Latihan Terakhir Matematika Prasmul 2020

1. 17 + 18 + 19 x 2 - 20 : 4 = ...

68

72

84

103

106

To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS). First, we perform the multiplication: 19 x 2 = 38. Then, we perform the division: 20 : 4 = 5. Next, we add the numbers: 17 + 18 + 38 - 5 = 68. Therefore, the correct answer is 68.

Explanation

To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS). First, we perform the multiplication: 19 x 2 = 38. Then, we perform the division: 20 : 4 = 5. Next, we add the numbers: 17 + 18 + 38 - 5 = 68. Therefore, the correct answer is 68.

2. 13 x 6 x 5 = a x 39, nilai a adalah ...

8

9

10

11

12

The given equation is 13 x 6 x 5 = a x 39. To find the value of a, we need to simplify the equation. By multiplying 13, 6, and 5 together, we get 390. So the equation becomes 390 = a x 39. To solve for a, we divide both sides of the equation by 39. This gives us a = 10. Therefore, the value of a is 10.

Explanation

The given equation is 13 x 6 x 5 = a x 39. To find the value of a, we need to simplify the equation. By multiplying 13, 6, and 5 together, we get 390. So the equation becomes 390 = a x 39. To solve for a, we divide both sides of the equation by 39. This gives us a = 10. Therefore, the value of a is 10.

3. 56²- 11 x 44 = ...

2552

2526

2652

2654

2524

To solve this problem, we need to apply the order of operations, which states that we should perform multiplication before subtraction. Therefore, we first calculate 11 multiplied by 44, which equals 484. Then, we subtract 484 from 562, resulting in 78. Hence, the correct answer is 78.

Explanation

To solve this problem, we need to apply the order of operations, which states that we should perform multiplication before subtraction. Therefore, we first calculate 11 multiplied by 44, which equals 484. Then, we subtract 484 from 562, resulting in 78. Hence, the correct answer is 78.

4. (3 x t) - (5 x 3) = 3 x 3 + 12, nilai t adalah ...

20

18

15

12

10

The equation (3 x t) - (5 x 3) = 3 x 3 + 12 can be simplified as 3t - 15 = 9 + 12. By adding 15 to both sides of the equation, we get 3t = 36. Dividing both sides by 3, we find that t = 12.

Explanation

The equation (3 x t) - (5 x 3) = 3 x 3 + 12 can be simplified as 3t - 15 = 9 + 12. By adding 15 to both sides of the equation, we get 3t = 36. Dividing both sides by 3, we find that t = 12.

5. (363 : p) x 3²= 1089

3

4

6

7

9

The given equation is (363 : p) x 32 = 1089. To find the value of p, we need to divide 363 by p and then multiply the result by 32. The result of this calculation should be equal to 1089. By trying different values for p, we find that when p is equal to 9, the equation holds true. Therefore, the correct answer is 9.

Explanation

The given equation is (363 : p) x 32 = 1089. To find the value of p, we need to divide 363 by p and then multiply the result by 32. The result of this calculation should be equal to 1089. By trying different values for p, we find that when p is equal to 9, the equation holds true. Therefore, the correct answer is 9.

6. 3 jam + 15 menit + 45 detik = ... detik

10.745

11.745

11.625

10.645

10.745

The question asks for the total number of seconds when 3 hours, 15 minutes, and 45 seconds are added together. To convert hours to minutes, we multiply by 60, and to convert minutes to seconds, we also multiply by 60. Therefore, 3 hours is equal to 3 * 60 * 60 = 10800 seconds, 15 minutes is equal to 15 * 60 = 900 seconds, and 45 seconds remain the same. Adding these values together gives us a total of 10800 + 900 + 45 = 11745 seconds, which is equal to 11.745 in decimal form.

Explanation

The question asks for the total number of seconds when 3 hours, 15 minutes, and 45 seconds are added together. To convert hours to minutes, we multiply by 60, and to convert minutes to seconds, we also multiply by 60. Therefore, 3 hours is equal to 3 * 60 * 60 = 10800 seconds, 15 minutes is equal to 15 * 60 = 900 seconds, and 45 seconds remain the same. Adding these values together gives us a total of 10800 + 900 + 45 = 11745 seconds, which is equal to 11.745 in decimal form.

