GRE Online Test

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Column A	X is a 3-digit number and Y is a 4- digit number. All the digits of X are greater than 4, and all the digits of Y are less than 5.	Column B
The sum of the digits of X	----------	The sum of the digits of Y

if the columns are equal

if Column B is larger

if Column A is larger

if there is not enough information to decide

2. If n is a positive integer, which one of the following numbers must have a remainder of 3 when
divided by any of the numbers 4, 5, and 6?

12n + 3

120n + 3

80n + 3

90n + 2

24n + 3

Column A	x is a two-digit number. The digits of the number differ by 6, and the squares of the digits differ by 60.	Column B
x	----------	60

if Column B is larger

if there is not enough information to decide

if the columns are equal

if Column A is larger

4. How many 3-digit numbers do not have an even digit or a zero?

125

5. The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

Column A	For any positive integer n, π(n) represents the number of factors of n, inclusive of 1 and itself. a and b are prime numbers	Column B
π(a) + π(b)	----------	π(a × b)

if Column B is larger

if there is not enough information to decide

if the columns are equal

if Column A is larger

Column A	----------	Column B
The first number larger than 300 that is a multiple of both 6 and 8	----------	324

if there is not enough information to decide

if Column A is larger

if the columns are equal

if Column B is larger

Column A	---------	Column B
The number of multiples of 3 between 102 and 729, inclusive	----------	( 729 −102)/3

if Column B is larger

if Column A is larger

if there is not enough information to decide

if the columns are equal

9. Which one of the following is the minimum value of the sum of two integers whose product is 36?

10. The number 3 divides a with a result of b and a remainder of 2. The number 3 divides b with a result of 2 and a remainder of 1. What is the value of a ?

11.

Column A	A palindrome number is a number that reads the same forward or backward. For example, 787 is a palindrome number.	Column B
Smallest palindrome number greater than 233	----------	Smallest palindrome greater than 239

if there is not enough information to decide

if Column B is larger

if Column A is larger

if the columns are equal

12.

Column A	---------	Column B
The number of prime numbers divisible by 2	----------	The number of prime numbers divisible by 3.

if Column B is larger

if Column A is larger

if the columns are equal

if there is not enough information to decide

13.

Column A	----------	Column B
Least common multiple of the two positive integers m and n	----------	mn

if there is not enough information to decide

if Column A is larger

if the columns are equal

if Column B is larger

14. The number 3072 is divisible by both 6 and 8. Which one of the following is the first integer larger
than 3072 that is also divisible by both 6 and 8?

3096

3078

3090

3084

3086

15.

Column A	a and b are the digits of a twodigit number ab, and b = a + 3.	Column B
The positive two-digit number ab	----------	The positive two-digit number ba

if there is not enough information to decide

if Column A is larger

if Column B is larger

if the columns are equal

16. Which one of the following equals the product of the smallest prime number greater than 21 and the
largest prime number less than 16?

13 ⋅ 29

13 ⋅ 16

13 ⋅ 23

15 ⋅ 23

16 ⋅ 21

17. The function Δ(m) is defined for all positive integers m as the product of m + 4, m + 5, and m + 6. If n
is a positive integer, then Δ(n) must be divisible by which one of the following numbers?

18. What is the remainder when 3^7 is divided by 8?

19.

Column A	a and b are the digits of a twodigit number ab, and a = b + 3.	Column B
The two-digit number ab	----------	40

if Column A is larger

if the columns are equal

if Column B is larger

if there is not enough information to decide

20. 2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple
of 13, then ab =

21. a, b, c, d, and e are five consecutive integers in increasing order of size. Which one of the following
expressions is not odd?

ab + c

ac + d

ac + e

a + b + c

ab + d

22.

Column A	The digits of a two-digit number x differ by 4.	Column B
The positive difference between the squares of the digits of x	----------	15

if the columns are equal

if there is not enough information to decide

if Column A is larger

if Column B is larger

23. What is the remainder when 7^2 ⋅ 8^2 is divided by 6?

24.

Column A	---------	Column B
The least number divisible by 2, 3, 4, 5, and 6	----------	The least number that is a multiple of 2, 3, 4, 5 and 6

if Column B is larger

if there is not enough information to decide

if Column A is larger

if the columns are equal

25. Which one of the following choices does not equal any of the other choices?
(A)
(B)
(C)
(D)
(E)

5.43 + 4.63 – 3.24 – 2.32

5.43 + 4.73 – 3.14 – 2.22

5.43 + 4.73 – 3.24 – 2.42

5.53 + 4.53 – 3.34 – 2.22

5.53 + 4.73 – 3.34 – 2.42

26. If A*B is the greatest common factor of A and B, A$B is defined as the least common multiple of A and B, and A∩B is defined as equal to (A*B) $ (A$B), then what is the value of 12∩15?

