SCAT Mathematical Reasoning: Number Properties 3 — Questions and Answers
Question 1: Which of the following is a prime number?
- 27
- 33
- 41 (Correct answer)
- 51
Correct answer: 41
41 has no factors other than 1 and itself; 27=3³, 33=3×11, and 51=3×17 are all composite.
Question 2: What is the prime factorization of 36?
- 2² × 3² (Correct answer)
- 2 × 18
- 4 × 9
- 2³ × 3
Correct answer: 2² × 3²
36 = 2 × 2 × 3 × 3 = 2² × 3², which uses only prime bases.
Question 3: How many prime numbers are there between 10 and 20?
- 3
- 4 (Correct answer)
- 5
- 2
Correct answer: 4
The primes between 10 and 20 are 11, 13, 17, and 19 — a total of 4 primes.
Question 4: Which of the following is a composite number?
- 2
- 17
- 23
- 25 (Correct answer)
Correct answer: 25
25 = 5 × 5, so it has factors other than 1 and itself, making it composite.
Question 5: What is the smallest prime number greater than 20?
- 21
- 22
- 23 (Correct answer)
- 24
Correct answer: 23
23 is prime because it has no factors other than 1 and 23; 21=3×7, 22=2×11, and 24 are composite.
Question 6: Which number is the product of exactly two distinct prime numbers?
- 9
- 15 (Correct answer)
- 16
- 8
Correct answer: 15
15 = 3 × 5, which is the product of exactly two distinct primes (3 and 5).
Question 7: If p is a prime number greater than 2, which statement must be true?
- p is even
- p is odd (Correct answer)
- p ends in 1 or 7
- p is divisible by 3
Correct answer: p is odd
All prime numbers greater than 2 must be odd, because any even number greater than 2 is divisible by 2.
SCAT Mathematical Reasoning: Number Properties 3
Which of the following is a prime number?