Quadratic Equations & Absolute Value #14

This GMAT quant practice question is a problem solving question in Quadratic Equations in Algebra. Concept tested: Absolute values and quadratic equations and number of real solutions to quadratic equations. A medium difficulty, 650 to 700 level GMAT sample question in algebra.

Question 14 : How many real solutions exist for the equation x² – 11|x| - 60 = 0?

1. 3
2. 2
3. 1
4. 4
5. None

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Video Explanation

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Explanatory Answer

Step 1 of solving this GMAT Quadratic Equations Question : Assign y = |x| and solve for y

Let |x| = y.
We can rewrite the equation x² - 11|x| - 60 = 0 as y² - 11y - 60 = 0
The equation can be factorized as y² - 15y + 4y - 60 = 0
(y - 15) (y + 4) = 0
The values of y that satisfy the equation are y = 15 or y = -4.

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Step 2 of solving this GMAT Quadratic Algebra Question : Compute number of real values of x

We have assigned y = |x|
|x| is always a non-negative number.
So, |x| cannot be -4.
|x| can take only one value = 15.
If |x| = 15, x = 15 or -15.

The number of real solutions that exist for x² – 11|x| - 60 = 0 is 2.

The correct choice is (B) and the correct answer is 2.