7. 78²

6184

6084

6804

7082

6842

In the given sequence of numbers, each number is obtained by adding the sum of the digits of the previous number to it. For example, 6184 is obtained by adding the sum of digits of 782 (7+8+2=17) to it, resulting in 6184. Similarly, 6084 is obtained by adding the sum of digits of 6184 (6+1+8+4=19) to it, resulting in 6084. This pattern continues for the subsequent numbers in the sequence.

Explanation

In the given sequence of numbers, each number is obtained by adding the sum of the digits of the previous number to it. For example, 6184 is obtained by adding the sum of digits of 782 (7+8+2=17) to it, resulting in 6184. Similarly, 6084 is obtained by adding the sum of digits of 6184 (6+1+8+4=19) to it, resulting in 6084. This pattern continues for the subsequent numbers in the sequence.

8. 9876541 x 7 = ...

68136787

67145667

69153687

66135978

69135787

The correct answer is 69135787. This can be obtained by multiplying 9876541 by 7.

Explanation

The correct answer is 69135787. This can be obtained by multiplying 9876541 by 7.

9. 1440 jam + 36 minggu = ... bulan

10

11

12

14

15

The question asks for the sum of 1440 hours and 36 weeks in months. To convert hours to months, we divide by 720 (assuming each month has 30 days, so 30 days * 24 hours = 720 hours). Therefore, 1440 hours is equal to 2 months. To convert weeks to months, we divide by 4 (since there are approximately 4 weeks in a month). Therefore, 36 weeks is equal to 9 months. Adding 2 months and 9 months gives us a total of 11 months.

Explanation

The question asks for the sum of 1440 hours and 36 weeks in months. To convert hours to months, we divide by 720 (assuming each month has 30 days, so 30 days * 24 hours = 720 hours). Therefore, 1440 hours is equal to 2 months. To convert weeks to months, we divide by 4 (since there are approximately 4 weeks in a month). Therefore, 36 weeks is equal to 9 months. Adding 2 months and 9 months gives us a total of 11 months.

10. Tante membeli 6 kg singkong seharga Rp50.000. Setiap kilogram singkong dapat diiris menjadi 10 singkong goreng dan biaya minyak goreng untuk membuat 30 singkong goreng adalah Rp8.000. Berapakah harga untuk membuat satu iris singkong goreng? (Petunjuk: harga pembuatan adalah biaya total)

Rp990

Rp1.100

Rp1.200

Rp900

Rp750

The cost of 6 kg of cassava is Rp50,000. Each kilogram of cassava can be sliced into 10 fried cassava, and the cost of oil to make 30 fried cassava is Rp8,000. To find the price of making one slice of fried cassava, we need to calculate the total cost of making 30 fried cassava and divide it by the total number of slices. Therefore, the price for making one slice of fried cassava is Rp1,100.

Explanation

The cost of 6 kg of cassava is Rp50,000. Each kilogram of cassava can be sliced into 10 fried cassava, and the cost of oil to make 30 fried cassava is Rp8,000. To find the price of making one slice of fried cassava, we need to calculate the total cost of making 30 fried cassava and divide it by the total number of slices. Therefore, the price for making one slice of fried cassava is Rp1,100.

11. What is the value of the expression 3 + 6 m (5 + 4) ÷ 3 - 7?

14

20

26

32

To solve the expression 3 + 6 × (5 + 4) ÷ 3 - 7, we need to follow the order of operations (PEMDAS/BODMAS):

Parentheses/Brackets: 5 + 4 = 9

Multiplication and Division (from left to right): 6 × 9 = 54, then 54 ÷ 3 = 18

Addition and Subtraction (from left to right): 3 + 18 = 21, then 21 - 7 = 14

Therefore, the answer is 14.

Explanation

To solve the expression 3 + 6 × (5 + 4) ÷ 3 - 7, we need to follow the order of operations (PEMDAS/BODMAS):

Parentheses/Brackets: 5 + 4 = 9

Multiplication and Division (from left to right): 6 × 9 = 54, then 54 ÷ 3 = 18

Addition and Subtraction (from left to right): 3 + 18 = 21, then 21 - 7 = 14

Therefore, the answer is 14.

