SCAT - School and College Ability Mathematical Reasoning: Number Properties Questions and Answers

Question 1

Which of the following numbers is a prime number?

Accepted Answer

59

Answer

A prime number is a whole number greater than 1 that has only two factors: 1 and itself. Let's check the factors for each option: 51 is divisible by 3 (5+1=6), so it's composite. 57 is divisible by 3 (5+7=12), so it's composite. 63 is divisible by 3 (6+3=9) and 7, so it's composite. 59 is only divisible by 1 and 59, making it a prime number.

Question 2

A certain number is a multiple of 3, a multiple of 5, and is even. Which of the following could be the number?

Accepted Answer

90

Answer

The number must satisfy three conditions. 'Even' means it is divisible by 2. 'Multiple of 3' means the sum of its digits is divisible by 3. 'Multiple of 5' means it ends in 0 or 5. Let's check the options: 15 is a multiple of 3 and 5 but not even. 45 is a multiple of 3 and 5 but not even. 75 is a multiple of 3 and 5 but not even. 90 is even, a multiple of 3 (9+0=9), and a multiple of 5 (ends in 0). Therefore, 90 is the correct answer.

Question 3

If the product of two integers is an odd number, which of the following must be true?

Accepted Answer

Both integers are odd.

Answer

The product of two integers is odd only if both integers are odd. If an even number is multiplied by any other integer (even or odd), the result is always even. For example, Odd x Odd = Odd (3 x 5 = 15). Even x Odd = Even (2 x 5 = 10). Even x Even = Even (2 x 4 = 8). Therefore, both integers must be odd.

Question 4

Which of the following numbers has the most factors?

Accepted Answer

36

Answer

Let's list the factors for each number: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 (8 factors). Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 (9 factors). Factors of 45 are 1, 3, 5, 9, 15, 45 (6 factors). Factors of 50 are 1, 2, 5, 10, 25, 50 (6 factors). The number 36 has the most factors (nine).

Question 5

A number is divisible by 9. Which of the following statements about this number must be true?

Accepted Answer

The sum of its digits is divisible by 9.

Answer

The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. Let's consider the other options: 18 is divisible by 9 but also by 6, but 27 is divisible by 9 and not by 6, so A is not always true. 18 is divisible by 9 and is even, so B is not true. 27 is divisible by 9 but does not end in 9 or 0, so D is not true. The only statement that is always true is C.

(SCAT) School and College Ability Test Practice Test

(SCAT) School and College Ability Test Practice Test

SCAT - School and College Ability Mathematical Reasoning: Number Properties Questions and Answers