If X and Y are integers, does x = y?
1) xy = y2 (2 here is square)
2) x2 = y2 (2 here is square)

xy = y^2
x=y
Statement A is sufficient

x^2 = y^2
If x = (-5)^2 and y =5^2
Then x and y are not equal
If x = 5 and y = 5
Then x=y

Statement B is insufficient

gviren wrote:the question is
If X and Y are integers, does x = y?
1) xy = y2 (2 here is square)
2) x2 = y2 (2 here is square)

I think the answer should be B but OA is D.

(1) is insufficient as y can be 0 and the eqn will not satisfy

I'm not too convinced (1) is sufficient.

1 - insufficient
xy = y^2
y(x-y) = 0
(please note that you cannot cancel out y from both sides
without knowing that y != 0)

So, either y = 0 or x = y. 0 is an integer, so we cannot rule out y=0

2 - insufficient as well.
Take x = y = 5. Ofcourse x = y
Take x = 5 and y = -5. x is not equal to y

Taking both together, we know x = y.

I'd vote for C

Can someone please correct me if there's something amiss in my
reasoning.

I completely agree with jayhawk's reasoning

I do not understand how the OA can be D

It should be C!!