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.
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
If
\[ \sqrt{x} = 3 \]then the value of \(x^4\) is:
A) \(6561\)
B) \(9\)
C) \(81\)
D) \(729\)
E) \(3\)
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
Evaluate:
\[ 8 \times 2^{100} + 4 \times 2^{101} \]
A) \(2^{101}\)
B) \(2^{102}\)
C) \(2^{103}\)
D) \(2^{104}\)
E) \(2^{105}\)
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) \(\frac{15}{2}\)
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
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) \(4\)
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) \(\frac{4}{3}(x - 1)\)
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) \(b = 2,\; c = 6\)
Evaluate:
\[ (\sqrt{12} - \sqrt{3})(-\sqrt{12} + \sqrt{3}) \]
A) \(9\)
B) \(-3\)
C) \(15\)
D) \(-15\)
E) \(18\)