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DS1-10 #24 Is x^2 - y^2 a positive number?

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Source: — Data Sufficiency |
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by mp2437 » Fri Sep 25, 2009 11:22 am
first off, I expect statement 2 to be : "x+y is a positive number."

That being the case, you should know that:
x^2 - y^2 = (x+y)*(x-y). If you are told that statement 1 is a positive number, and statement 2 is a positive number, than 2 positive numbers multiplied by each other also equals a positive number.

Choice C is your answer.
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by swatirpr » Fri Sep 25, 2009 12:09 pm
Sorry for typo.

Here is the question again -

Is x^2 - y^2 a positive number?
(1) x - y is a positive number.
(2) x + y is a positive number.


Thanks for the reply.

My approch was:

First consider statement 1 alone -

since X - Y is positive
So X >Y
So X^2 > Y^2
(I guess I was wrong here, because even if y is smaller then x , y^2 could be greater then x^2 provided y is negative so Stat 1 is not sufficient)
Hence x^2 - y^2 is positive

Statement 1 is SUFFICIENT

Now consider statement 2 alone

x + y is positive number

it doesn't give any information whether x>y or y>x

so we can't find whether x^2>y^2 or y^2>x^2

statement 2 is NOT SUFFICIANT

so answer is A

I agree Answer is C

Thanks again.
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