Free GRE Practice Questions with Solutions
Sample 2

10 questions similar to GRE quantitative reasoning questions , with detailed solutions similar to the questions in the GRE test.

Question 1

If $ w $ is the average of the numbers $ a, b, c $ and $ d $, then the average of $ m(a + k),\quad m(b + k),\quad m(c + k),\quad m(d + k) $ is given by

A) $ m(w \cdot k) $
B) $ m(w + k) $
C) $ mw + k $
D) $ w + mk $
E) $ w + m + k $

Question 2

What is the ratio of the area of the larger circle to the area of the smaller circle such that the radius of the larger circle is three times the radius of the smaller circle?

A) 3
B) 6
C) 12
D) 15
E) 9

Question 3

A group of 20 employees in a company have an average (arithmetic mean) salary of $35,000 while a second group of 30 employees in the same company have an average salary of $40,000. What is the average salary of the 50 employees making the two groups?

A) $37,500
B) $38,000
C) $40,500
D) $39,000
E) $38,500

Question 4

Which of the following is equal to $ \sqrt{48}$?

A) 16
B) $ 3\sqrt4 $
C) $ 4\sqrt3 $
D) $ 18\sqrt3 $
E) 24

Question 5

The sizes of the interior angles A, B and C of a triangle are in the ratio 2:4:3. What is the measure, in degrees, of the smallest angle?

A) 40
B) 45
C) 32
D) 70
E) 30

Question 6

If n is even and m is odd, then which of the following is true?

A) $ (n + m) $ is even
B) $ n - m $ is even
C) $ n \times m $ is odd
D) $ n^2 + m^2 + 1 $ is even
E) $ 2n + 3m + 1 $ is odd

Question 7

\[ 5^{100} + 25^{50} + 3 \left( \dfrac{125^{34}}{25} \right) = \]

A) $ 33 \cdot 5^{50} $
B) $ 405^{34} $
C) $ 33^{100} $
D) $ 5^{100} $
E) $ 5^{101} $

Question 8

\[ \dfrac{6x^{10} - 2x^9}{9x^2 - 1} = \]

A) $ \frac{6x^9 - 2x^8}{9x - 1} $
B) $ \frac{2x^9}{3x + 1} $
C) $ \frac{2}{3}x^8 - 2x^9 $
D) $ \frac{2}{3}x^8 + 2x^9 $
E) $ \frac{2x^9}{3x - 1} $

Question 9

\[ (-2x + 6)^2 =\ ? \]

A) $ 4x^2 + 36 $
B) $ -4x^2 + 36 $
C) $ 4x^2 + 24x + 36 $
D) $4x^2 - 24x + 36 $
E) $4x^2 - 24x - 36 $

Question 10

The sum of all interior angle of a regular polygon is $ 1800^\circ $ How many sides does this polygon have?

A) 10
B) 11
C) 12
D) 13
E) 14

Free GRE Practice Questions with Solutions Sample 2