Math Challenge : n, n + 2, and n + 4 are prime numbers

GRE Math Challenge Question

Q: n, n + 2, and n + 4 are prime numbers.

Quantity A	Quantity B
n(n + 2)(n + 4)	105

a) Quantity A is greater.
b) Quantity B is greater.
c) The two quantities are equal.
d) The relationship cannot be determined from the information given.

Explanation:

If n were even, so would be n + 2 and n + 4. Since there is only one even prime, n must be odd. What are the odd primes? 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, etc. Notice that as the primes increase, the spacing between them (generally, not strictly) increases. In this list of odd primes up to 41, there is only one set of three primes, each spaced two apart: 3, 5, and 7, which have a product of 105.

Is there any other set of three odd primes, each spaced two apart? Consider the odds that were skipped in the prime list above: 9, 15, 21, 25, 27, 33, 35, 39. They were skipped because they were either multiples of 3 or 5 (or both). Every third odd number is a multiple of 3, and thus not a prime. So the only three consecutive odds that are all primes are 3, 5, and 7. Quantity A can only be 105.

The correct answer is C.