factors

[anksgupta]

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

OA is E

Please discuss your approach also

[SanjeevK]

Since pq have only 4 factors, both p and q should be prime number (other wise the number of factors will be more than 4)
The factors will be 1,p,q,pq

a: p+q is odd integer. This is posible only when either p or q is 2. Remember 2 is the only even prime number.
pq can be 2x3, 2x5, 2x7 ...

Hence insufficient

b: q<p. This doesn't provide any information
Together A and B doesn't provide unique solution. It just tells that q = 2
IMO E

[yogami]

Under such situations when they say a certain number has lets say m factors, does it mean that those m factors are distinct or not? I am going to assume that they are not distinct unless otherwise stated

[Claret]

The answer is 'E'

f(pq) = 4 implies that p and q are prime nos.

Statement 1 : Insufficient
p+q = odd, this possible when one in b/w p and q is 2

Statement 2 : insufficient

q<p this statement by itself does not give any specific pair of prime nos
hence insufficient

statement 1 & 2 : insufficient
Together these statements imply that q=2 but a unique value of p is still not possible (p can be any prime no other than 2)

Confirm the answer..

@yogami : yes they imply distinct factors