumbu-y.</li>
<li style="text-align: justify;">Grafik fungsi <em>f </em>berpotongan dengan sumbu-y positif.</li>
<li style="text-align: justify;">Grafik fungsi <em>f</em> bisa berpotongan, bersinggungan, atau tidak berpotongan dengan sumbu-x.</li>
</ol>
<p style="text-align: justify;">Jadi, didapat kemungkinan grafik fungsi <em style="background-color: transparent;">f </em>ketika berpotongan dengan sumbu-x sebagai berikut.</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/32-1.jpg" alt="32-1" width="256" style="width: 256px;"></p>
<p style="text-align: justify;">Ingat bahwa grafik fungsi <em style="background-color: transparent;">f </em>tetap berpotongan dengan sumbu-y positif.</p>
<p style="text-align: justify;">Selanjutnya, didapat kemungkinan grafik fungsi <em style="background-color: transparent;">f </em>ketika bersinggungan dengan sumbu-x sebagai berikut.</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/33-2.jpg" alt="33-2" width="236" style="width: 236px;"></p>
<p style="text-align: justify;">Kemudian, didapat kemungkinan grafik fungsi <em style="background-color: transparent;">f</em> ketika tidak berpotongan dengan sumbu-x sebagai berikut.</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/34-1.jpg" alt="34-1" width="227" style="width: 227px;"></p>
<p style="text-align: justify;"><strong><u>Dari kelima pilihan pada soal, pilihan yang tepat adalah D.</u></strong></p>
<p style="text-align: justify;"><span><strong><u><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM" width="1709" style="width: 1709px;"></u></strong></span></p>
<p style="text-align: justify;"><strong><span>SOAL 6</span></strong></p>
<p style="text-align: justify;">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>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/35-2.jpg" alt="35-2" width="76" style="width: 76px;"></p>
<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 style="text-align: justify;">Printer Y dapat melakukan pekerjaan selama 12 jam, artinya printer Y dapat melakukan pekerjaan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/36-1.jpg" alt="36-1" width="19" style="width: 19px;"> dalam satu jam. Printer Z dapat melakukan pekerjaan selama 16 jam, artinya printer Z dapat melakukan pekerjaan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/37-1.jpg" alt="37-1" width="15" style="width: 15px;"> dalam satu jam. Ketika bersama, printer Y dan Z dapat melakukan pekerjaan sebanyak <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/38-1.jpg" alt="38-1" width="151" style="width: 151px;"> dalam satu jam. Artinya printer Y dan Z membutuhkan <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/39-1.jpg" alt="39-1" width="19" style="width: 19px;"> jam untuk menyelesaikan pekerjaan.</p>
<p style="text-align: justify;">Printer X dapat melakukan pekerjaan selama 8 jam, maka rasio dari waktu yang diperlukan printer X untuk dapat menyelesaikan pekerjaan dibandingkan wakty yang dibutuhkan jika printer Y dan Z bekerja bersama adalah</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/40-1.jpg" alt="40-1" width="121" style="width: 121px;"></p>
<p style="text-align: justify;"><strong><u>Jadi, jawaban yang tepat adalah B.</u></strong></p>
<p style="text-align: justify;"><strong><u><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM" width="1709" style="width: 1709px;"></span></u></strong></p>
<p style="text-align: justify;"><strong><span>SOAL 7</span></strong></p>
<p style="margin-top: 0in; margin-right: 0in; margin-bottom: 0in; text-align: justify; padding-left: 0in;">Each employee of a certain company is in either Department P or Q, and there are more than thrice as many employees in Department P as in Department Q. The average salary is $20,000 for the employees in Department P and $10,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees of the company?</p>
<p style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt; padding-left: 21.3pt;">(1) $17,600</p>
<p style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt; padding-left: 21.3pt;">(2) $16,500</p>
<p style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt; padding-left: 21.3pt;">(3) $18,400</p>
<p style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt; padding-left: 21.3pt;">(4) $15,300</p>
<p style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt; padding-left: 21.3pt;"> </p>
<ol style="list-style-type: upper-alpha;">
