Probability Problem

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by Anurag@Gurome » Mon Aug 20, 2012 7:43 pm
everything's eventual wrote:If two out of four expressions x+y , x+5y, x-y, 5x - y, are chosen at rando, what is the possibility that their product will be of the form x^2 - (by)^2 where 'b' is an integer?

a) 1/2

b) 1/3

c) 1/4

d) 1/5

e) 1/6

OA : E
(x + y)(x + 5y) = x^2 + 6xy + 5y^2: Not in the form x^2- (by)^2
(x + y)(5x - y) = 5x^2 + 4xy - y^2: Not in the form
(x + 5y)(x - y) = x^2 + 4xy - 5y^2: Not in the form
(x + 5y)(5x - y) = 5x^2 + 24xy - 5y^2: Not in the form
(x - y)(5x - y) = 5x^2 - 6xy + y^2: Not in the form
(x + y)(x - y) = x^2 - y^2: This is in the required form

Hence, the required probability = [spoiler]1/6[/spoiler]

The correct answer is E.
Anurag Mairal, Ph.D., MBA
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