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Modulus Question - Difficulty Level High - Kaplan

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Source: — Data Sufficiency |
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by sl750 » Sun Sep 18, 2011 3:30 am
Statement 1

|x|=x-y

x could be positive, in which case x=x-y
x could be negative, in which case -x=x-y

Does x/-(x) = 1? No in the first case. Does x/-(-x) = 1? Yes. Insufficient

Statement 2
x^3<0, so x is negative. Does x/y-x = 1? It could equal one when y=-2 and x=-1. In other cases it doesn't satisfy the condition. Insufficient

Statement 1 and 2
x is negative and -x=x-y from statement 1, so Does x/-(-x)=1. Yes. Sufficient
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by GMATGuruNY » Sun Sep 18, 2011 4:23 am
imhimanshu wrote:If x is not equal to y , does x/(y-x) = 1

St 1: |x|= x-y
St 2: x^3< 0

Pls post detailed solution
Thanks
Rephrase the question:
x/(y-x) = 1
x = y-x
2x = y.

Question rephrased: Does y = 2x?

Statement 1: |x|= x-y
If x<0, then x-y = -x:
x-y = -x.
2x = y.

If x>0, then x-y = x:
x-y = x
y=0.
If y=0, then x can be any positive value and y ≠ 2x.
Insufficient.

Statement 2: x³<0.
Thus, x<0.
No information about y.
Insufficient.

Statements 1 and 2 combined:
To satisfy statement 2, x<0.
If x<0 in statement 1, then y = 2x.
Sufficient.

The correct answer is C.
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by mehrasa » Sun Sep 18, 2011 4:43 am
the Q is asking whether 2x=y or not?

stat1) we have two condition
if x>0 ==> x=x-y ==> ye0
if x<0 ==> -x=x-y ==> y=2x state 1 alone in not sufficient

stat 2) x^3 <o when x<0 alone insufficient

together, we have negative x and according to stat 1: y=2x ==> sufficient
IMO: C
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