GMAT Test 2_PS Primes #25

kwah wrote:Attached is a question from GMAT Prep Test 2.

Please advise how to achieve the result.

Answer: C

Thanks,
K

Length of an integer is the sum of the powers of its prime factors.

Length of 6 implies that the sum of the powers of primes of two-digit integer must be 6.
Now 5 can not be a factor of this integer because the smallest integer with the length of 6 that has 5 as prime factor is 2^5 * 5 = 160, which is not a two-digit integer.

So, the primes of the two-digit integers are 2 and 3, which implies n = 2^a * 3^b, so that a + b = 6
If a = 6, b = 0, then n = 2^6 = 64 (length = 6 + 0 = 6)
If a = 5, b = 1, then n = 2^5 * 3^1 = 32 * 3 = 96 (length = 5 + 1 = 6)
If a = 4, b = 2, then n = 2^4 * 3^2 = 16 * 9 = 144 (length = 5 + 1 = 6) but 144 is not a two-digit integer.

The correct answer is C.