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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The remainder when the positive integer m is divided by 7 is  Question banks Downloads My Bookmarks Reviews Important topics
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Intern Joined: 30 Oct 2017
Posts: 31
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Kudos [?]: 7 , given: 6

The remainder when the positive integer m is divided by 7 is [#permalink] 00:00

Question Stats: 80% (01:15) correct 20% (02:42) wrong based on 15 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
Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3037 , given: 394

Re: The remainder when the positive integer m is divided by 7 is [#permalink]
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.
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Sandy
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Intern Joined: 27 Jun 2019
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Kudos [?]: 9 , given: 3

Re: The remainder when the positive integer m is divided by 7 is [#permalink]
Plugging in is the quickest way here. Re: The remainder when the positive integer m is divided by 7 is   [#permalink] 29 Aug 2019, 08:17
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