GMAT Quantitative: Number Properties 5 — Questions and Answers
Question 1: If a number leaves a remainder of 3 when divided by 5, what is its remainder when divided by 5 after adding 4?
- 0
- 1
- 2 (Correct answer)
- 3
Correct answer: 2
Adding 4 to a remainder of 3 gives 7, and 7 mod 5 = 2.
Question 2: Which of the following must be divisible by 6?
- Product of any two integers
- Product of three consecutive integers (Correct answer)
- Sum of two even integers
- Any even integer
Correct answer: Product of three consecutive integers
Three consecutive integers always include a multiple of 2 and a multiple of 3, so their product is divisible by 6.
Question 3: What is the units digit of 9^10?
- 1 (Correct answer)
- 3
- 7
- 9
Correct answer: 1
Powers of 9 alternate 9,1; even exponents end in 1, so 9^10 ends in 1.
Question 4: If the product of two integers is negative, then:
- Both are positive
- Both are negative
- One is positive and one negative (Correct answer)
- Both are zero
Correct answer: One is positive and one negative
A negative product results only when exactly one factor is negative.
Question 5: How many factors of 2 are in the prime factorization of 24?
- 1
- 2
- 3 (Correct answer)
- 4
Correct answer: 3
Since 24 = 2^3 * 3, there are three factors of 2.
Question 6: Which value of n makes 3n + 1 divisible by 4?
- n = 1 (Correct answer)
- n = 2
- n = 3
- n = 4
Correct answer: n = 1
When n = 1, 3(1) + 1 = 4, which is divisible by 4.
Question 7: What is the remainder when 100 is divided by 9?
- 0
- 1 (Correct answer)
- 2
- 4
Correct answer: 1
Since 9 * 11 = 99, the remainder is 100 - 99 = 1.
GMAT Quantitative: Number Properties 5
If a number leaves a remainder of 3 when divided by 5, what is its remainder when divided by 5 after adding 4?