MathRevolution wrote:

[GMAT math practice question]

How many solutions has the equation ||x-3|-2|=1?

A. 0

B. 1

C. 2

D. 3

E. 4

We see that |x-3| - 2 could be 1 or -1 since both |1| and |-1| are equal to 1.

1) If |x - 3| - 2 = 1, then |x - 3| = 3. So x - 3 could be 3 or -3.

i) If x - 3 = 3, then x = 6.

ii) If x - 3 = -3, then x = 0.

2) If |x - 3| - 2 = -1, then |x - 3| = 1. So x - 3 could be 1 or -1.

i) If x - 3 = 1, then x = 4.

ii) If x - 3 = -1, then x = 2.

We see that the equation has 4 solutions.

Answer: E

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