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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6966
GMAT 1: 760 Q51 V42
GPA: 3.82

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23 Mar 2016, 17:53
1
4
00:00

Difficulty:

75% (hard)

Question Stats:

58% (01:50) correct 42% (01:59) wrong based on 153 sessions

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

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

* A solution will be posted in two days.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Joined: 13 Apr 2015
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Location: India
Concentration: Strategy, General Management
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Re: Is |x-y|<|x-z|?  [#permalink]

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23 Mar 2016, 19:22
1
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.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6966
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is |x-y|<|x-z|?  [#permalink]

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27 Mar 2016, 00:35
2
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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25 Dec 2017, 07:03
best way to attack this problem is using number line

case 1:
----z-------------------x----y----0---------- => |x-z| > |x-y|

case 2:
----z---x--------------------y----0---------- => |x-z| < |x-y|

two cases satisfies both the statements, but still not sufficient to answer the question => (E)
Intern
Joined: 26 Jul 2017
Posts: 5
Re: Is |x-y|<|x-z|?  [#permalink]

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25 Dec 2017, 08:07
MathRevolution wrote:
Is |x-y|<|x-z|?

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

* A solution will be posted in two days.

Using number Line Approach.
Question is asking whether the distance of Y from X is smaller than the distance of Z from X

Statement 1: It tells us that Y is Closer to zero than Z. But we still don't know the Location of X wrt Y and Z. INSUFFICIENT
Statement 2: X is on the left of 0 on the number line. No information about Y or Z. INSUFFICIENT

Statement 1+2: We still don't know the location of X wrt Y and Z. INSUFFICIENT

Ans: E
Re: Is |x-y|<|x-z|?   [#permalink] 25 Dec 2017, 08:07
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# Is |x-y|<|x-z|?

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