Multiples

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vongdn: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Aug 14, 2010 9:24 pm

by vongdn » Sat Oct 02, 2010 10:20 pm

Is the integer N a multiple of 15?

(1) N is a multiple of 20
(2) N+6 is a multiple of 3

What is the method or process to solving this?

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Source: Beat The GMAT — Data Sufficiency | Sat Oct 02, 2010 10:20 pm

gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sat Oct 02, 2010 11:44 pm

Plug in numbers.

Pick C

Let N = 60,

N is a multiple of 20 -- YES

N+6 is a multiple of 3 - YES

Is the integer N a multiple of 15? --YES

Another example N = 120

N is a multiple of 20 -- YES

N+6 is a multiple of 3 - YES

Is the integer N a multiple of 15? --YES

St 1 & St2 alone is insufficient

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 amFollowed by: 24 members; Location: Bangalore, India; Thanked: 146 times

by shovan85 » Sat Oct 02, 2010 11:52 pm

from 1 N=20k (k=1,2,3....)
when N=60 then multiple of 15 but when N=80 the not a multiple of 15. So Not Suff.

from 2 N+6 = 3k (k=2,3,4....)
6 is a multiple of 3 so N will be also a multiple of 3 (Say 9=3+6 so N=3)
but we cannot say as some cases it will be multiple of 15 and some cases it will not be. So NS.

Combine both
if N=20k when k=1 then N=20 at the same time from 2 N+6 = 26 which will not be a multiple of 3
if N=20k when k=2 then N=40 at the same time from 2 N+6 = 46 which will not be a multiple of 3
if N=20k when k=3 then N=60 at the same time from 2 N+6 = 66 which will be a multiple of 3
if N=20k when k=4 then N=80 at the same time from 2 N+6 = 86 which will not be a multiple of 3
if N=20k when k=5 then N=100 at the same time from 2 N+6 = 106 which will not be a multiple of 3
if N=20k when k=6 then N=120 at the same time from 2 N+6 = 126 which will be a multiple of 3...

So when both (1) and (2) are satisfied we are getting a proper result.

IMOC

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sun Oct 03, 2010 7:01 am

(1) If N = 40, then N is not a multiple of 15
If N = 60, then N is a multiple of 15.
No unique answer.
So, (1) is NOT SUFFICIENT.

(2) If N = 30, then N + 6 = 36, is a multiple of 3 and N is a multiple of 15.
If N = 33, then N + 6 = 39, is a multiple of 3 and N is not a multiple of 15.
No unique answer.
So, (2) is NOT SUFFICIENT.

Combining (1) and (2), If N = 60, then N + 6 = 66, a multiple of 3; here N is a multiple of 15.
If N = 90, then N + 6 = 96, again a multiple of 3; here also N is a multiple of 15.
We can see for any other value also, that combining (1) and (2), we see that N is a multiple of 15.

[spoiler]The correct answer is (C).[/spoiler]

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sun Oct 03, 2010 10:21 am

vongdn wrote:Is the integer N a multiple of 15?

(1) N is a multiple of 20
(2) N+6 is a multiple of 3

What is the method or process to solving this?

N is a multiple of 15 if N is a multiple of both 3 and 5. From Statement 1, we learn that N is a multiple of 5. From Statement 2 we learn that N is a multiple of 3. So the answer is C.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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