GRE Number Theory and Integer Properties

Question 1

What is the greatest common divisor (GCD) of 252 and 198?
(A) 6
(B) 9
(C) 18
(D) 36

Accepted Answer

18

Answer

6

Answer

9

Answer

36

Question 2

What is the least common multiple (LCM) of 12, 18, and 24?
(A) 36
(B) 48
(C) 72
(D) 144

Accepted Answer

72

Answer

36

Answer

48

Answer

144

Question 3

How many prime numbers are between 50 and 70?
(A) 4
(B) 5
(C) 6
(D) 7

Accepted Answer

5

Answer

4

Answer

6

Answer

7

Question 4

If n is an integer, which of the following must be even?
(A) n² + 1
(B) n(n+1)
(C) 2n + 1
(D) n² − n + 1

Accepted Answer

n(n+1)

Answer

n² + 1

Answer

2n + 1

Answer

n² − n + 1

Question 5

What is the remainder when 7^100 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 4

Accepted Answer

1

Answer

0

Answer

2

Answer

4

Question 6

A positive integer n has exactly 6 factors. Which of the following could be n?
(A) 16
(B) 18
(C) 25
(D) 30

Accepted Answer

18

Answer

16

Answer

25

Answer

30

Question 7

If the sum of three consecutive odd integers is 99, what is the largest of the three integers?
(A) 31
(B) 33
(C) 35
(D) 37

Accepted Answer

35

Answer

31

Answer

33

Answer

37

Question 8

What is the units digit of 3^47?
(A) 1
(B) 3
(C) 7
(D) 9

Accepted Answer

3

Answer

1

Answer

7

Answer

9

Question 9

How many integers between 1 and 100 (inclusive) are divisible by either 3 or 5?
(A) 47
(B) 50
(C) 53
(D) 55

Accepted Answer

47

Answer

50

Answer

53

Answer

55

Question 10

If p and q are prime numbers and p × q = 77, what is the value of p + q?
(A) 11
(B) 18
(C) 22
(D) 78

Accepted Answer

18

Answer

11

Answer

22

Answer

78