IMO C


x ^ 2 = XY ???

(1) x ^ 2 – y ^ 2 = (x + 5) (y - 5)

In sufficient we dont know anything about X and Y

(2) x = y
In sufficient
When X is negtive and Y is positive this relationship doesnt hold good
When X and Y are positive it holds good

Combine
Substitue 2 in 1
0= (X+5)(y - 5)
so X=-5 and y= 5

We are sure now that the relationship is not true which means this is sufficient.
So C

Ans is A:
WHEN x=y
that leads to that fact that x^2=xy.

IMO B

Yes ,X= Y is enough

IMO B.

1.
x^2 - y^2 = xy - 5(x-y) -25
(x-y)(x+y) + 5 (x-y)= xy -25
(x-y)(x+y +5) = xy - 25

This is not leading to any result.

2.
x = y
Therefore, xy = x * x = x^2
Sufficient.

sanju09 wrote:Is x ^ 2 equal to x y?

(1) x ^ 2 – y ^ 2 = (x + 5) (y - 5)

(2) x = y


OA after few posts

question: lxl = lyl ?


Statement I

(x+y)(x-y) = (x+5)(y-5)

case I (a)

x+y = x+5

y=5

case I (b)

x-y = y -5

since y =5

x=5

x=y

case II (a)

x+y = y-5

x = -5

case II (b)

x-y = x+5

y=-5

x=y

Either case the statement is Sufficient.

Statement II

x=y

This is exactly what we need

Hence D.

OA?

DISCLAIMER: I am not an expert in GMAT and above is/are my two cents on the topic.

karmyogi's two cents answered it correctly.

Morgoth tried some extra hard to find some seed in 1 but it really never works.

hmboy17 picked the statement right but missed on the right choice name.