SCAT - School and College Ability Mathematical Reasoning: Number Properties Questions and Answers 1 — Questions and Answers
Question 1: Which of the following numbers is a prime number?
- 51
- 57
- 59 (Correct answer)
- 63
Correct answer: 59
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?
- 15
- 45
- 75
- 90 (Correct answer)
Correct answer: 90
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?
- Both integers are odd. (Correct answer)
- Both integers are even.
- One integer is odd and one is even.
- At least one integer is odd.
Correct answer: Both integers are odd.
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?
- 24
- 36 (Correct answer)
- 45
- 50
Correct answer: 36
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?
- It is also divisible by 6.
- It must be an odd number.
- The sum of its digits is divisible by 9. (Correct answer)
- It ends in a 9 or a 0.
Correct answer: The sum of its digits is divisible by 9.
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.
Question 6: What is the smallest composite number?
- 1
- 2
- 3
- 4 (Correct answer)
Correct answer: 4
A composite number is a whole number that has more than two factors. Let's examine the options: 1 has only one factor (1) and is neither prime nor composite. 2 is a prime number because it has exactly two factors (1 and 2). 3 is a prime number with two factors (1 and 3). 4 is a composite number because it has three factors (1, 2, and 4). Therefore, 4 is the smallest composite number.
SCAT - School and College Ability Mathematical Reasoning: Number Properties Questions and Answers 1
Which of the following numbers is a prime number?