GRE Practice Tests

GRE Problem Solving (Multiple Answer) Practice Test 3

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

If x is an integer and 2 < |x| leq 5, which of the following could be values of x? Indicate **all** such values.

Please select 4 correct answers

Consider integers whose absolute value is greater than 2 AND less than or equal to 5. This includes positive and negative integers.
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Correct! Wrong!

Select all possible integer values for x.

Which of the following are perfect squares? Indicate **all** such values.

Please select 3 correct answers

A perfect square is an integer that can be expressed as the product of an integer by itself.
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Correct! Wrong!

Select all numbers that are the square of an integer.

If a and b are positive integers such that a+b=7, which of the following could be the value of ab? Indicate **all** such values.

Please select 3 correct answers

List pairs of positive integers (a,b) that sum to 7 (e.g., 1+6, 2+5, 3+4) and calculate their products.
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Correct! Wrong!

Select all possible values for the product ab.

The number N = 2^3 imes 3^2 imes 5^1. Which of the following are factors of N? Indicate **all** such values.

Please select 3 correct answers

A factor of N can only contain prime factors 2, 3, or 5, with powers less than or equal to those in N.
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Correct! Wrong!

Select all factors of N.

If x is a real number such that x^2 = x, which of the following could be values of x? Indicate **all** such values.

Please select 2 correct answers

Rearrange the equation to x^2 - x = 0 and factor out x.
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Correct! Wrong!

Select all possible values for x.

Which of the following integers are divisible by 4? Indicate **all** such values.

Please select 3 correct answers

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
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Correct! Wrong!

Select all numbers divisible by 4.

If y = 2x and x is a positive integer, which of the following must be true about y? Indicate **all** such statements.

Please select 3 correct answers

If x is a positive integer (1, 2, 3...), what kind of numbers will y be?
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Correct! Wrong!

Select all statements that must be true about y.

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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Correct! Wrong!

Select all possible prime numbers that could be part of the pair.

If x is an integer, for which of the following values of x is x^2 + x an even integer? Indicate **all** such values.

Please select 5 correct answers

Consider when x is even and when x is odd. x^2+x = x(x+1). The product of two consecutive integers is always even.
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Correct! Wrong!

Select all values of x for which the expression is even.

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

Please select 3 correct answers

Test each set with the Pythagorean theorem. The longest side would be the hypotenuse.
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Correct! Wrong!

Select all sets that satisfy the Pythagorean theorem (a^2 + b^2 = c^2, where c is the hypotenuse).

GRE Problem Solving (Multiple Answers) Practice Quiz 3
Multi-Answer Maverick!
You expertly navigate questions with multiple correct answers!
Option Optimizer!
Good job identifying several correct choices. Keep practicing that critical evaluation.
Selection Strategist!
Remember to consider all options thoroughly in multiple-answer problems.

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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.