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DS - absolute values

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DS - absolute values

by oks » Sun Jul 05, 2009 2:29 pm
Is ¦x - y¦>¦x - z¦?
(1) ¦y¦>¦z¦
(2) x < 0

OA is E.

I must be missing something while solving this type of problem (absolute values). Could someone please explain the correct approach? Thanks!!
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Source: — Data Sufficiency |
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by GMATQuantCoach » Sun Jul 05, 2009 4:28 pm
(1) Let x = 1. y = 3. z = -1. Then |x-y| = |x-z| = 2.
Let x = -1, y = 3, z = -1, then |x - y| = 4, |x - z| = 2.
Insufficient.

(2) Let x = -1, y = 3, z = -1, then |x - y| = 4, |x - z| = 2, then |x - y| > |x - z|
Let x = -1, y = z = 1, then |x - y| = |x - z|
Insufficient.

When combined,
Let x = -1, y = 3, z = -1, then |x - y| = 4, |x - z| = 2, then |x - y| > |x - z|
Let x = -2, y = -3, z = -1 then |x - y| = |x - z| = 1
Insufficient.

Then answer is E.

You may wonder how did I pick those numbers. The question asks is |x - y| > |x - z|. |x - y| represents the distance between x and y. |x - z| represents the distance between x and z.

Visualize the question by drawing a number line.

(1) |y - 0| > |z - 0| means the distance between y and 0 is greater than the distance between z and 0. Pick any y and z that satisfy this condition on the number line and move x around.

(2) x can be only left of 0 on the number line. Draw some scenarios for those.

Once you can visualize the problem on a number line, there is no need for algebra here.
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