Stmt1:
xy=y2
lets take x=1,y=0
and x=2,y=2
so not sufficient

Stmt2:
x2=y2
lets take x=-1,y=1
and x=2,y=2
so not sufficient

stmt1 & stmt2 together:

xy=y2 and x2=y2

lets take,
a) x=1,y=0
b) x=2,y=2
c) x=-1,y=1

a) can't be a choice due to stmt2
b) holds true
c) can't be a choice due to stmt1
Hence C

It is not D because of two issues:
1. statement 1: x could be 0 and y could be 1 and the statement would be true. Statement would also be true if x =1 and y=1. so different numbers make it true
2. x could be -2 and you could be 2, yet x2=y2. they would also equal if x=2 and y=2. therefore, we cannot definetely say that x=y according to statement 2.

If x and y are integers, does x = y?

1. xy=y^2
2. x^2=y^2

Statement 1

xy = y^2

Dividing by 'y' on both sides we have x=y, but be careful of doing this.

The statement also holds true when y=0, x can take any value and still satisfy the condition - Insufficient

Statement 2:

x^2=y^2

can be x=y=-2 (or) x=2 and y = -2 (satisfies condition but 2 possibilities - Insufficient)

Together,

From (1) and (2) we can say, when y=0, x will also be = 0 and 'x' and 'y' have equal signs (using 1) hence x=y - sufficient C

Seyitbek wrote:It is not D because of two issues:
1. statement 1: x could be 0 and y could be 1 and the statement would be true. Statement would also be true if x =1 and y=1. so different numbers make it true
2. x could be -2 and you could be 2, yet x2=y2. they would also equal if x=2 and y=2. therefore, we cannot definetely say that x=y according to statement 2.

My earlier post was not intended for this topic. Sorry for that!