If r and s are positive integers, is r/s an integer?
1) Every factor of s is also a factor of r.
2) Every prime factor of s is also a prime factor of r.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Is r/s an integer?
This topic has expert replies
-
Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Joined: Fri May 21, 2010 1:30 am
- Thanked: 335 times
- Followed by:98 members
the difference between the two statements is subtle but important. If every factor of s is a factor of r, then s itself must be a factor of r (every integer is a factor of itself) and r/s must be an integer. On the other hand, if every prime factor of s is a prime factor of r, s and r could be the same thing (r/s would be an integer) but they could also be s=2^2 and r=2 (r/s would not be an integer). The full solution below is taken from the GMATFix App.
-Patrick
-Patrick
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi EricKryk,
This DS question is based on Number Properties - a group of specific math rules that the GMAT tends to test frequently.
We're told that R and S are positive integers. We're asked "Is R/S an integer?" This is a YES/NO question.
Fact 1: EVERY factor of S is also a factor of R
This means that EVERY number that divides evenly into S also divides evenly into R. By definition, R/S will be an integer. Here's why:
If S = 4, then we know that S is evenly divisible by 1, 2 and 4. According to Fact 1, those numbers must also divide into R...
R could = 4, 8, 12, 16, etc.
4/4 = 1 = YES
8/4 = 2 = YES
12/4 = 3 = YES
16/4 = 4 = YES
Since everything that divides into S must divide into R, we know that R is a MULTIPLE of S. By extension, R/S will be an integer.
Fact 1 is SUFFICIENT
Fact 2: Every PRIME factor of S is also a prime factor of R.
Here we have a different Number Property: All of the PRIME numbers that divide into S will also divide into R. The problem with this piece of information is that repetition of primes is something you have to account for.
If S = 4, then it has just one prime factor: 2. So, 2 must divide into R.
If R = 2, then R/S = 2/4 = NOT an integer = NO
If R = 4, then R/S = 1 = YES
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This DS question is based on Number Properties - a group of specific math rules that the GMAT tends to test frequently.
We're told that R and S are positive integers. We're asked "Is R/S an integer?" This is a YES/NO question.
Fact 1: EVERY factor of S is also a factor of R
This means that EVERY number that divides evenly into S also divides evenly into R. By definition, R/S will be an integer. Here's why:
If S = 4, then we know that S is evenly divisible by 1, 2 and 4. According to Fact 1, those numbers must also divide into R...
R could = 4, 8, 12, 16, etc.
4/4 = 1 = YES
8/4 = 2 = YES
12/4 = 3 = YES
16/4 = 4 = YES
Since everything that divides into S must divide into R, we know that R is a MULTIPLE of S. By extension, R/S will be an integer.
Fact 1 is SUFFICIENT
Fact 2: Every PRIME factor of S is also a prime factor of R.
Here we have a different Number Property: All of the PRIME numbers that divide into S will also divide into R. The problem with this piece of information is that repetition of primes is something you have to account for.
If S = 4, then it has just one prime factor: 2. So, 2 must divide into R.
If R = 2, then R/S = 2/4 = NOT an integer = NO
If R = 4, then R/S = 1 = YES
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
