GRE Arithmetic and Number Properties 3 — Questions and Answers
Question 1: What is the value of (-3)^4 - (-2)^3?
- 73
- 89 (Correct answer)
- 81
- -73
Correct answer: 89
(-3)^4 = 81 and (-2)^3 = -8, so 81 - (-8) = 89.
Question 2: If x and y are positive integers and xy = 36, what is the greatest possible value of x + y?
- 12
- 13
- 20
- 37 (Correct answer)
Correct answer: 37
The sum is largest when the factors are most spread apart: 1·36 gives 1 + 36 = 37.
Question 3: What is 0.25 expressed as a fraction in lowest terms?
- 1/5
- 1/4 (Correct answer)
- 2/5
- 1/8
Correct answer: 1/4
0.25 = 25/100 = 1/4.
Question 4: If 3^x = 81, what is the value of x?
- 3
- 4 (Correct answer)
- 9
- 27
Correct answer: 4
81 = 3^4, so x = 4.
Question 5: Which of the following numbers is divisible by 9?
- 123
- 234 (Correct answer)
- 345
- 456
Correct answer: 234
The digits of 234 sum to 9, which is divisible by 9.
Question 6: The product of two consecutive even integers is 168. What is the smaller integer?
- 10
- 12 (Correct answer)
- 14
- 16
Correct answer: 12
12 × 14 = 168, so the smaller integer is 12.
Question 7: What is the sum of the first 10 positive even integers?
- 90
- 100
- 110 (Correct answer)
- 120
Correct answer: 110
The sum is 2(1+2+…+10) = 2·55 = 110.
GRE Arithmetic and Number Properties 3
What is the value of (-3)^4 - (-2)^3?