BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

If positive integer x..

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Sun Jul 31, 2011 9:39 pm
Thanked: 2 times
Followed by:1 members

If positive integer x..

by Elena89 » Wed Dec 14, 2011 2:35 am
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?
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
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

by Anurag@Gurome » Wed Dec 14, 2011 2:42 am
Elena89 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?
x = 2 * 3
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/
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Sat Oct 03, 2009 5:18 am

by smiles@Gmat » Mon Aug 27, 2012 9:47 pm
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
Top
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Mon Aug 27, 2012 10:53 pm
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?'
(1) x is a multiple of 9
If x = 18 then the value of m is 3. m is not 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.
(2) y is a multiple of 25
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.
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/
Top
Post new topic Post Reply
• Page 1 of 1