MGMAT Challenge Questions Archive

[jainvikasvirgo]

Source: MGMAT Challenge Questions Archive

Q: In question in 28-October-2002 archive:
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

In the explanation section, the following explanation DOES NOT hold true for numbers
2 and 4. Please explain?
"Any product pq must have the following factors: {1, p, q, and pq}. If the product pq has no additional factors, the p and q must be prime"

[ps63739]

Yes, never thought of 2 and 4. If not considering, then it should be C.

What's the right answer?

[shailesh244]

1) p+q= odd, means one of p and q is even and other is odd. OR both are odd.
lets consider one even and one odd.
then it indicates pq is even.
p=1, q= 6,p+q-> odd , pq -->even ,f(6)=n(1,2,3,6)=4
p=2, q= 3,p+q->odd, pq -->even ,f(6)=n(1,2,3,6)=4

P could have more than 1 value so st.1 is insufficient.

2)q< p
lets
p=6, q= 1, q< p, f(6)=n(1,2,3,6)=4
p=3, q= 2, q< p, f(6)=n(1,2,3,6)=4

Still P can have more than 1 value so st.2 is also Insufficient.

Combining 1 and 2
p=6, q= 1, q< p and p+q-> odd
p=3, q= 2, q< p and p+q-> odd

So p can still have more than 1 value ,so E should be the answer.