Data Sufficiency

Mo2men wrote:Is |x−z−y| > x−z+y?

(1) 0<x<z<y
(2) (x-z-y) is negative

OA: A

Source: Veritas

Hi Mo2men,

Statement 1: 0<x<z<y

0<x<z<y implies that each of x, y, and z is positive.

|x-z-y| must be a negative number since x < (y+z).

Thus, we have: Is -(x-z-y) > x-z+y?

=> -x+z+y > x-z+y

=> 2z > 2x; y cancells

=> z > x--> This is a fact given in the statement. Sufficient.

Statement 2: (x-z-y) is negative

x-z-y < 0

=> x < (y+z)

|x-z-y| must be a negative number since x < (y+z), Thus, we have: Is |a negative number| > x-z+y?

Now we have the same situation as was in statement 1.

So, we reach at: Is x < z? We do not know this. This fact belonged to statement 1 and not to statement 2. Insufficient.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Number Properties Guide

-Jay
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Mo2men wrote:

Jay@ManhattanReview wrote:

Mo2men wrote:Is |x−z−y| > x−z+y?

(1) 0<x<z<y
(2) (x-z-y) is negative

OA: A

Source: Veritas

Hi Mo2men,

Statement 1: 0<x<z<y

0<x<z<y implies that each of x, y, and z is positive.

|x-z-y| must be a negative number since x < (y+z).

Thus, we have: Is -(x-z-y) < x-z+y?; mind the reversal of inequality sign

=> -x+z+y < x-z+y

=> 2x < 2z; y cancells

=> x < z--> This is a fact given in the statement. Sufficient.

I feel something wrong here in red.Following your final step, it gives:

-x+z+y < x-z+y

2z < 2x.

Hi Mo2men,

Thanks for pointing it out. It's incorrect, I edit my response.

-Jay