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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]

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11 May 2013, 11:24
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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Kudos [?]: 105915 [0], given: 11593

Re: When positive integer n is divided by 5, the remainder is 1 [#permalink]

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12 May 2013, 02:32
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]

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23 Jun 2014, 23:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: When positive integer n is divided by 5, the remainder is 1 [#permalink]

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24 Jun 2014, 02:12
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!

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Kudos [?]: 105915 [0], given: 11593

Re: When positive integer n is divided by 5, the remainder is 1 [#permalink]

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24 Jun 2014, 03:55
OPEN DISCUSSION OF THIS QUESTION IS HERE: when-positive-integer-n-is-divided-by-5-the-remainder-is-166831.html
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Re: When positive integer n is divided by 5, the remainder is 1   [#permalink] 24 Jun 2014, 03:55

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