Hi,
I got the correct answer but how would you explain the solution to this question?
If k, m, and t are positve integers and k/6+m/4=t/12, do t and 12 have a common factor greater than 1?
(1) k is a multiple of 3
(2) m is a multiple of 3
Cheers,
ds - factor difficult
This topic has expert replies
- MAAJ
- Master | Next Rank: 500 Posts
- Posts: 243
- Joined: Sun Jul 12, 2009 7:12 am
- Location: Dominican Republic
- Thanked: 31 times
- Followed by:2 members
- GMAT Score:480
IMO [spoiler](A)[/spoiler]
If k, m, and t are positive integers and (k/6) + (m/4) = (t/12), do t and 12 have a common factor greater than 1?
Multiply by 12 -> 2k + 3m = t
Prime factors of 12: 2,2,3
t and 12 share a prime factor other than 1?
Does t contains 2 or 3 in its prime factors?
(1) k is a multiple of 3
k -> 3,...?
2(3,...?) + 3m = t
(2,3,...?) + (3,m...?) = t
In words: Multiple of 3 + Multiple of 3 = t (THUS t must be a multiple of 3)
The rule is that a multiple of N (+/-) a multiple of N results in a multiple of N
So t -> 3,...? So YES, it shares a factor greater than 1
Sufficient
(2) m is a multiple of 3
2k + 3(3,...?) = t
(2,k,...?) + (3,3...?) = t
In words: Multiple of 2 + Multiple of 9 = t
In this case, we cannot determine if t is a multiple of 2 or 3
Example 1: 2 + 9 = 11 (neither multiple of 2, nor 3)
Example 2: 2 + 18 = 20 (multiple of 2)
Example 3: 6 + 9 = 15 (multiple of 3)
So this is insufficient
If k, m, and t are positive integers and (k/6) + (m/4) = (t/12), do t and 12 have a common factor greater than 1?
Multiply by 12 -> 2k + 3m = t
Prime factors of 12: 2,2,3
t and 12 share a prime factor other than 1?
Does t contains 2 or 3 in its prime factors?
(1) k is a multiple of 3
k -> 3,...?
2(3,...?) + 3m = t
(2,3,...?) + (3,m...?) = t
In words: Multiple of 3 + Multiple of 3 = t (THUS t must be a multiple of 3)
The rule is that a multiple of N (+/-) a multiple of N results in a multiple of N
So t -> 3,...? So YES, it shares a factor greater than 1
Sufficient
(2) m is a multiple of 3
2k + 3(3,...?) = t
(2,k,...?) + (3,3...?) = t
In words: Multiple of 2 + Multiple of 9 = t
In this case, we cannot determine if t is a multiple of 2 or 3
Example 1: 2 + 9 = 11 (neither multiple of 2, nor 3)
Example 2: 2 + 18 = 20 (multiple of 2)
Example 3: 6 + 9 = 15 (multiple of 3)
So this is insufficient
ccassel wrote:Hi,
I got the correct answer but how would you explain the solution to this question?
If k, m, and t are positve integers and k/6+m/4=t/12, do t and 12 have a common factor greater than 1?
(1) k is a multiple of 3
(2) m is a multiple of 3
Cheers,
Last edited by MAAJ on Tue Apr 05, 2011 8:26 pm, edited 1 time in total.
"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Solution:
It is given that k/6 + m/4 = t/12.
Multiply both right and left hand side with 12.
Or, 2k + 3m = t.
Consider first (1) alone.
It means that k = 3n, n being a positive integer.
Or, 6n + 3m = t.
Or, t = 3(m+2n).
This means that t is a multiple of 3.
So, t and 12 will always have a common factor of 3 apart from 1.
Hence, (1) alone is sufficient to answer the question.
Next, consider (2) alone.
It means that m = 3n, n being a positive integer.
Or, t = 9n + 2k.
This clearly does not indicate whether t and 12 have any common factor apart from 1.
Or (2) alone is not sufficient.
The correct answer is (A).
It is given that k/6 + m/4 = t/12.
Multiply both right and left hand side with 12.
Or, 2k + 3m = t.
Consider first (1) alone.
It means that k = 3n, n being a positive integer.
Or, 6n + 3m = t.
Or, t = 3(m+2n).
This means that t is a multiple of 3.
So, t and 12 will always have a common factor of 3 apart from 1.
Hence, (1) alone is sufficient to answer the question.
Next, consider (2) alone.
It means that m = 3n, n being a positive integer.
Or, t = 9n + 2k.
This clearly does not indicate whether t and 12 have any common factor apart from 1.
Or (2) alone is not sufficient.
The correct answer is (A).
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/