If n=3x4xp, where p is a prime number greater than 3, how many different positive non-prime divisors does n have, excluding 1 and n ?
A) Six
B) Seven
C) Eight
D) Nine
E) Ten
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
PS Question
This topic has expert replies
-
adthedaddy
- Master | Next Rank: 500 Posts
- Posts: 167
- Joined: Fri Mar 09, 2012 8:35 pm
- Thanked: 39 times
- Followed by:3 members
"Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma - which is living with the results of other people's thinking. Don't let the noise of others' opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary" - Steve Jobs
-
Matt@VeritasPrep
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Your number has a prime factorization of 3¹ 4² p¹, so it has (1+1) * (2+1) * (1+1) = 12 unique factors.
It has THREE unique primes (2, 3, p) and TWO invalid factors (1, n), so 12 - 3 - 2 = 7.
This is easily checked by choosing a p value, e.g. p = 5. 3 * 4 * 5 = 60, which has the factors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The factors we want are 4, 6, 10, 12, 15, 20, and 30, so there are 7.
It has THREE unique primes (2, 3, p) and TWO invalid factors (1, n), so 12 - 3 - 2 = 7.
This is easily checked by choosing a p value, e.g. p = 5. 3 * 4 * 5 = 60, which has the factors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The factors we want are 4, 6, 10, 12, 15, 20, and 30, so there are 7.
