f(n) = the number of factors of n

[abhi332]

The function f(n) = the number of factors of n. If p and q are positive integers and f(pq) = 4, what is the value of p?

(1) p + q is an odd integer

(2) q is less than p

[spoiler]OA : E[/spoiler]

[firdaus117]

As 4=2*2 and 4*1,
pq=Product of two prime numbers or a*a^2 or 1 and a^3 where a is a prime number.
Condition 1.The set of p,q can be 2 and 5/7/11/13.....any prime number.Another possible set can be: 1 and 8.........Hence no unique value of p.Insufficient.
Condition 2.Here no restriction on p+q to be odd.We can have set of p,q as 2,4 or 5,25 or 7,49.Again,no unique p.Insuff.
Combining both,still no unique value for p.
Hence,Option E

[vineetbatra]

As 4=2*2 and 4*1,
pq=Product of two prime numbers or a*a^2 or 1 and a^3 where a is a prime number.
,Option E

Why do you say that P and Q are Prime Numbers?

[sivareddy]

this can be solved easily..

to get 4 factors.. u can have a cube term like 8 (2power 3) which has four factors like 1,2,4,8 or a 2*2 factors like a 6 which has 1,2,3,6 as factors..

first statement says sum is odd, true for both cases and second statement too is true for both cases and u cant decice..

So none of the statements is sufficient.. and together they are not sufficient too..

Cheers,
Siva
GMAT Aspirant

[sivareddy]

sorry p and q for cases are 1 and 8 for the cube case and 2 and 3 for the 2*2 case..


Cheers,
Siva
GMAT Aspirant