* Divisibility Question

[kyle.steiner123]

I think the answer to a question I was reviewing might be wrong but I am terrible with # properties so I wanted to check with someone on here.

Q: If N=6P where P is a prime number greater that 2, how many different positive even divisors does N have, including itself?

A) Two
B) Three
C) Four
D) Six
E) Eight

The provided answer key says that (C) Four is the correct answer but if you use P=3 (satisfies both the prime constraint and is greater than 2) the only positive even factors are 2, 6, and 18 (three total). However, if you use P=5 (also satisfies all constraints) the only positive even factors are 2, 6, 10 and 30 (four total) meaning the answer cannot be determined with the given information (sometimes 3 and sometimes 4).

Please let me know what I am missing here or if the answer key is wrong. Thanks.

**This problem is from the GMAT Math Bible written by Jeff Sackmann copyright 2007**

[RonPurewal]

Hi,
Yes, this problem has issues.

To generalize, if p is 3, then the factors 2p and 6 are the same number (so that there are only three even factors -- 2, 6, and 18).

If p is any number greater than 3, then 2p and 6 are different numbers. In that case, there will be four different even factors: 2, 2p, 6, and 6p[/i].

By the way, please read the forum rules (top thread of every folder, including the one you're in). When you post questions in this folder, you must cite the original source of the problem.
Please do so within the next week or two, or else we'll have to lock and/or delete the thread.

Thanks.