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How many values of x satisfy the equation ||x-7|-9|=11?

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by Max@Math Revolution » Tue Feb 06, 2018 11:42 pm
[GMAT math practice question]

How many values of x satisfy the equation ||x-7|-9|=11?

A. 1
B. 2
C. 3
D. 4
E. 5
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by GMATGuruNY » Wed Feb 07, 2018 3:57 am
Max@Math Revolution wrote:[GMAT math practice question]

How many values of x satisfy the equation ||x-7|-9|=11?

A. 1
B. 2
C. 3
D. 4
E. 5
Case 1: |x-7| - 9 = 11
|x-7| = 20
If x-7 = 20, then x=27.
If x-7 = -20, then x = -13.

Case 2: |x-7| - 9 = -11
|x-7| = -2
Since an absolute value cannot be equal to a negative, Case 2 is not possible.

Only the values in blue are viable solutions.

The correct answer is B.
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by Max@Math Revolution » Fri Feb 09, 2018 12:31 am
=>

||x-7|-9| = 11
=> |x-7|-9 = ±11
=> |x-7| = 9 ±11
=> |x-7| = 20 or |x-7| = -2
=> |x-7| = 20 since |x-7| ≥ 0
=> x-7 = ±20
=> x = 7±20
=> x = 27 or x = -13

Therefore, the answer is B.

Answer: B
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