please explain this probability problem

[vishalrb]

What is the probability that two distinct members of set S={p-q,7p+q,7p-q,7p+7q,7p-7q} when chosen at random, will have a product of the form (mp)^2-(nq)^2, where m & n are integers?

Options:

A: 1
B:1/2
C:1/3
D:1/4
E:1/5

Thanks for helping.

Source: Knewton

[clock60]

if i got the problem my answer is E
imagine we have 5 distinct numbers
x1=(p-q), x2=(7p+q), x3=(7p-q), x4=(7p+7q), x5=(7p-7q), from them we can form 10 distinct pairs, 5C2=10.
and only pairs (x2 x3)=(7p+q)(7p-q)=49p^2-q^2,and (x4 x5)=(7p+7q)(7p-7q)=49p^2-49q^2 will give the desired result
2/10=1/5

[vishalrb]

Thanks Clock60,

After looking at ur reply, I realized that question is asking to find out product of pairs which can form as below,

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

thanks again.