If a number is the square of an integer, then in the prime factorization of that number, all of the exponents will be even. For example, (3^8)(5^6) is the square of an integer (it is the square of (3^4)(5^3) ) whereas (3^7)(5^6) is not.
Statement 1 tells us that in the prime factorization of (2^2)(n), all of the exponents are even. The prime factorization of n is identical to that of (2^2)(n) except that in n, the exponent on the '2' is smaller by two, and subtracting two doesn't change an even number to an odd number. So if the exponents in (2^2)(n) are even, so are the exponents in n, and Statement 1 is sufficient.
Statement 2 tells us that in the prime factorization of n^3, all of the exponents are even. The exponents in the prime factorization n^3 are all 3 times as big as the exponents in the prime factorization of n. Multiplying by 3 doesn't change evenness or oddness, so if all the exponents in n^3 are even, so are the exponents in n, and Statement 2 is also sufficient.
The answer is D.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com