Free GRE Practice Questions with Solutions -
Sample 1

A set of 10 questions similar to GRE quantitative reasoning questions , with detailed solutions are presented.

Question 1

Which of the following would be the value of the digit \( B \) so that the number \( 3B324 \) is divisible by 6?
A) 0
B) 1
C) 2
D) 3
E) 4
F) 5
G) 6
H) 7
I) 8
J) 9

Question 2

Which of these is NOT a prime number?
A) 27
B) 13
C) 43
D) 49
E) 119
F) 1111

Question 3

If \( a, b, c, d \) are real numbers such that \( a \lt b \lt c \lt d \), which of the following statements is always true?
A) The average (arithmetic mean) of \( a, b, c, d \) is smaller than \( d \)
B) The average of \( a, b, c, d \) is greater than \( d \)
C) The average of \( a, b, c, d \) is greater than \( a \)
D) Three times the average of \( a, b, c, d \) is greater than \( d \)

Question 4

If \( x \) is distant by 5 units from \( -1 \), what are the possible values of \( x \)?
A) 4
B) -4
C) -6
D) 6
E) 5

Question 5

Which of these fractions are equivalent to \( \dfrac{6}{8} \)?
A) \( \dfrac{30}{40} \)
B) \( \dfrac{4}{5} \)
C) \( \dfrac{12}{16} \)
D) \( \dfrac{3}{4} \)
E) \( \dfrac{99}{132} \)
F) \( \dfrac{4}{3} \)

Question 6

Which of the triangles below, defined by their three sides, are right triangles?
A) 1, 2, 3
B) 6, 8, 10
C) 1.2, 1.6, 2.0
D) 3, 5, \( \sqrt{34} \)
E) 10, 12, 20

Question 7

The lengths of the sides \( AB \) and \( AC \) of triangle \( ABC \) are both equal to 10, and the interior angle at vertex \( A \) is \( 30^\circ \). Which is true about triangle \( ABC \)?
A) Angles \( ABC \) and \( ACB \) are equal in size.
B) Angle \( ABC \) has a size of \( 30^\circ \)
C) Angle \( ACB \) has a size of \( 75^\circ \)
D) The area of triangle \( ABC \) is equal to 25

Question 8

Which of the following is true?
A) \( x^2 > 0 \) for all real values of \( x \)
B) \( |x| > 0 \) for all real values of \( x \)
C) \( x^2 + 1 > 0 \) for all real values of \( x \)
D) \( |x + 1| > 0 \) for all real values of \( x \)
E) \( |x| + 1 > 0 \) for all real values of \( x \)

Question 9

Which of the following is true for all real numbers \( x \) and \( y \)?
A) \( |-x - y| = |x + y| \)
B) \( |x - y| = |x + y| \)
C) \( |y - x| = |x - y| \)
D) \( |-x + y| = |x - y| \)

Question 10

Let \( a, b, c, d, e, f, h \) be numbers such that: \( a \times b \times c = 100 \), \( a \times d \times e = 0 \), and \( b \times f \times h = 0 \). Which of the following could be true?
A) \( a = 0 \)
B) \( d = 0 \) or \( f = 0 \)
C) \( d \times e \ne 0 \)
D) \( f = 0 \) or \( h = 0 \)

Free GRE Practice Questions with Solutions - Sample 1