Bunuel wrote:

If A and B are positive integers, is B divisible by A?

(1) 2B/A is an integer.

(2) B^2/A is an integer.

From (1) 2B = k1*A => B = k1*A/2

If k1 is a non zero multiple of 2, then B is divisible by A. Since we do not know that information, (1) alone is insufficient.

From (2) B^2 = k2*A;

Can't say if B is a multiple of A or not. So (2) alone is insufficient.

Combining (1) & (2)

Substituting B = k1*A/2 in B^2 = k2*A

(k1^2*A^2)/4 = k2*A

k1^2 * A^2 = 4*k2*A

k1^2 * A = 4*k2

if A is equal to 1, then k1 is a multiple of 2, then answer would have been (C).

Since that is not the case here, answer is (E).