If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105 ?
(1) x is a multiple of 9
(2) y is a multiple of 25
Source: OG-12
[spoiler]OA: (B)[/spoiler]
Im unable to understand OG's explanation for this problem. Can someone explain how to solve such kind of DS problems in a simpler way?
If positive integer x..
This topic has expert replies
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
x = 2 * 3Elena89 wrote:If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105 ?
(1) x is a multiple of 9
(2) y is a multiple of 25
Source: OG-12
[spoiler]OA: (B)[/spoiler]
Im unable to understand OG's explanation for this problem. Can someone explain how to solve such kind of DS problems in a simpler way?
y = 2 * 7
105 = 3 * 5 * 7
x * y = 2² * 3 * 7
For xy to be a multiple of 105, we need at least one 3, 5, and 7 among the factors. So, the missing number is 5, as 3 and 7 are already there.
(1) x is a multiple of 9 but this does not imply anything about the missing factor, 5; NOT sufficient.
(2) y is a multiple of 25 and 25 = 5 * 5, which answers the question; SUFFICIENT.
The correct answer is B.
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/
-
- Newbie | Next Rank: 10 Posts
- Posts: 2
- Joined: Sat Oct 03, 2009 5:18 am
Anurag ,
x = 2 * 3
y = 2 * 7
105 = 3 * 5 * 7
x * y = 2² * 3 * 7
My thought was X * Y can have 2 * 3 * 7 definitely (Where 2 in either X or Y can be redundant).
Please clarify
x = 2 * 3
y = 2 * 7
105 = 3 * 5 * 7
x * y = 2² * 3 * 7
My thought was X * Y can have 2 * 3 * 7 definitely (Where 2 in either X or Y can be redundant).
Please clarify
- neelgandham
- Community Manager
- Posts: 1060
- Joined: Fri May 13, 2011 6:46 am
- Location: Utrecht, The Netherlands
- Thanked: 318 times
- Followed by:52 members
If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105 ?.
I will try and rephrase the question for better understanding.
Since, x is a multiple of 6 it can be written in the form x = 6*m, where m is a non zero integer.
Since, y is a multiple of 14 it can be written in the form y = 14*n, where y is a non zero integer.
x*y = 6*m*14*m = 2*3*7*2*m*n = (105)*(4*m*n/5). For x*y to be a multiple of 105, 4*m*n/5 should be an integer. i.e. m or n should be a multiple of 5. The question can be rephrased to
'If x = 6*m and y = 14*n, Is m or n a multiple of 5?'
If x = 90 then the value of m is 15. m is a multiple of 5.
So, statement I is insufficient to answer the question.
Now, y = 350*l = 14*n.
25*l = n. So, n is a multiple of 25(and of 5).
Statement II is sufficient to answer the question.
IMO B
p.s: It is just another approach but Anurag's approach is the better one.
I will try and rephrase the question for better understanding.
Since, x is a multiple of 6 it can be written in the form x = 6*m, where m is a non zero integer.
Since, y is a multiple of 14 it can be written in the form y = 14*n, where y is a non zero integer.
x*y = 6*m*14*m = 2*3*7*2*m*n = (105)*(4*m*n/5). For x*y to be a multiple of 105, 4*m*n/5 should be an integer. i.e. m or n should be a multiple of 5. The question can be rephrased to
'If x = 6*m and y = 14*n, Is m or n a multiple of 5?'
If x = 18 then the value of m is 3. m is not a multiple of 5.(1) x is a multiple of 9
If x = 90 then the value of m is 15. m is a multiple of 5.
So, statement I is insufficient to answer the question.
y is a multiple of 25 and 14. So, y is a multiple of 25*14(because you con't have any common multiples between 25 and 14). i.e. y = 350*l, where l is a non zero integer.(2) y is a multiple of 25
Now, y = 350*l = 14*n.
25*l = n. So, n is a multiple of 25(and of 5).
Statement II is sufficient to answer the question.
IMO B
p.s: It is just another approach but Anurag's approach is the better one.
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/