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Is |x-y|<|x-z|?

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Is |x-y|<|x-z|? [#permalink]

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New post 23 Mar 2016, 18:53
Expert's post
2
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (00:58) correct 41% (01:10) wrong based on 90 sessions

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Is |x-y|<|x-z|?

1) |y|<|z|
2) x<0


* A solution will be posted in two days.
[Reveal] Spoiler: OA

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Re: Is |x-y|<|x-z|? [#permalink]

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New post 23 Mar 2016, 20:22
MathRevolution wrote:
Is |x-y|<|x-z|?

1) |y|<|z|
2) x<0



St1: Assume x = 2; y = -2; z = 3
|2 - (-2)| < |2 - 3| ? No
Assume x = 2; y = -2; z = -3
|2 - (-2)| < |2 - (-3)| ? Yes
St1 is not sufficient

St2: Assume x = -1; y = -2; z = 3
|-1 - (-2)| < |-1 - 3| ? Yes
Assume x = -1; y = 2; z = -3
|-1 - 2| < |-1 - (-3)| ? No
St2 is not sufficient

Combining St1 and St2 is also not helpful.

Answer: E

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Re: Is |x-y|<|x-z|? [#permalink]

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New post 27 Mar 2016, 01:35
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Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is |x-y|<|x-z|?

1) |y|<|z|
2) x<0


In the original condition, there are 3 variables(x,y,z), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation. So you need 1 equation, which is likely to make E the answer.
When 1) & 2), y=-2, x=-1, z=10 yes but y=2, z=-10, x=-9 no, which is not sufficient.
Thus, the answer is E.
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Re: Is |x-y|<|x-z|? [#permalink]

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New post 11 Aug 2017, 22:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is |x-y|<|x-z|?   [#permalink] 11 Aug 2017, 22:24
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