GMAT Algebra Sample Questions

In GMAT quant section, typically you’ll find questions from algebra – Linear Equations. These types of questions are usually a part of Data Sufficiency which analyzes your understanding of the different types of solutions.

Here are few sample questions on GMAT Algebra to equip an idea on Quant section – 

Solving Equations With Absolute Values

1) \(Solve \; for \; x, \; Where \; |x + 5| – 10 = 0\)

Solution – \(|x + 5| – 10 = 0\)

By adding 10 in both sides –

\(|x + 5| = 10\)

Without brackets,

\(x + 5 = 10\)

\(x = 5\)

Without brackets, multiply the right side by -1 since the expression in the absolute value brackets could be negative due to the effect of the absolute value.

\(x + 5 = (10) (-1)\)

\(x + 5 = -10\)

Therefore, x = 5 or x = -15

Solving an Exponential Equation

2) \(Find \; x, \; where \; (8^{2x})^{2} = 64^{x – 2}\)

Solution – \(As \; 8 = 2^{3} \; and \; 64 = 2^{6}\)

\((8^{2x})^{2} = 64^{x – 2}\)

\(((2^{3})^{2x})^{2} = (2^{6})^{x – 2}\)

\(2^{3 \times 4x} = 2^{6x – 12}\)

\(2^{12x} = 2^{6x – 12}\)

We can state as further –

\(12x = 6x – 12\)

\(6x = – 12\) (by subtracting 6x from both sides)

Therefore, \(x = – 2\)

3) \(Find \; x, \; when \; 9x – 3 = \frac{2x – 4}{3}\)

Solution:

By multiplying 3 on both sides,

\(27x – 9 = 2x – 4\)

\(25x = 5\)

Therefore, \(x = \frac{1}{5}\)

4) \(Find \; x, \; if \; x^{2} + 6x + 6 = 0\)

Solution:

Using the formula, \(x = \frac{-b \pm \sqrt{b^{2} – 4ac}}{2a}\)

\(x = \frac{-6 \pm \sqrt{6^{2} – 4(1)(6)}}{2(1)}\)

\(x = \frac{-6 \pm \sqrt{36 – 24}}{2}\)

\(x = -3 \pm \frac{\sqrt{12}}{2}\)

\(x = -3 \pm 2\frac{\sqrt{3}}{2}\)

\(x = -3 \pm \sqrt{3}\)

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