is k the square of an integer?

[showbu]

If k is a positive integer, is k the square of an integer?
(1) k is divisible by 4.
(2) k is divisible by exactly 4 different prime numbers.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

[peddisetty]

Statament 1: k is divisible by 4.
So K = 4,8,12,16,20,24.
4, 16 are squares of an integer. But 8,12,20 and 24 not.

(1) is insufficient.

Statement2 : k is divisible by exactly 4 different prime numbers
so k = 2*3*5*7, 3*5*7*11, 5*7*11*13.
Any k is not a square, which is sufficient.

So I choose B.

[Ian Stewart]

Statement2 : k is divisible by exactly 4 different prime numbers
so k = 2*3*5*7, 3*5*7*11, 5*7*11*13.
Any k is not a square, which is sufficient.

So I choose B.

But k could also be equal to (2^2)*(3^2)*(5^2)*(7^2), which is a perfect square (any number which has only even powers in its prime factorization is a perfect square). The answer is E.