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is |x| = y-z?

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by vineetbatra » Mon Sep 21, 2009 3:14 pm
is |x| = y-z?

1. X+y = z
2. X,0

OA is C
Why is A wrong.

x+y = z => x=z-y => x = -Y+Z => -x = y-z. since X is absolute above equation proves true.

what is incorrect in my thinkning.
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Source: — Data Sufficiency |

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Re: is |x| = y-z?

by Brent@GMATPrepNow » Mon Sep 21, 2009 5:34 pm
vineetbatra wrote:is |x| = y-z?

1. X+y = z
2. X,0

OA is C
Why is A wrong.

x+y = z => x=z-y => x = -Y+Z => -x = y-z. since X is absolute above equation proves true.

what is incorrect in my thinkning.
To see what's wrong with (1), it's probably easiest to examine two sets of numbers that satisfy the conditions in statement (1) but yield conflicting answers to the question "is |x| = y-z?"
a) x=1, y=2, and z=3 --> here |x| DOES NOT equal y-z?
b) x=-1, y=3, and z=2 --> here |x| DOES equal y-z?
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by vineetbatra » Mon Sep 21, 2009 5:40 pm
Thanks for the reply Brent, but algebrically what is wrong in the way I tried to solve the question. I am trying to find a fault in my approach, as in which rule I violated.
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Re: is |x| = y-z?

by Brent@GMATPrepNow » Mon Sep 21, 2009 5:58 pm
vineetbatra wrote:is |x| = y-z?

1. X+y = z
2. X,0

OA is C
Why is A wrong.

x+y = z => x=z-y => x = -Y+Z => -x = y-z. since X is absolute above equation proves true.

what is incorrect in my thinkning.
Here's the problem: x+y = z => x=z-y => x = -Y+Z => -x = y-z
While all of the above conclusions are correct, we can't then conclude that |x|=y-z.
The conclusion is true if x is a negative number.
However, if x is positive, we have a problem (see my earlier sets of numbers to see this).
If x is positive then y-z is a negative number.
So, when we find the abolute value of x, the result is positive. But, this positive value is supposed to be (by your conclusion) equal to y-z, which happens to be a negative value.
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by grockit_jake » Tue Sep 22, 2009 9:14 am
|x| = y-z?

1. X+y = z
2. X,0


I would rearrange 1. to read x = z - y

Only if x is negative, will taking the absolute value switch its sign. (This would then switch the sign of (z - y), which leaves you at (y - z).

So A is insufficient, since if x > 0, then the answer is no, and if x<0 the answer is yes.

2. Clarifies this.

Answer C
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