ABS Practice Questions

21 Total Questions Quantitative Reasoning

Master GMAT ABS with comprehensive practice questions. Build your quantitative reasoning skills through detailed explanations and strategic practice.

Key Skills

Problem Solving
Analytical Thinking
Mathematical Reasoning
Strategic Analysis

Study Tips

Focus on understanding ABS concepts fundamentally
Practice with timer to improve speed and accuracy
Review explanations thoroughly to learn solution methods
Identify common patterns and shortcuts for this topic

Free Preview: Try 3 questions below. Sign up free to access all 21 questions.

Question 1 of 5 Medium

If $ 3|3 - x| = 7 $, what is the product of all the possible values of $ x $?

$ \frac{1}{9} $

$ \frac{1}{3} $

$ \frac{2}{3} $

$ \frac{16}{9} $

$ \frac{32}{9} $

View Explanation

Correct Answer: E

When solving an absolute value equation, it helps to first isolate the absolute value expression:

$ 3|3 - x| = 7 $
$ |3 - x| = \frac{7}{3} $

When removing the absolute value bars, we need to keep in mind that the expression inside the absolute value bars $ (3 - x) $ could be positive or negative. Let's consider both possibilities:

When $ (3 - x) $ is positive:
$ (3 - x) = \frac{7}{3} $
$ 3 - \frac{7}{3} = x $
$ \frac{9}{3} - \frac{7}{3} = x $
$ x = \frac{2}{3} $

When $ (3 - x) $ is negative:
$ -(3 - x) = \frac{7}{3} $
$ x - 3 = \frac{7}{3} $
$ x = \frac{7}{3} + 3 $
$ x = \frac{7}{3} + \frac{9}{3} $
$ x = \frac{16}{3} $
So, the two possible values for $ x $ are $ \frac{2}{3} $ and $ \frac{16}{3} $. The product of these values is $ \frac{32}{9} $.
The correct answer is E.

Question 2 of 5 Medium

If $ |a| = \frac{1}{3} $ and $ |b| = \frac{2}{3} $, which of the following CANNOT be the result of $ a + b $?

$ -1 $

$ -\frac{1}{3} $

$ \frac{1}{3} $

$ \frac{2}{3} $

$ 1 $

View Explanation

Correct Answer: D

The possible values for $ a $ and $ b $ are $ \pm \frac{1}{3} $ and $ \pm \frac{2}{3} $ respectively.
We can list the possible sums:

$$\begin{array}{|c|c|c|} \hline a & b & a+b \\ \hline \frac{1}{3} & \frac{2}{3} & 1 \\ \hline \frac{1}{3} & -\frac{2}{3} & -\frac{1}{3} \\ \hline -\frac{1}{3} & \frac{2}{3} & \frac{1}{3} \\ \hline -\frac{1}{3} & -\frac{2}{3} & -1 \\ \hline \end{array}$$

Comparing with the options, $ \frac{2}{3} $ is NOT a possible sum.
The correct answer is D.

Question 3 of 5 Medium

If $ \sqrt{(x + 4)^2} = 3 $, which of the following could be the value of $ x - 4 $?

$ -11 $

$ -7 $

$ -4 $

$ -3 $

$ 5 $

View Explanation

Correct Answer: A

Solutions to the equation: $ (x + 4) = 3 $ or $ (x + 4) = -3 $.
On the GMAT, the negative solution is often the correct one, so evaluate that one first.
$ x + 4 = -3 \implies x = -3 - 4 \implies x = -7 $.

Watch out! Although -7 is an answer choice, it is not correct. The question does not ask for the value of $ x $, but rather for the value of $ x - 4 $.
$ x - 4 = -7 - 4 = -11 $.

Alternatively, the expression $ \sqrt{(x+4)^2} $ can be simplified to $ |x + 4| $, and the original equation can be solved accordingly.
If $ |x + 4| = 3 $, either $ x = -1 $ or $ x = -7 $.
The correct answer is A.

Question 4 of 5 Medium

If $ x > y $, $ x^2 - 2xy + y^2 - 9 = 0 $, and $ x + y = 15 $, what is $ x $?

$ 3 $

$ 6 $

$ 12 $

$ 18 $

$ 9 $

Unlock 16+ More Questions

Question 5 of 5 Medium

If $ b < c < d $ and $ c > 0 $, which of the following cannot be true if $ b, c $ and $ d $ are integers?

$ bcd > 0 $

$ b + cd < 0 $

$ b - cd > 0 $

$ b/cd < 0 $

$ b^3 cd < 0 $

Unlock 16+ More Questions

Ready for more practice?

Access 21 ABS questions plus thousands more across all GMAT topics

Create Free Account Sign In