Absolute value

[harsh8686]

If $$\left|X^2\ -\ 6\right|\ =\ X$$ , which of the following could be the value of x?

A) -2
B) 0
C) 1
D) 3
E) 5

[Brent@GMATPrepNow]

If $$\left|X^2\ -\ 6\right|\ =\ X$$ , which of the following could be the value of x?

A) -2
B) 0
C) 1
D) 3
E) 5

A quick approach is to simply test the answer choices

A) -2 No good. The absolute value of something cannot be negative
B) 0 Plug in to get |0² - 6| = 0. Doesn't work.
C) 1 Plug in to get |1² - 6| = 1. Doesn't work.
D) 3 Plug in to get |3² - 6| = 3. WORKS!!!

Answer: D

Cheers,
Brent

[GMATGuruNY]

If $$\left|X^2\ -\ 6\right|\ =\ X$$ , which of the following could be the value of x?

A) -2
B) 0
C) 1
D) 3
E) 5

Alternate approach:

Since an absolute value cannot be negative -- implying that the right side of the equation must be NONNEGATIVE -- we know that x≥0.
If x²-6=x, we get:
x²-x-6=0
(x-3)(x+2) = 0
Only the factor in green implies a nonnegative option for x:
x-3=0
x=3.

The correct answer is D.

[jaetpu]

If $$\left|X^2\ -\ 6\right|\ =\ X$$ , which of the following could be the value of x?

A) -2
B) 0
C) 1
D) 3
E) 5

Absolute values can be time-consuming to deal with, because you have to split into two different cases and work them out. In this situation, the approach Brent mentioned, testing the answer choices, will be the fastest approach.

[Scott@TargetTestPrep]

If $$\left|X^2\ -\ 6\right|\ =\ X$$ , which of the following could be the value of x?

A) -2
B) 0
C) 1
D) 3
E) 5

Looking at the answer choices we see that when x = 3, we have:

|9 - 6| = 3

3 = 3

Answer: D