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 x^{2} – 11|x| - 60 = 0?

- 3
- 2
- 1
- 4
- None

@ INR

Let |x| = y.

We can rewrite the equation x^{2} - 11|x| - 60 = 0 as y^{2} - 11y - 60 = 0

The equation can be factorized as y^{2} - 15y + 4y - 60 = 0

(y - 15) (y + 4) = 0

The values of y that satisfy the equation are y = 15 or y = -4.

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 x^{2} – 11|x| - 60 = 0 is 2.

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