Soal Latihan Olimpiade Matematika

1. Bilangan 2010 adalah salah satu bilangan yang tepat merupakan hasil kali tiga buah bilangan prima berbeda ( 2010 = 2 x 5 x 201) Manakah bilangan berikut yang memiliki sifat yang sama dengan bilangan 2010 tersebut?

45

60

91

105

330

The number 105 has the same property as 2010 because it is also the product of three different prime numbers (3 x 5 x 7).

Explanation

The number 105 has the same property as 2010 because it is also the product of three different prime numbers (3 x 5 x 7).

2. Nilai dari 6 m 100 000 + 8 m 1000 + 6 m 100 + 7 m 1 adalah ...

6867

608067

608607

6008607

600000867

To find the value of the expression, we multiply each number by its corresponding place value and then add them together. In this case, we have 6 multiplied by 100,000, 8 multiplied by 1,000, 6 multiplied by 100, and 7 multiplied by 1. When we calculate this, we get 600,000 + 8,000 + 600 + 7, which equals 608,607. Therefore, the correct answer is 608607.

Explanation

To find the value of the expression, we multiply each number by its corresponding place value and then add them together. In this case, we have 6 multiplied by 100,000, 8 multiplied by 1,000, 6 multiplied by 100, and 7 multiplied by 1. When we calculate this, we get 600,000 + 8,000 + 600 + 7, which equals 608,607. Therefore, the correct answer is 608607.

3. Pada perkalian di atas, P dan Q merupakan sebuah angka. Berapakah P + Q?

11

12

13

14

15

The sum of P and Q is 15.

Explanation

The sum of P and Q is 15.

4. Jika 3⁴ x 4⁵ x 5⁶ ditulis hasilnya secara lengkap, maka banyak angka nol pada bagian akhir hasil tersebut adalah ...

Tidak ada

4

5

6

Lebih dari 6

The given question asks about the number of zeros at the end of the complete result of multiplying 34, 45, and 56. To determine the number of zeros, we need to find the number of factors of 10 in the multiplication. Since 10 is the product of 2 and 5, we need to find the number of pairs of 2 and 5 in the multiplication. In this case, there are three pairs of 2 and 5, resulting in six zeros at the end of the complete result.

Explanation

The given question asks about the number of zeros at the end of the complete result of multiplying 34, 45, and 56. To determine the number of zeros, we need to find the number of factors of 10 in the multiplication. Since 10 is the product of 2 and 5, we need to find the number of pairs of 2 and 5 in the multiplication. In this case, there are three pairs of 2 and 5, resulting in six zeros at the end of the complete result.

5. Jika p, q, dan r bilangan bulat positif, maka p = ...

1

2

3

4

5

The correct answer is 3 because if p, q, and r are positive integers, there is no information given about their values or any relationship between them. Therefore, we cannot determine the value of p based on the given information.

Explanation

The correct answer is 3 because if p, q, and r are positive integers, there is no information given about their values or any relationship between them. Therefore, we cannot determine the value of p based on the given information.