Problem Solving

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

I picked B) because to get that form you have to have (x+y) (x-y) format. Since b exists there must be an integer in front of y.

Total of 4 equations pick 2 = 4! / 2!2! = 12/6 = 6 combinations possible

(x+y) x (x - y)
(x + 5y) ( x - y)

Both work, no? Where b is an integer (doesn't 1 couint too?)

2/6 = 1/3

Thanks for your help!

You need to rule out (x+5y)(x-y).

The above equation gives you x^2+4xy-5y^2, which doesn't fit the pattern.

Tud, thanks! Didn't realize that... silly mistakes get me again!

This type of error is what I need to fix to get past 45 in Quant : (

the simplar think is is as he is asking the

x^2 - y^2 = (x+y)(x-y)

this is attaained only when the format is in the above fashion so we had only one option in the list above.

hence it is 1/6