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;">(1), (2), and (3) ONLY.</li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;">(1) and (3) ONLY.</li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;">(2) and (4) ONLY.</li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;">(4) ONLY.</li>
<li style="text-align: justify; margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;">(1), (2), (3), and (4).</li>
</ol>
<p style="text-align: justify;"><strong> </strong></p>
<p style="text-align: justify;"><strong>JAWABAN : B</strong></p>
<p style="text-align: justify;"><strong>PEMBAHASAN :</strong></p>
<p style="text-align: justify;">Perhatikan bahwa salah satu strategi menjawab pernyataan semacam ini adalah menemukan kemungkinan nilai paling kecil dan paling besar.</p>
<p style="text-align: justify;">Jelas bahwa gaji rata-rata berada diantara $10,000 dan $20,000 dan semua pilihan jawabannya berada pada interval tersebut.</p>
<p style="text-align: justify;">Diketahui bahwa banyaknya karyawan di departemen P adalah lebih dari 3 kali banyaknya karyawan di Departemen Q. Kemudian, gaji karyawan di Departemen P lebih besar dibandingkan dengan gaji karyawan di departemen Q. Maka batas bawah rata-rata gaji semua karyawan adalah</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/41-1.jpg" alt="41-1" width="372" style="width: 372px;"></p>
<p style="text-align: justify;">Misalkan rerata gaji semua karyawan di perusahaan tersebut adalah<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/42-1.jpg" alt="42-1" width="244" style="width: 244px;"></p>
<p style="text-align: justify;">Jadi, berdasarkan pilihan yang ada, maka kemungkinan rata-rata gaji semua karyawan di perusahaan tersebut adalah $17,600 dan $18,400.</p>
<p style="text-align: justify;"><strong><u>Jadi, jawaban yang tepat adalah B.</u></strong></p>
<p style="text-align: justify;"><strong><u><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM" width="1709" style="width: 1709px;"></span></u></strong></p>
<p style="text-align: justify;"><strong><span>SOAL 8</span></strong></p>
<p style="text-align: justify;"><span>Determine whether the data provided by the statements is sufficient to answer the following question.</span></p>
<p style="text-align: justify;"><span>If the length of a rectangle is 1 greater than the width of the rectangle, what is the perimeter of the rectangle?</span></p>
<p style="margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt; padding-left: 21.3pt; text-align: justify;"><span>(1) The length of the diagonal of the rectangle is 5.</span></p>
<p style="margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt; padding-left: 21.3pt; text-align: justify;"><span>(2) The area of the rectangular region is 12.</span></p>
<p style="margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt; padding-left: 21.3pt; text-align: justify;"><span> </span></p>
<ol style="text-align: justify; list-style-type: upper-alpha;">
<li style="margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> Statement (1) ALONE is sufficient, but statement (2) ALONE is NOT sufficient.</span></li>
<li style="margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> Statement (2) ALONE is sufficient, but statement (1) ALONE is NOT sufficient.</span></li>
<li style="margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.</span></li>
<li style="margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> EACH statement ALONE is sufficient.</span></li>
<li style="margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt;"><span> Statements (1) and (2) TOGETHER are NOT sufficient.</span></li>
</ol>
<p style="margin-top: 0in; margin-right: 0in; margin-bottom: 0.0001pt; padding-left: 21.3pt; text-align: justify;"> </p>
<p style="text-align: justify;"><strong>JAWABAN : </strong></p>
<p style="text-align: justify;"><strong>PEMBAHASAN :</strong></p>
<p style="text-align: justify;">Diketahui bahwa “<span>the length of a rectangle is 1 greater than the width of the rectangle”. Hal ini berarti panjang dari persegi panjang adalah 1 lebihnya dari lebar persegi panjang tersebut. Misalkan panjangnya adalah <em>p</em> </span><span>dan lebarnya adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/1-4.jpg" alt="1-4" width="19" style="width: 19px;"></span><span>maka <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/43-1.jpg" alt="43-1" width="66" style="width: 66px;"></span></p>
<p style="text-align: justify;">Kemudian ditanyakan “<span>what is the perimeter of the rectangle?” yang menanyakan keliling persegi panjang.</span></p>
<p style="text-align: justify;">Perhatikan pernyataan (1).</p>