27. 1. If x is divisible by both 3 and 4, then the number x must be a multiple of which one of the following?

28. Which one of the following is divisible by both 2 and 3?

1005

1406

1351

1296

1414

29.

Column A	For any positive integer n, n! denotes the product of all the integers from 1 through n.	Column B
1!(10 – 1)!	----------	2!(10 – 2)!

if there is not enough information to decide

if Column B is larger

if Column A is larger

if the columns are equal

30. The remainder when m + n is divided by 12 is 8, and the remainder when m – n is divided by 12 is 6.
If m > n, then what is the remainder when mn divided by 6?

31.

Column A	m and n are two positive integers. 5m + 7n = 46.	Column B
m	----------	n

if there is not enough information to decide

if Column B is larger

if the columns are equal

if Column A is larger

32. If the least common multiple of m and n is 24, then what is the first integer larger than 3070 that is
divisible by both m and n?

3072

3094

3088

3078

3084

33. If each of the three nonzero numbers a, b, and c is divisible by 3, then abc must be divisible by which
one of the following the numbers?

159

121

34.

Column A	The sum of the positive integers from 1 through n can be calculated by the formula n(n +1)/2	Column B
The sum of the multiples of 6 between 0 and 100	----------	The sum of the multiples of 8 between 0 and 100

if there is not enough information to decide

if Column A is larger

if Column B is larger

if the columns are equal

35.

Column A	The positive integers m and n leave a remainder of 2 and 3, respectively, when divided by 6. m > n.	Column B
The remainder when m + n is divided by 6	----------	The remainder when m – n is divided by 6

if there is not enough information to decide

if the columns are equal

if Column B is larger

if Column A is larger

36. How many positive integers less than 500 can be formed using the numbers 1, 2, 3, and 5 for the
digits?

37. A set has exactly five consecutive positive integers starting with 1. What is the percentage decrease in
the average of the numbers when the greatest one of the numbers is removed from the set?

15.2

16.66

12.5

8.5

38. Which one of the following equals the product of exactly two prime numbers?

14 ⋅ 23

11 ⋅ 6

13 ⋅ 23

13 ⋅ 22

17 ⋅ 21

39.

Column A	x < 0	Column B
The last digit in the number (252)^56	----------	The last digit in the number (152)^56

if Column B is larger

if Column A is larger

if there is not enough information to decide

if the columns are equal

40. The remainder when the positive integer m is divided by 7 is x. The remainder when m is divided by
14 is x + 7. Which one of the following could m equal?

100

41. If a and b are positive integers, and x = 2 ⋅ 3 ⋅ 7 ⋅ a, and y = 2 ⋅ 2 ⋅ 8 ⋅ b, and the values of both x and y
lie between 120 and 130 (not including the two), then a – b =

-1

-2

42.

Column A	a * b =( a/b)− (b/a), m > n > 0	Column B
	----------	0

if Column A is larger

if the columns are equal

if there is not enough information to decide

if Column B is larger

43.

Column A	p and q are two positive integers and p/q = 7.15	Column B
q	----------	15

if Column A is larger

if the columns are equal

if Column B is larger

if there is not enough information to decide

44. Each of the two positive integers a and b ends with the digit 2. With which one of the following
numbers does a – b end?

45.

Column A	A function * is defined for all even positive integers n as the number of even factors of n other than n itself.	Column B
*(48)	----------	[*(122)

if Column A is larger

if there is not enough information to decide

if the columns are equal

if Column B is larger

46. a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five
numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of
the following numbers was deleted?

47. Define x* by the equation x* = π/x. Then ((–π)*)* =

1/π

–1/2

–π

–1/π

48. The last digit of the positive even number n equals the last digit of n2. Which one of the following
could be n ?

49.

Column A	a, b, and c are consecutive integers in increasing order of size.	Column B
a/5 – b/6	----------	b/5 – c/6

if Column B is larger

if the columns are equal

if there is not enough information to decide

if Column A is larger

50. What is the maximum value of m such that 7m divides into 14! evenly?

51. How many positive five-digit numbers can be formed with the digits 0, 3, and 5?

162

243

108

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