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Is p = q?

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Is p = q?

by sanju09 » Mon Mar 26, 2012 12:52 am
Is p = q?
(1) (p + q)^2 / pq = 4.
(2) p^2 − q^2 − 150p + 150q = 0.
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by Anurag@Gurome » Mon Mar 26, 2012 1:04 am
sanju09 wrote:Is p = q?
(1) (p + q)^2 / pq = 4.
(2) p^2 − q^2 − 150p + 150q = 0.
(1) (p + q)² / pq = 4 implies (p + q)² = 4pq
p² + q² + 2pq = 4pq
p² + q² - 2pq = 0
(p - q)² = 0 implies p = q; SUFFICIENT.

(2) p² − q² − 150p + 150q = 0
(p + q)(p - q) − 150p + 150q = 0
(p + q)(p - q) − 150[p - q] = 0
(p - q)[p + q - 150] = 0 implies p = q or p + q = 150; NOT sufficient.

The correct answer is A.
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