Am I missing something when I conclude that a divisor is the same thing as a factor?
eg
What is the greatest common divisor of positive integers m and n?
(1) m is a prime number
(2) 2n = 7m
I probably wasted 30 seconds trying to figure out what they meant by divisor. Aren't they just asking for the greatest common factor?
BTW- answer is C (need both)
Divisor = Factor?
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 152
- Joined: Wed Mar 12, 2008 4:36 pm
- Thanked: 8 times
- Followed by:2 members
The answer is C: If m is prime, the only way for 2n to be a factor of m is if m itself is 2, meaning n must be 7.
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Thought I'd post a full solution to this question.JDesai01 wrote: What is the greatest common divisor of positive integers m and n?
(1) m is a prime number
(2) 2n = 7m
Statement 1:
If m is a prime number, it has exactly 2 divisors (1 and m), so this tells us that the GCD of m and n must be either 1 or m.
Since we know nothing about n, statement 1 is not sufficient.
Statement 2:
If 2n = 7m then we can rearrange the equation to get n = (7/2)m
Important aside: Notice that if m were to equal an odd number, then n would not be an integer. For example, if m=3, then n=21/2. Similarly, if m=11, then n=77/2. For n to be an integer, m must be even.
If m must be even, it could be the case that m=2 and n=7, in which case the GCD=1
Or it could be the case that m=4 and n=14, in which case the GCD=2
Or it could be the case that m=10 and n=35, in which case the GCD=5 . . . and so on.
Since we cannot determine the GCD with any certainty, statement 2 is not sufficient.
Statements 1 & 2 combined
From statement 1, we know that m is prime, and from statement 2, we know that m is even.
Since 2 is the only even prime number, we can conclude that m must equal 2.
If m=2, then n must equal 7, which means that the GCD must be 1.
Since we are able to determine the GCD with certainty, statements 1 & 2 combined are sufficient, and the answer is C
Cheers,
Brent