<p style="text-align: justify;"><span>“The length of the diagonal of the rectangle is 5.”</span></p>
<p style="text-align: justify;"><span>Hal ini berarti panjang diagonal persegi panjang adalah 5.</span></p>
<p style="text-align: justify;"><span>Ingat bahwa panjang diagonal persegi panjang (d), dapat dihitung sebagai berikut</span></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/44-1.jpg" alt="44-1" width="144" style="width: 144px;"></p>
<p style="text-align: justify;">Karena lebar persegi panjang tidak mungkin bernilai negatif, maka <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/45-1.jpg" alt="45-1" width="46" style="width: 46px;"></p>
<p style="text-align: justify;">Jadi, <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/46-1.jpg" alt="46-1" width="148" style="width: 148px;"></p>
<p style="text-align: justify;">Keliling dari persegi panjang tersebut adalah</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/47-1.jpg" alt="47-1" width="95" style="width: 95px;"></p>
<p style="text-align: justify;">Jadi, dari pernyataan (1) dapat diketahui keliling dari persegi panjang.</p>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">Selanjutnya, perhatikan pernyataan (1).</p>
<p style="text-align: justify;"><span>“The area of the rectangular region is 12.”</span></p>
<p style="text-align: justify;"><span>Hal ini berarti luas persegi panjang adalah 12.</span></p>
<p style="text-align: justify;"><span>Ingat bahwa luas persegi panjang (L), dapat dihitung sebagai berikut</span></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/48-1.jpg" alt="48-1" width="147" style="width: 147px;"></p>
<p style="text-align: justify;">Karena lebar persegi panjang tidak mungkin bernilai negatif, maka <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/45-1.jpg" alt="45-1" width="46" style="width: 46px;"></p>
<p style="text-align: justify;">Jadi, <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/46-1.jpg" alt="46-1" width="148" style="width: 148px;"></p>
<p style="text-align: justify;">Keliling dari persegi panjang tersebut adalah</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/47-1.jpg" alt="47-1" width="95" style="width: 95px;"></p>
<p style="text-align: justify;">Jadi, dari pernyataan (2) dapat diketahui keliling dari persegi panjang.</p>
<p style="text-align: justify;">Oleh karena itu, baik pernyataan (1) maupun pernyataan (2) masing-masing cukup untuk menjawab pertanyaan.</p>
<p style="text-align: justify;"><strong><u>Jadi, jawaban yang tepat adalah D.</u></strong></p>
<p style="text-align: justify;"><strong><u><span><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM.png" alt="LS_-_Separator_Semua_Mapel_TPS-Jun-26-2020-06-30-13-30-AM" width="1709" style="width: 1709px;"></span></u></strong></p>
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<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<div class="col-lg-9">
<div class="row">
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Ruangguru</p>
<ul type="none">
<li><a href="https://roboguru.ruangguru.com" target="_blank">Roboguru</a></li>
<li><a href="https://www.ruangguru.com/roboguruplus">Roboguru Plus</a></li>
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<li><a href="https://www.ruangguru.com/for-kids/kursus">Kursus for Kids</a></li>
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<li><a href="https://pengajar.ruangguru.com/">Ruangpengajar</a></li>
<li><a href="https://www.ruangguru.com/privat">Ruangguru Privat</a></li>
<li><a href="https://www.ruangpeduli.org/" target="_blank">Ruangpeduli</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Bantuan & Panduan</p>
<ul type="none">
<li><a href="https://www.ruangguru.com/company-credentials">Company Credentials</a></li>
<li><a href="https://www.ruangguru.com/beasiswa">Beasiswa Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
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<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</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>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</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>
</a>
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<picture>
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</a>
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<picture>
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</a>
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<picture>
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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>