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If two of the four expressions x+y, x+5y, x-y, 5x+y are chosen at random

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If two of the four expressions x+y, x+5y, x-y, 5x+y are chosen at random, what is the probability that their product will be of the form of x^2 - (by)^2, where b is an integer?
A. ½
B. 1/3
C. ¼
D. 1/5
E. 1/6


Official Answer

1 Best Answer

Best answer

There are 4 expression which can be combined 4C2 ways i.e. 6 ways.

Since this has only 6 ways, it always better to compute/write all the expressions. Mostly one gets these questions wrong because of hurry. 

x+y, x+5y, x-y, 5x+y 

(x+y) ( x+5y) = NOT
(x+y) ( x-y )  = YES x^2 - y^2
(x+y) (5x+y)  = NOT
(x+5y)(x -y)  = NOT

(x+5y) (5x+y)= NOT
(5x+y)   = NOT
Hence only 1 forms the required expression. 
Probability =  1/6 
hence E is the answer

answered Jun 12, 2014 by Partner (696 points)
selected Jul 21, 2014 by
perfect. i made the same mistake did it in a hurry and that costed me the question.
commented Jun 12, 2014 by Senior Associate (475 points)
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