Question from practice.beatthegmat

[arnabis2good]

This is one DS question from practice.beatthegmat.com. Correct answer is A. Do we need to consider that x+y can be zero? Why so?

[djiddish98]

x+y can't be 0, since a number over x+y = 6 (provided in statement 1).

This is one of those problems where you can solve for x-y by reducing a statement

Statement 1: x^2 - y^2 -> (x-y)(x+y). We can cancel out the x+y portions of the statement and we're left with x-y = 6

Statement 2: we can consolidate to (x-y)^2 = 36. However, x-y could equal -6 or 6, so we're not quite sure yet.

[cans]

A) (x2-y2)/(x+y) = (x-y)(x+y)/(x+y)
If we consider x+y = 0, we get 0/0 which is indeterminate. But we know that L.H.S = 6,
It means x+y is not equal to 0, and thus x-y =6
Sufficient.

[VivianKerr]

Quick thought: I always like to keep in mind for this type of DS that we will never need to solve for the variables independently. Finding x - y does not mean we have to be able to find x and y separately.