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If y =|x|- x, is y> 0?

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Jan 13, 2017 8:04 am
NandishSS wrote:If y =|x|- x, is y> 0?
(1) x < 0
(2) y > 2
Statement 1:
Since y = |x| - x, we get:
y = |negative| - (negative) = positive + positive = positive.
Thus, y > 0.
SUFFICIENT.

Statement 2:
Since y > 2, it must be true that y > 0.
SUFFICIENT.

The correct answer is D.
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by [email protected] » Fri Jan 13, 2017 10:14 am
Hi NandishSS,

This question can be solved with Number Properties or by TESTing VALUES.

We're told that Y = |X| - X. We're asked if Y is greater than 0. This is a YES/NO question.

1) X < 0

IF...
X = -1
Y = |-1| - (-1) = 2 and the answer to the question is YES.

Notice how the math 'works' here: the absolute value of a negative (which is POSITIVE) minus a negative (which creates another POSITIVE)... means that Y will ALWAYS be positive when X is negative. Thus, the answer to the question would ALWAYS be YES.
Fact 1 is SUFFICIENT.

2) Y > 2

If Y is greater than 2, then the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer: D

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by Jay@ManhattanReview » Sat Jan 14, 2017 11:58 pm
NandishSS wrote:If y =|x|- x, is y> 0?
(1) x < 0
(2) y > 2

OA:D

Source:Math Revolution
Hi Nandish,

y =|x|- x can rewritten as:

1. y =|x| - |x|, if x is positive
=> y = 0
=> y is not less than 0.

2. y =|x| - x = 0, if x = 0
=> y = 0
=> y is not less than 0.

3. y =|x| + |x|, if x is negative
=> y = 2*|x| = a positive quantity
=> y > 0.

Let us see each statement one by one.

S1: x < 0 => x is negative. This is case 3 scenerio. Suffcient.

S2: y > 2 itself answers the question. A number greater than 2 means that the number is greater than 0. Sufficient.

Answer: D

Hope this helps!

-Jay
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