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When positive integer n is divided by 5, the remainder is 1

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Re: When positive integer n is divided by 5, the remainder is 1 [#permalink] New post 11 May 2013, 10:24
Virgilius wrote:
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35 ?

A) 3
B) 4
C) 12
D) 32
E) 35



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Re: When positive integer n is divided by 5, the remainder is 1 [#permalink] New post 12 May 2013, 01:32
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Virgilius wrote:
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 35 ?

A) 3
B) 4
C) 12
D) 32
E) 35


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Re: When positive integer n is divided by 5, the remainder is 1 [#permalink] New post 23 Jun 2014, 22:55
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Re: When positive integer n is divided by 5, the remainder is 1 [#permalink] New post 24 Jun 2014, 01:12
When positive integer n is divided by 5, the remainder is 1 => n=5a+1
When positive integer n is divided by 7, the remainder is 3 => n=7b+3

Therefore, n+k = 5a+1+k = 7b+3+k

Since it's divisible by 35, it must be divisible by both 5 and 7,

for 5a+1+k to be divisible by 5, (1+k) should be divisible by and similarly for the next case, (3+k) should be divisible by 7.

Obviously,the least value for which this is true is 4!

Answer: B
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Re: When positive integer n is divided by 5, the remainder is 1 [#permalink] New post 24 Jun 2014, 02:55
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Re: When positive integer n is divided by 5, the remainder is 1   [#permalink] 24 Jun 2014, 02:55
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