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Source: — Data Sufficiency |

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by Mike@Magoosh » Tue Dec 03, 2013 2:17 pm
abhasjha wrote:Is |x -y| > |x| + |y|?

(1) y < x

(2) xy < 0
Dear abhasjha
I'm happy to help. :-)
You may find this blog helpful:
https://magoosh.com/gmat/2013/gmat-quant ... qualities/

I believe this is a faulty DS question. The prompt is never true. Never. Answer to the prompt is always "NO", and the statements are irrelevant. This is an exceedingly poorly written question. What is the source?

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by [email protected] » Wed Dec 04, 2013 12:50 am
Hi abhasjha,

I agree with Mike that the prompt that you've provided is "faulty" in that you don't need either of the two Facts to answer it. The GMAT does NOT present DS prompts in this style. My guess is that there's a typo in it, since I can see the idea that this question is *probably* based on.

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by sanju09 » Wed Dec 04, 2013 1:35 am
abhasjha wrote:Is |x -y| > |x| + |y|?

(1) y < x

(2) xy < 0
For any real values of x and y the above inequality is never true. Purpose lost, we need no further info. It cannot be a GMAT problem for sure. DS died in the stem only!
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by GMATGuruNY » Wed Dec 04, 2013 4:30 am
I suspect that the question stem should read as follows:
Is |x-y| > |x| - |y| ?
1) y < x
2) xy < 0
One approach is to plot the distances on a NUMBER LINE.

|x|= the distance between x and 0 = the RED segment on the number lines below.
|y| = the distance between y and 0 = the BLUE segment on the number lines below.
|x-y| = the distance BETWEEN X AND Y.

Statement 1: y<x
Case 1:
Image
|x| - |y| = RED - BLUE.
|x-y| = RED - BLUE.
Thus, |x-y| = |x| - |y|.

Case 2:
Image
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
INSUFFICIENT.

Statement 2: xy<0
Since x and y have different signs, they are on OPPOSITE SIDES OF 0.
Image
In each case:
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
SUFFICIENT.

The correct answer is B.
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by abhasjha » Wed Dec 04, 2013 7:44 am
I am sorry that was a typo .... from my side .... Thanks mitch for pointing that out .
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by [email protected] » Wed Dec 04, 2013 4:38 pm
Hey Mitch,


Have a doubt if we try and test values for the stem statement:
Basis statement 2 I get that the signs of values of x and y are opposite hence for example

X=-5 and Y= 3 which gives us|-5+3|=|2|

Now of we place the same values in |x|-|y|=|5|-|3|=2 aren't we getting the same value?

Please help me understand!



|x| - |y| =
|x-y| = RED + BLUE.






GMATGuruNY wrote:I suspect that the question stem should read as follows:
Is |x-y| > |x| - |y| ?
1) y < x
2) xy < 0
One approach is to plot the distances on a NUMBER LINE.

|x|= the distance between x and 0 = the RED segment on the number lines below.
|y| = the distance between y and 0 = the BLUE segment on the number lines below.
|x-y| = the distance BETWEEN X AND Y.

Statement 1: y<x
Case 1:
Image
|x| - |y| = RED - BLUE.
|x-y| = RED - BLUE.
Thus, |x-y| = |x| - |y|.

Case 2:
Image
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
INSUFFICIENT.

Statement 2: xy<0
Since x and y have different signs, they are on OPPOSITE SIDES OF 0.
Image
In each case:
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
SUFFICIENT.

The correct answer is B.
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by GMATGuruNY » Thu Dec 05, 2013 8:38 am
[email protected] wrote:Hey Mitch,
statement 2:

Now of we place the same values in |x|-|y|=|5|-|3|=2 aren't we getting the same value?
Statement 2 requires that xy < 0, so we cannot consider x=5 and y=3.
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