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

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The remainder when the positive integer m is divided by 7 is [#permalink] New post 30 May 2018, 01:07
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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
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Re: The remainder when the positive integer m is divided by 7 is [#permalink] New post 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.
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Re: The remainder when the positive integer m is divided by 7 is   [#permalink] 05 Jun 2018, 13:22
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The remainder when the positive integer m is divided by 7 is

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