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Source: — Data Sufficiency |
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by Uva@90 » Thu Jan 16, 2014 7:44 pm
greenwich wrote:Is |x-z|=|z-y|?

(1) x=y
(2)|x|-z=|y|-z
Hi Greenwich,

Question states that,
is distance between x and z is same as z and y ?

so we need to know whether distance of x and y are equal.

statement 1:x=y
since x =y distance of x => distance of x is same as distance of y
hence sufficient.

statement 2: |x|-z=|y|-z
which can be re-written as |x| = |y|
x=y or x = -y
example: x = -4 and y =4 and z = 1
distance between x and z is 5 and distance between z and y 3
hence distance between x and z may not be same as z and y
hence insufficient.

Answer is A

Note: Modified the solution.

Regards,
Uva.
Last edited by Uva@90 on Thu Jan 16, 2014 9:15 pm, edited 1 time in total.
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by GMATGuruNY » Thu Jan 16, 2014 8:33 pm
greenwich wrote:Is |x-z|=|z-y|?

(1) x=y
(2)|x|-z=|y|-z
|a-b| = |b-a| = the DISTANCE between a and b.

Question rephrased: Is the distance between z and x equal to the distance between z and y?
Put more succinctly:
Is z equidistant from x and y?

Statement 1: x=y
Since x and y are the same value, z must be equidistant from x and y.
SUFFICIENT.

Statement 2: |x|-z = |y|-z
Adding z to each side, we get:
|x| = |y|.

If x=-1, z=0, and y=1, then z is equidistant from x and y:
.....x=-1.....z=0.....y=1.....

If x=-1, y=1, and z=2, then z is closer to y than to x and thus is NOT equidistant from x and y:
.....x=-1................y=1.....z=2.....
INSUFFICIENT.

The correct answer is A.
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