sum of area of black squares(1000) + sum of area of white rectangles(X) = area of the larger square (Y)

From the options, X is an integer, hence Y (= X + 1000) is an integer too.

As Y is a square number, From the properties of square numbers, Y can only end with 0,1,4,6,9 or 25.

From the given options, only B (ending 6) is a possible solution, as +1000 doesn't change unit digit value.

Number ending 2 or 8 + 1000 (as in all other options) can never be a square number.

Besides, all of the above ways are equally correct.

_________________

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