GMAT Quantitative: Number Properties 3 — Questions and Answers
Question 1: What is the greatest common divisor (GCD) of 48 and 60?
- 6
- 8
- 12 (Correct answer)
- 24
Correct answer: 12
48 = 2^4*3 and 60 = 2^2*3*5, so the GCD is 2^2*3 = 12.
Question 2: What is the least common multiple (LCM) of 9 and 12?
- 27
- 36 (Correct answer)
- 72
- 108
Correct answer: 36
9 = 3^2 and 12 = 2^2*3, so the LCM is 2^2*3^2 = 36.
Question 3: If an integer is divisible by both 4 and 9, it must also be divisible by:
- 13
- 18
- 36 (Correct answer)
- 72
Correct answer: 36
Since 4 and 9 are coprime, divisibility by both forces divisibility by 4*9 = 36.
Question 4: Which number is NOT divisible by 3?
- 123
- 234
- 451 (Correct answer)
- 612
Correct answer: 451
The digits of 451 sum to 10, which is not divisible by 3.
Question 5: If p and q are both prime numbers greater than 2, then p + q is always:
- Prime
- Odd
- Even (Correct answer)
- Divisible by 3
Correct answer: Even
Primes greater than 2 are odd, and the sum of two odd numbers is even.
Question 6: What is the smallest positive integer with exactly 3 divisors?
- 4 (Correct answer)
- 6
- 8
- 9
Correct answer: 4
A number has exactly 3 divisors only when it is the square of a prime, and the smallest is 2^2 = 4.
Question 7: What is the remainder when 5^4 is divided by 7?
- 1
- 2
- 4 (Correct answer)
- 6
Correct answer: 4
5^4 = 625, and 7*89 = 623, so the remainder is 625 - 623 = 2.
GMAT Quantitative: Number Properties 3
What is the greatest common divisor (GCD) of 48 and 60?