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Is x > y?

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by VJesus12 » Fri Apr 06, 2018 2:24 am
Is x > y?

(1) x + y > 0

(2) x^2 - y^2 > 0

The OA is C .

Why is not sufficient the statement (1)? Also, how can I use both statements to get an answer? Help!!! <i class="em em-frowning"></i>
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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Apr 06, 2018 5:40 am
VJesus12 wrote:Is x > y?

(1) x + y > 0

(2) x^2 - y^2 > 0
Statement 1:
If x=1 and y=0, then the answer to the question stem is YES.
If x=0 and y=1, then the answer to the question stem is NO.
INSUFFICIENT.

Statement 2:
If x=1 and y=0, then the answer to the question stem is YES.
If x=-1 and y=0, then the answer to the question stem is NO.
INSUFFICIENT.

Statements combined:
Statement 2 can be rephrased as follows:
(x+y)(x-y) > 0.
Since x+y is POSITIVE, x-y must also be POSITIVE:
x-y > 0
x > y.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is C.
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by [email protected] » Sat Apr 14, 2018 4:48 pm
Hi VJesus12,

We're asked if X is greater than Y. This is a YES/NO question. It can be solved by TESTing VALUES (as Mitch has shown); it can also be dealt with 'conceptually.'

1) (X + Y) > 0

Since (X+Y) is greater than 0, we know that AT LEAST one of the two variables is POSITIVE, but we don't know whether it's just one or both AND we don't know whether X is greater than Y or not.
Fact 1 is INSUFFICIENT

2) X^2 - Y^2 > 0

Fact 2 can be rewritten as X^2 > Y^2. This ultimately means that |X| is great than |Y|, but we don't know whether X is actually greater than Y or not (for example, X=2 and Y=1 is a possible solution.... but so is X = -2, Y = 1).
Fact 2 is INSUFFICIENT

Combined, we know...
(X + Y) > 0
X^2 > Y^2
If X and Y are both positive, then we now that X will be greater than Y (since X^2 > Y^2) and the answer to the question is YES.
If there is one positive and one negative, then for (X+Y) to be greater than 0, one of the variables must be "more positive" than the other is "negative" (for example +3 and -2). With the added information that X^2 > Y^2, we know that X would have to be the positive value, so X would ALWAYS be greater than Y and the answer would also be YES.
Thus, the answer is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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