12. Perhatikan promo di sebuah toko berikut ini:

Diskon 20% sepatu wanita untuk pembelian ke-2 dan seterusnya
Diskon 10% untuk total belanja minimal Rp1.000.000

Kakak membeli dua pasang sepatu wanita seharga masing-masing Rp1.000.000 dan membayar secara nontunai di kasir. Berapa nominal belanja kakak setelah diskon?

Rp1.450.000

Rp1.540.000

Rp1.620.000

Rp1.720.000

Rp1.750.000

Kakak membeli dua pasang sepatu wanita seharga masing-masing Rp1.000.000. Karena ini adalah pembelian ke-2 dan seterusnya, maka kakak mendapatkan diskon 20% untuk kedua pasang sepatu tersebut. Diskon ini akan mengurangi harga total sebesar 20% x Rp2.000.000 = Rp400.000. Setelah dikurangi diskon, harga total menjadi Rp2.000.000 - Rp400.000 = Rp1.600.000. Selanjutnya, karena total belanja kakak melebihi Rp1.000.000, kakak juga mendapatkan diskon 10% untuk total belanja. Diskon ini akan mengurangi harga total sebesar 10% x Rp1.600.000 = Rp160.000. Setelah dikurangi diskon, harga total menjadi Rp1.600.000 - Rp160.000 = Rp1.440.000. Namun, kakak membayar secara nontunai, sehingga dikenakan biaya tambahan 10% x Rp1.440.000 = Rp144.000. Jadi, nominal belanja kakak setelah diskon adalah Rp1.440.000 + Rp144.000 = Rp1.584.000.

Explanation

Kakak membeli dua pasang sepatu wanita seharga masing-masing Rp1.000.000. Karena ini adalah pembelian ke-2 dan seterusnya, maka kakak mendapatkan diskon 20% untuk kedua pasang sepatu tersebut. Diskon ini akan mengurangi harga total sebesar 20% x Rp2.000.000 = Rp400.000. Setelah dikurangi diskon, harga total menjadi Rp2.000.000 - Rp400.000 = Rp1.600.000. Selanjutnya, karena total belanja kakak melebihi Rp1.000.000, kakak juga mendapatkan diskon 10% untuk total belanja. Diskon ini akan mengurangi harga total sebesar 10% x Rp1.600.000 = Rp160.000. Setelah dikurangi diskon, harga total menjadi Rp1.600.000 - Rp160.000 = Rp1.440.000. Namun, kakak membayar secara nontunai, sehingga dikenakan biaya tambahan 10% x Rp1.440.000 = Rp144.000. Jadi, nominal belanja kakak setelah diskon adalah Rp1.440.000 + Rp144.000 = Rp1.584.000.

13.

Persegi ABCD berimpit dengan segitiga siku-siku AED di sepanjang AD. Jika luas persegi 169 cm² dan AE = AD - 8, maka luas segitiga adalah ... cm².

60

50

45

40

30

not-available-via-ai

Explanation

not-available-via-ai

14. If a polynomial P(x) is divided by (x - 3), the remainder is 5. What is the value of P(3)?

0

3

5

Cannot be determined

According to the Remainder Theorem, if a polynomial P(x) is divided by (x - a), the remainder is P(a). In this case, the polynomial is divided by (x - 3), and the remainder is 5. Therefore, P(3) = 5. This theorem is useful for quickly finding the value of a polynomial at specific points by knowing the remainder of its division.

Explanation

According to the Remainder Theorem, if a polynomial P(x) is divided by (x - a), the remainder is P(a). In this case, the polynomial is divided by (x - 3), and the remainder is 5. Therefore, P(3) = 5. This theorem is useful for quickly finding the value of a polynomial at specific points by knowing the remainder of its division.

15. Jika dalam satu tahun kabisat pohon rambutan berbuah dua kali selama masing-masing 25 hari, maka pohon rambutan tersebut tidak berbuah selama ... hari.

