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positive?

by sanju09 » Thu Aug 26, 2010 8:52 pm
Is a b positive?

(1) (a + b )^2 < (a - b) ^2.
(2) a = b.


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by vijaynaik » Thu Aug 26, 2010 8:59 pm
B.

1) a, b can be any numbers. Not suff.
2) since a = b, ab will be always postive. Suff.
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by sanju09 » Thu Aug 26, 2010 9:12 pm
vijaynaik wrote:B.

1) a, b can be any numbers. Not suff.
2) since a = b, ab will be always postive. Suff.
what if a = b = 0?
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by Rahul@gurome » Thu Aug 26, 2010 9:15 pm
Consider first (1) alone.
It says (a + b )^2 < (a - b) ^2 or a^2 + b^2 + 2ab < a^2 + b^2 -2ab.
Or 4ab < 0.
Or ab < 0.
So ab is not positive .
Or (1) alone is sufficient to answer the question.

Next consider statement (2) alone.
It says a = b.
If a and b are not zero, ab = a^2 which has to be positive being a square.
But if a = b = 0, then ab is 0 which is not positive.
So we cannot say whether ab is positive or not.
Or (2) alone is not sufficient to answer the question.

The correct answer is (A).
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by vijaynaik » Thu Aug 26, 2010 9:46 pm
Thanks Rahul for the correct answer.
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