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If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?

A. 0 B. 1 C. 2 D. 3 E. 4

When positive integer n is dived by 18 the remainder is 7: \(n=18q+7=(18q+6)+1=6(3q+1)+1\) --> since first term \(6(3q+1)\) is divisible by 6 then the remainder will only be from the second term 1 --> 1 divided by 6 yields remainder of 1.

If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?

A. 0 B. 1 C. 2 D. 3 E. 4

Answer in less than 10 secs once you understand the theory of divisibility and remainders. Check out the theory on this link and then read the explanation given below: http://www.veritasprep.com/blog/2011/04 ... unraveled/

When you divide by 6, you further divide the groups of 18 in 3 groups. The last group of 7 will form another group of 6 and you will have 1 leftover. Answer should be (B)
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Re: If the remainder is 7 when positive integer n is divided by [#permalink]

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30 Sep 2013, 07:19

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what if the question is reversed, example if 23 is the remainder when n is divided by 36, what is the remainder when n is divided by 72?

When you divide n by 36, you have groups of 36 balls each and 23 balls leftover. If you want to divide by 72 now, you will join two groups of 36 to make groups of 72. You don't know whether you have even number of groups or odd number of groups of 36. If the number of groups of 36 is even (quotient is even), you will be able to pair them all up to make groups of 72 such that remainder is 23 only. If the number of groups of 36 is odd (quotient is odd), you will not be able to pair them all up. One group will be leftover and the remainder will be 36+23 = 59.
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Re: If the remainder is 7 when positive integer n is divided by [#permalink]

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01 Sep 2015, 01:52

1

This post was BOOKMARKED

BANON wrote:

B) by taking numbers we can solve this easily

multiples of 18 are 18,36,54....etc

so to get a remainder of 7 we add 7 to multiples so the integer may be 25,43,61..etc

so if we divide these numbers with 6.. remainder is 1..

If numerator is smaller than Denominator then the numerator could be a remainder also...example 7/18(here 7 is remainder),6/15(here 6 is remainder)
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Re: If the remainder is 7 when positive integer n is divided by [#permalink]

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05 Sep 2016, 06:22

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: If the remainder is 7 when positive integer n is divided by [#permalink]

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19 Feb 2017, 23:05

I think easiest way to tackle this question is to find least possible value of n which 25 for 18 to get remainder 7 then check 25/6 remainder will be 1

gmatclubot

Re: If the remainder is 7 when positive integer n is divided by
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19 Feb 2017, 23:05

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