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Statement (1)

E = xy, and y is odd; E can be odd or even because for say y = 1 and x =1, E = 1, an odd number; whereas for x = 2 and y = 1, E = 2, an even number. No unique value. This statement alone is insufficient.

The correct answer would be among B/C/E.

Statement (2)

E = x/y, and x is odd; y*E = x = odd. For the product of two numbers (y*E) to be odd, both the numbers must be odd. Hence E cannot be even.

This statement alone is sufficient.

Correct choice is B.