If xxyy is a perfect square then x + y =?

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Question

If xxyy is a perfect square then x + y =?

Options:

A . 9

B . 10

C . 11

D . 12

Answer: Option C
:
C

xxyy = xx00 + yy = 11(x00 + y) = 11(x0y)

xxyy is a perfect square, so if one divisor is 11, then there should be one more 11 to get $11^{2}$ .

As xxyy = 11(x0y), x0y should be divisible by 11, so x + y has to 11.

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