Free GMAT Math Practice Problems with Solutions

This page presents a sample set of GMAT-style problem-solving questions. Each problem focuses on key quantitative concepts tested on the GMAT. Detailed solutions are available here.

Question 1

Triangle \(ABC\) has sides \(AB = 3\) and \(BC = 5\). Which of the following could be the length of side \(AC\)?

(I) \(8\)
(II) \(12\)
(III) \(0.5\)

A) (I) only
B) (II) only
C) (III) only
D) (I) and (II) only
E) None

Question 2

If

\[ \sqrt{x} = 3 \]

then the value of \(x^4\) is:

A) \(6561\)
B) \(9\)
C) \(81\)
D) \(729\)
E) \(3\)

Question 3

If \(n\) is an odd integer, which of the following expressions is even?

(I) \(n^2\)
(II) \(n^2 + 1\)
(III) \(3n^2 - 1\)

A) (I) only
B) (II) only
C) (III) only
D) (I) and (II) only
E) (II) and (III) only

Question 4

Evaluate:

\[ 8 \times 2^{100} + 4 \times 2^{101} \]

A) \(2^{101}\)
B) \(2^{102}\)
C) \(2^{103}\)
D) \(2^{104}\)
E) \(2^{105}\)

Question 5

If

\[ \begin{cases} 3x + 5y = 5 \\ x + 3y = 20 \end{cases} \]

then the value of \(2x + 4y\) is:

A) \(25\)
B) \(\frac{25}{2}\)
C) \(\frac{25}{4}\)
D) \(15\)
E) \(\frac{15}{2}\)

Question 6

If \(0 < n < 1\), which of the following statements is true?

(I) \(n^2 - n < 0\)
(II) \(n^3 < n\)
(III) \(n + 1 < 1\)

A) (I) only
B) (II) only
C) (III) only
D) (I) and (II) only
E) (II) and (III) only

Question 7

Which of the following has the greatest value?

A) \(250\%\)
B) \(2 + \frac{1}{2}\)
C) \(5 \times 0.5\)
D) \(\frac{1}{0.1}\)
E) \(4\)

Question 8

Simplify:

\[ \frac{4x^2 - 4}{-3x + 3} \]

A) \(-\frac{4}{3}(x + 1)\)
B) \(x + 1\)
C) \(\frac{4}{3}(x + 1)\)
D) \(4(x - 1)\)
E) \(\frac{4}{3}(x - 1)\)

Question 9

For which values of \(b\) and \(c\) does the equation

\[ x^2 + bx = c \]

have solutions \(x = 2\) and \(x = -3\)?

A) \(b = 2,\; c = -3\)
B) \(b = 1,\; c = 3\)
C) \(b = 1,\; c = -6\)
D) \(b = 1,\; c = 6\)
E) \(b = 2,\; c = 6\)

Question 10

Evaluate:

\[ (\sqrt{12} - \sqrt{3})(-\sqrt{12} + \sqrt{3}) \]

A) \(9\)
B) \(-3\)
C) \(15\)
D) \(-15\)
E) \(18\)

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