Hi M7MBA,

It looks like the prompt that you posted is incomplete. Here is the full version:

If p and q are positive integers such that pq has exactly 4 unique positive factors and p < q, what is the value of the integer p?

(1) The sum of p and q is an odd integer.
(2) The difference between p and q is 1.

We're told that P and Q are POSITIVE INTEGERS, (P)(Q) has EXACTLY 4 factors and P < Q. We're asked for the value of P. This question can be solved with a mix of Number Properties and by TESTing VALUES.

(1) The sum of P and Q is an ODD integer.

Fact 1 tells us that P+Q = ODD, so one of the values is EVEN and one is ODD.
IF....
P=1, Q=6, then P+Q = 7, (P)(Q) = 6, the factors are 1, 2, 3 and 6 and the answer to the question is 1.
P=2, Q=3, then P+Q = 5, (P)(Q) = 6, the factors are 1, 2, 3 and 6 and the answer to the question is 2.
Fact 1 is INSUFFICIENT

(2) The difference between P and Q is 1.

The information in Fact 2 ALSO proves that one of the values is EVEN and one is ODD, but also includes the 'restriction' that the two values differ by just 1 - and that severely limits the possibilities. If the even integer is anything greater than 2, then we'll end up with MORE than 4 factors. If P=1, Q=2, then we only end up with TWO factors - but we're supposed to have FOUR. Thus, the only pair of positive integers that 'fit' these restrictions is P=2 and Q=3 and the answer to the question is ALWAYS 2.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Maybe I'm not caffeinated enough, but I disagree with the answer here.

Here's how I would approach this. For pq to have exactly 4 factors, p and q would both need to be prime numbers, so the four factors would be 1, p, q, and pq. So in the stem we are essentially given an additional piece of info that p and q are prime numbers.

For the first statement if p + q is odd, we must be adding an odd and an even number. The only even prime is 2, so one of the numbers must be 2. We also know that 2 must be the smaller number since the only positive number smaller than 2 is 1 and 1 is not prime. So then we know p has to be 2 and this statement is sufficient. Narrow down the choices to A and D.

For the second statement, we also know we have to have an even and an odd...specifically two consecutive numbers to give us a difference of 1. So again we know 2 has to be one of the numbers since it is the only even, prime number and the other number has to be 3 since 1 is not prime. Since p has to be the smaller of the two numbers, p again is 2 and the answer is D.

Anyone else think the answer is actually D?