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Numbers - General Aptitude

Q1:

It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

A (216 + 1)

B (216 - 1)

C (7 x 223)

D (296 + 1)

ANS:D - (296 + 1)

Let 232 = x. Then, (232 + 1) = (x + 1). Let (x + 1) be completely divisible by the natural number N. Then, (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.