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GMAT PREP 1 QUESTION 3

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Feb 05, 2016 12:41 pm
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 didieravoaka » Sun Feb 07, 2016 5:39 pm
Thanks GuruNY
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by Matt@VeritasPrep » Mon Feb 08, 2016 9:31 am
Another approach:

|x - y| = the distance from x to y.

|x| = the distance from x to 0.

|y| = the distance from y to 0.

So we want to know

Is (distance from x to y) > (distance from x to 0) - (distance from y to 0) ?

S1::

If x > y, consider two options.

i: They're both positive. In this case, |x - y| = |x| - |y|, so the answer is NO.

ii: 0 > x and 0 > y. In this case, |x - y| is positive and |x| - |y| is negative, so the answer is YES.

Conflicting results, so insufficient.

S2::

One is positive, one is negative. Now the distance from x to y is the same as the distance from x to 0, then from 0 to y! In our equations, this can be written as

(the distance from x to y) = (the distance from x to 0) + (the distance from y to 0)

or

|x - y| = |x| + |y|

Since |x| + |y| must now be greater than |x| - |y|, this is SUFFICIENT.
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by ceilidh.erickson » Thu Feb 11, 2016 5:37 pm
Absolute value questions are testing properties of positives & negatives. One way to help translate this question is to create a chart, testing out the possibilities for x and y:

Image

Here, we can see that we will only get a "yes" answer to the question when one of the two is positive, and the other negative. If they are both positive or both negative, the two expressions will be equal.

Target question: do x and y have different signs?

(1) y < x

This doesn't tell us anything about signs. Insufficient.

(2) xy < 0

This tells us that they must have different signs. Sufficient.

The answer is B.
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