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

Redeem

m and n non-zero integers

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Feb 21, 2016 9:33 pm
If m and n are nonzero integers, is m/n an integer?
(1) 2m is divisible by n
(2) m is divisible by 2n
Let's rephrase this target question.
If m/n is an integer, then we know that m = nk where k is an integer.
So, let's rephrase this target question as: Does m = kn for some integer k?

Statement 1: 2m is divisible by n
This means that 2m = qn for some integer q.
Divide both sides by 2 to get: m = (q/2)n
Do we have enough information to answer the target question? In other words, Does m = kn for some integer k?
Since (q/2) may or may not be an integer, we do not have sufficient information.

Statement 2: m is divisible by 2n
This means that m = q(2n) for some integer q.
Or we can write: m = 2qn
Do we have enough information to answer the target question? In other words, Does m = kn for some integer k?
Yes! Since q is an integer, we know that (2q) must be an integer.
So, we can be certain that m = kn for some integer k?
As such, statement 2 is sufficient, and the answer is B.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pm
Thanked: 1443 times
Followed by:247 members

by ceilidh.erickson » Mon Feb 22, 2016 9:38 am
The other option here is to TEST NUMBERS, trying to prove insufficiency.

Target question: If m and n are nonzero integers, is m/n an integer?

(1) 2m is divisible by n

ex.: m = 6 and n = 3 --> this obeys the statement, because (2)(6) is divisible by 3. 6 is divisible by 3, so this gives us a "YES" answer to the question.

Now try to come up with an example that keeps the statement true but gives us a "NO" answer...

ex.: m = 3 and n = 6 --> this obeys the statement, because (2)(3) is divisible by 6. However, 3 is NOT divisible by 6, so this gives us a "NO" answer to the question.

Insufficient.

(2) m is divisible by 2n

ex.: m = 6 and n = 3 --> this obeys the statement, because 6 is divisible by (2)(3). 6 is divisible by 3, so this gives us a "YES" answer to the question.

Now try to come up with an example that keeps the statement true but gives us a "NO" answer...

We can't! If m is divisible by 2n, it must be divisible by both component pieces: 2 and n. There are no numbers we could come up with that would keep the statement true but give us a "NO" answer to the question.

Sufficient. The answer is B.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pm
Thanked: 1443 times
Followed by:247 members

by ceilidh.erickson » Mon Feb 22, 2016 9:40 am
For a more complex variation on the same idea, try DS #149 in OG 2016:
A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?

(1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.

(2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
Top
Post new topic Post Reply
• Page 1 of 1