M09-19

Question

Is  |x - 5| > 4 ?

(1)  x^2-4 < 0 
 
(2)  x^2-1 < 0

Bunuel · Accepted Answer

Official Solution: Is |x - 5| > 4 ? Is |x-5| > 4 ? Is x - 5 < -4 or x - 5 > 4 ? Is x < 1 or x > 9 ? (1) x^2-4 < 0 " x^2 < 4 ; -2 < x < 2 . We can have an YES answer as well as a NO answer (consider x=0 and x=1.5 ). Not sufficient. (2) x^2 - 1 < 0 : x^2 < 1 ; -1 < x < 1 . Therefore, the answer to the question is YES. Sufficient. Answer: B

summerbummer · Answer

----------------------------- Please guide me where I'm making a mistake. For an inequality such as this: |x - 5| > 4? We have two cases: Case 1: If x>=0, then x-5 > 4 x> 9 Case 2: If x<0, then x-5 < -4 x < 1 But x should be less than 0, right? So this case should be discarded then. If this happens, then D is my correct answer. I ain't sure where I'm going wrong in my approach! Bunuel KarishmaB ScottTargetTestPrep BrentGMATPrepNow

ScottTargetTestPrep · Answer

Recall that |z| = z if z ≥ 0, and |z| = -z if z < 0. If you substitute z = x - 5, then you'll obtain |x - 5| = x - 5 if x - 5 ≥ 0, and |x - 5| = -(x - 5) if x - 5 < 0. When you substitute z = x - 5 for z within the absolute value bars, you need to remember to substitute z = x - 5 in z ≥ 0 and z < 0 as well. Thus, your two cases should be: Case 1: If x ≥ 5, then x - 5 > 4 x > 9 Case 2: If x < 5, then -(x - 5) > 4 -x + 5 > 4 -x > -1 x < 1

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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