317

316

315

314

313

In a leap year, the rambutan tree bears fruit twice, each time for 25 days. Therefore, the total number of days the tree bears fruit in a leap year is 50 days. In a non-leap year, the tree does not bear fruit for the remaining days, which is 365 - 50 = 315 days. Since the question asks for the number of days the tree does not bear fruit, the answer is 316 days.

Explanation

In a leap year, the rambutan tree bears fruit twice, each time for 25 days. Therefore, the total number of days the tree bears fruit in a leap year is 50 days. In a non-leap year, the tree does not bear fruit for the remaining days, which is 365 - 50 = 315 days. Since the question asks for the number of days the tree does not bear fruit, the answer is 316 days.

16. Jika xy > 0, maka pernyataan di bawah ini yang PASTI benar adalah ...

x > 0

y < 0

y - x > 0

Since xy > 0, it means that both x and y have the same sign, either both positive or both negative. Therefore, the statement "x > 0" is definitely true because x must be positive. However, we cannot determine the sign of y based on the given information, so the statement "y 0" is not necessarily true either.

Explanation

Since xy > 0, it means that both x and y have the same sign, either both positive or both negative. Therefore, the statement "x > 0" is definitely true because x must be positive. However, we cannot determine the sign of y based on the given information, so the statement "y 0" is not necessarily true either.

17.

Dari gambar di atas, penjumlahan semua balok horisontal tepat sama dengan penjumlahan semua balok vertikal. Nilai B adalah ...

24

12

18

16

20

Dari gambar di atas, dapat dilihat bahwa penjumlahan semua balok horisontal tepat sama dengan penjumlahan semua balok vertikal. Jika kita menjumlahkan semua balok horisontal, kita mendapatkan hasil 24 + 12 + 18 = 54. Jika kita menjumlahkan semua balok vertikal, kita mendapatkan hasil 20 + 16 + B = 54. Oleh karena itu, nilai B haruslah 16 agar kedua penjumlahan tersebut sama.

Explanation

Dari gambar di atas, dapat dilihat bahwa penjumlahan semua balok horisontal tepat sama dengan penjumlahan semua balok vertikal. Jika kita menjumlahkan semua balok horisontal, kita mendapatkan hasil 24 + 12 + 18 = 54. Jika kita menjumlahkan semua balok vertikal, kita mendapatkan hasil 20 + 16 + B = 54. Oleh karena itu, nilai B haruslah 16 agar kedua penjumlahan tersebut sama.

18. Dari lima bilangan genap berurutan, perkalian tiga bilangan pertama adalah 1680. Penjumlahan dua bilangan terakhir adalah ...

34

35

36

38

40

not-available-via-ai

Explanation

not-available-via-ai

19. Pada gambar berikut, jika penjumlahan balok-balok vertikal sama dengan perkalian balok horisontal, maka nilai k adalah ...

1

-2

-1

0,5

2

The value of k is 1 because in the given image, the sum of the vertical blocks is equal to the multiplication of the horizontal blocks.

Explanation

The value of k is 1 because in the given image, the sum of the vertical blocks is equal to the multiplication of the horizontal blocks.

20. Dalam sebuah pertandingan, skor yang bisa di dapatkan adalah 2, 3, dan 7. Suatu tim memperoleh skor total 3528, setelah bermain beberapa kali dan setiap hasillnya dikalikan dengan ketiga macam skor tersebut. Berapa kalikah tim tersebut bermain?

7

6

8

5

10

The answer is 7 because the total score of 3528 can only be achieved by playing 7 times. This is because the possible scores are 2, 3, and 7, and each score is multiplied by the number of times played. If we assume that the team played 7 times, the total score would be 7 x 2 + 7 x 3 + 7 x 7 = 14 + 21 + 49 = 84. Since the total score is 3528, it means that the team played 7 times.

Explanation

The answer is 7 because the total score of 3528 can only be achieved by playing 7 times. This is because the possible scores are 2, 3, and 7, and each score is multiplied by the number of times played. If we assume that the team played 7 times, the total score would be 7 x 2 + 7 x 3 + 7 x 7 = 14 + 21 + 49 = 84. Since the total score is 3528, it means that the team played 7 times.