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 value
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- Brent@GMATPrepNow
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A quick approach is to simply test the answer choicesharsh8686 wrote: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) -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
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Alternate approach:harsh8686 wrote: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
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.
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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.harsh8686 wrote: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
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Looking at the answer choices we see that when x = 3, we have:harsh8686 wrote: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
|9 - 6| = 3
3 = 3
Answer: D
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