MathRevolution wrote:

[GMAT math practice question]

How many real numbers \(x\) satisfy \(||x-3|-4|=4\)?

A. 1

B. 2

C. 3

D. 4

E. 5

Open the outer Modulus and make the RHS + or -

|x-3|-4=+or-4. Now isolate the remaining Mod.

|x-3|=4+-4. So |x-3|=8. Or |x-3|=0. Both 0 and 8 are non negative, so no need to discard either formula. Now use both formulas to retrieve solutions.

(1) |x-3|=8

x=-5 or 11(2) |x-3|=0

x=3So 3 solutions. Good question.

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