smclean23 wrote:If x, y, and z are positive integers, is x – y odd ?
(1) x=z^2
(2) y=(z-1)^2



Answer is C.

What is a quicker way?

i am not sure if its a quickest way.. but plugging can also help u do this problem in less than 2 mints...u shud realise that X can either Even/Odd depending on Z. and Y can be Even/Odd depending on Z though Mutually exclusive i mean both cant be even or odd at the same time .

if u realise that its a plain ride from there on.

I go with C as well..

smclean23 wrote:If x, y, and z are positive integers, is x – y odd ?
(1) x=z^2
(2) y=(z-1)^2



Answer is C.

What is a quicker way?

Since you don't post any way, it's hard to say what's a "quicker way"!

However, here goes:

(1) nothing about y, so insufficient.

(2) nothing about x, so insufficient.

Together: Out of z and (z-1), one will be even and one will be odd (since they're consecutive integers). Accordingly, out of z^2 and (z-1)^2 one will be even and one will be odd.

So, we know that out of x and y, one is even and one is odd. Since:

O - E = O

and

E - O = O

we know for sure that x - y IS odd: together sufficient, choose (C).