GRE Practice Tests

GRE Problem Solving (Multiple Answer) Practice Test 4

Student working through a multi-step GRE Problem Solving math question on a practice test.
Written by Farrukh Mehmood

If x is an integer such that x^3 is between -30 and 30 (exclusive of -30 and 30), which of the following could be values of x? Indicate **all** such values.

Please select 6 correct answers

Consider integers whose cubes fall in the range (-30, 30). Test -3, -2, -1, 0, 1, 2, 3.
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Correct! Wrong!

Select all possible integer values for x.

Which of the following numbers have exactly 3 positive divisors? Indicate **all** such values.

Please select 3 correct answers

Only squares of prime numbers have exactly 3 positive divisors (1, the prime, and its square).
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Correct! Wrong!

Select all numbers with exactly 3 positive divisors.

If x and y are integers and x+y=5, which of the following could be the value of x-y? Indicate **all** such values.

Please select 3 correct answers

Consider pairs of integers (x,y) that sum to 5 (e.g., x=3, y=2; x=4, y=1; x=6, y=-1). Calculate x-y for each pair. Notice that x-y will have the same parity (odd/even) as x+y if x and y are integers.
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Select all possible values for x-y.

The set P contains all prime numbers less than 20. Which of the following are elements of P? Indicate **all** such values.

Please select 3 correct answers

List prime numbers: 2, 3, 5, 7, 11, 13, 17, 19.
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Correct! Wrong!

Select all prime numbers less than 20.

If n is a positive integer, which of the following expressions must be greater than n? Indicate **all** such expressions.

Please select 2 correct answers

Test small positive integer values for n (e.g., 1, 2, 3).
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Select all expressions that are always greater than n.

Which of the following could be the lengths of the sides of an isosceles triangle? Indicate **all** such sets of lengths.

Please select 4 correct answers

An isosceles triangle has at least two sides of equal length. Also, the triangle inequality must hold (sum of two shorter sides > longest side).
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Select all sets where at least two sides are equal and they can form a triangle.

If x is an integer, which of the following expressions must represent an odd integer? Indicate **all** such expressions.

Please select 2 correct answers

Consider cases where x is even and where x is odd. (Even+1=Odd, 2*Even=Even, 2*Odd=Even, Odd+Odd=Even, Even+Even=Even).
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Select all expressions that are always odd.

The sum of two distinct prime numbers is 15. Which of the following could be one of the prime numbers? Indicate **all** such values.

Please select 2 correct answers

List prime numbers and see which pairs sum to 15. Remember 2 is the only even prime.
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Select all possible prime numbers that could be part of the pair.

If x and y are positive integers and x/y = 0.4, which of the following could be the value of y? Indicate **all** such values.

Please select 3 correct answers

0.4 can be written as 2/5. So x/y = 2/5. This means y must be a multiple of 5 (after simplification).
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Select all possible values for y.

Which of the following inequalities are true? Indicate **all** such values.

Please select 3 correct answers

Evaluate each inequality separately.
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Correct! Wrong!

Select all true inequalities.

GRE Problem Solving (Multiple Answers) Practice Quiz 4
All-Star Selector!
You have a great eye for identifying all correct options!
Choice Champion!
Good work selecting multiple correct answers. Keep practicing thoroughness.
Option Investigator!
Remember to evaluate every option carefully in these question types.

About the author

Farrukh Mehmood

An expert in standardized testing, Farrukh Mehmood brings over 6 years of valuable teaching experience. His expertise spans the GRE, GMAT, and SATs, providing students with the insights and strategies needed to excel on these crucial exams.