Challenging question 10/28/2002

[a.amitgarg]

Question:
10/28/02
Question
The function f(n) = the number of factors of n. If f(pq) = 4, what is the value of the integer p?

(1) p + q is an odd integer

(2) q < p

(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.


It is assumed that P and Q are prime numbers while providing the solution. Hence it was said using both (1) and (2) that Q =2. There could be a case where Q = 1, P = 2pow3. In that q < P, and P+Q = odd. Also the number of factors = 4 which satisfies f(pq) = 4.

Answer E is correct as in the solution but the explanation is not correct. Please tell me if i am missing any concept here.

[esledge]

It is assumed that P and Q are prime numbers while providing the solution. Hence it was said using both (1) and (2) that Q =2. There could be a case where Q = 1, P = 2pow3. In that q < P, and P+Q = odd. Also the number of factors = 4 which satisfies f(pq) = 4.

Answer E is correct as in the solution but the explanation is not correct. Please tell me if i am missing any concept here.

You are correct, we shouldn't assume that p and q are primes. In addition to the case you cite, it could be that q = 1 and p = 6, which satisfies both q < p and p+q = odd.

I'll recommend a revision to the explanation. Nice catch, thanks!