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If X>Y is |X| > |Y| ?

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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Thu Jan 19, 2017 6:34 am
NandishSS wrote:If X>Y is |X| > |Y| ?

A)X>0

B)Y>0

OA:B

Source:Math Revolution
Test some simple numbers.

Statement 1:
Case 1: x = 1, y = 0; |1| > |0|, so we get a YES
Case 2: x = 1, y = -2; |1| < |-2|, so we get a NO

1 alone is not sufficient

Statement 2
Case 3: x = 3, y = 2; |3| > |2|, so we get a YES
Case 4 x = 5, y = 4; |5| > |4|, so we get a YES
Notice that no matter we pick for y, x will have to be larger. Because the numbers are both positive, the absolute value of x will always be greater than the absolute value of y. This statement alone is sufficient and the answer is B
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by GMATGuruNY » Thu Jan 19, 2017 7:50 am
NandishSS wrote:If X>Y is |X| > |Y| ?

A)X>0

B)Y>0
|a| = the distance between a and 0.

Question stem, rephrased:
If X is to the right of Y on the number line, is X farther from 0 than is Y?

Statement 1:
Case 1:
-----------0--Y--X---------
Case 2:
Y----------0-----X---------

In Case 1, X is farther from 0 than is Y.
In Case 2, Y is farther from 0 than is X.
INSUFFICIENT.

Statement 2:
The number line must look as it does in Case 1:
-----------0--Y--X---------
Thus, X is farther from 0 than is Y.
SUFFICIENT.

The correct answer is B.
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by [email protected] » Thu Jan 19, 2017 10:21 am
Hi NandishSS,

This question can be dealt with in a couple of different ways - conceptually or by TESTing VALUES.

We're told that X > Y. We're asked if |X| > |Y|? This is a YES/NO question. Before we start working through it, it's important to note that absolute value questions almost always involve negative values at some point, so you have to consider more than just the obvious values for X and Y (re: other options besides positive numbers).

1) X > 0

IF X is positive AND Y is positive, then the |X| will be greater than |Y| - and the answer to the question is YES.
IF X is positive AND Y is "more negative" than X is positive, then the |X| will be LESS than |Y| - and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) Y > 0

IF Y is positive, then X must be "more positive" than Y (since X > Y), so |X| will be greater than |Y| - and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

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by Jay@ManhattanReview » Sat Jan 21, 2017 12:58 am
NandishSS wrote:If X>Y, is |X| > |Y| ?

A)X>0

B)Y>0

OA:B

Source:Math Revolution
We have to see whether |X| > |Y|.

|X| > |Y| => X > Y OR X < -Y.

We are already given that X > Y. So the question reduces to whether X < -Y.

S1: X>0

Say X = 2 > 0 and Y = -3 => X < -Y. The answer is YES.
However, if X = 2 > 0 and Y = 1 => X > -Y. The answer is NO. No unique answer. Insufficient.

S2: Y>0

Since X > Y and Y > 0, X is also positive, so the inequality X < -Y does not exist. Sufficient.

Answer: B

Hope this helps!

-Jay
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