It is currently 17 Nov 2018, 03:22

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The remainder when the positive integer m is divided by 7 is

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Intern
Joined: 30 Oct 2017
Posts: 30
Followers: 0

Kudos [?]: 7 [0], given: 6

The remainder when the positive integer m is divided by 7 is [#permalink]  30 May 2018, 01:07
00:00

Question Stats:

100% (01:07) correct 0% (00:00) wrong based on 3 sessions
The remainder when the positive integer m is divided by 7 is x. The remainder when m is divided by 14 is x + 7. Which one of the following could m equal?

(A) 45

(B) 53

(C) 72

(D) 85

(E) 100
[Reveal] Spoiler: OA

Last edited by Carcass on 30 May 2018, 16:07, edited 1 time in total.
Edited by Carcass
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

Re: The remainder when the positive integer m is divided by 7 is [#permalink]  05 Jun 2018, 13:22
Expert's post
Lets re-write $$m= 7k+x$$. In this way when you divide $$m$$ by 7 you get a remainder of $$x$$.

Also given that $$\frac{m}{14}= \frac{7k+x}{14}$$ has a remainder $$x+7$$.

So rearranging $$7k+x$$ as $$7(k-1)+ x+7$$. Since $$\frac{7k+x}{14}=\frac{7(k-1)+ x+7}{14}$$ has a remainder $$x+7$$. $$7(k-1)$$ must be divisible by 14 or $$k-1$$ must be divisible by 2.

k can be any odd number 3,5,... and x has to be less than 7.

So looking at the options one by one...

(A) 45 = 7*6 + 3 No

(B) 53 = 7*7+ 4 yes

(C) 72 = 7*8 No

(D) 85 = 7*12 +1 No

(E) 100= 7*14 +2 No

Hence B.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Re: The remainder when the positive integer m is divided by 7 is   [#permalink] 05 Jun 2018, 13:22
Display posts from previous: Sort by

# The remainder when the positive integer m is divided by 7 is

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.