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# What is the remainder when the positive integer n is divided

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What is the remainder when the positive integer n is divided [#permalink]

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14 Oct 2012, 04:46
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What is the remainder when the positive integer n is divided by 6?

(1) n is multiple of 5
(2) n is a multiple of 12
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Joined: 02 Sep 2009
Posts: 45251
Re: What is the remainder when the positive integer n is divided [#permalink]

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14 Oct 2012, 04:53
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What is the remainder when the positive integer n is divided by 6?

(1) n is multiple of 5. If n=5, then n yields the remainder of 5 when divided by 6 but if n=10, then n yields the remainder of 4 when divided by 6. We already have two different answers, which means that this statement is not sufficient.

(2) n is a multiple of 12. Every multiple of 12 is also a multiple of 6, thus n divided by 6 yields the remainder of 0. Sufficient.

Hope it's clear.
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Re: What is the remainder when the positive integer n is divided [#permalink]

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14 Oct 2012, 04:55
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co801dw wrote:
What is the remainder when the positive integer n is divided by 6?

(1) n is multiple of 5
(2) n is a multiple of 12

* this is a question fromt the GMATprep test 1. Can someone please kindly provide solution and explanation?

Thanks

Check our question banks (viewforumtags.php) for more questions on remainders.

DS questions on remainders: search.php?search_id=tag&tag_id=198
PS questions on remainders: search.php?search_id=tag&tag_id=199

Hope it helps.
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Re: What is the remainder when the positive integer n is divided [#permalink]

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14 Oct 2012, 04:57
Thanks a lot for the resources! Will do!
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Re: What is the remainder when the positive integer n is divided [#permalink]

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10 Aug 2013, 08:48
(1).

N=5A N can be 5,10,15,20,25 .... Now these values have different remainders when divided by 6 hence Insufficient

(2).

N= 12B = > N => 6 (2B) = > N = 6C .... Hence Remainder when N is divided by '6' is '0' => Sufficient

Hence (B) !!
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Re: What is the remainder when the positive integer n is divided [#permalink]

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21 Dec 2013, 18:58
I need some clarification on the first statement...

I know the numbers go like this: 3, 9, 15.....

But when 3 is divided by 6...how is that a remainder of 3?
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Re: What is the remainder when the positive integer n is divided [#permalink]

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22 Dec 2013, 04:40
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b00gigi wrote:
I need some clarification on the first statement...

I know the numbers go like this: 3, 9, 15.....

But when 3 is divided by 6...how is that a remainder of 3?

THEORY:
Positive integer $$a$$ divided by positive integer $$d$$ yields a reminder of $$r$$ can always be expressed as $$a=qd+r$$, where $$q$$ is called a quotient and $$r$$ is called a remainder, note here that $$0\leq{r}<d$$ (remainder is non-negative integer and always less than divisor).

For example positive integer n is divided by 25 yields the remainder of 13 can be expressed as: $$n=25q+13$$. Now, the lowest value of $$q$$ can be zero and in this case $$n=13$$ --> 13 divided by 25 yields the remainder of 13. Generally when divisor (25 in our case) is more than dividend (13 in our case) then the reminder equals to the dividend. For example:
3 divided by 24 yields a reminder of 3 --> $$3=0*24+3$$;
or:
5 divided by 6 yields a reminder of 5 --> $$5=0*6+5$$,
2 divided by 5 yields a reminder of 2 --> $$2=0*5+2$$.

Hope it's clear.
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Re: What is the remainder when the positive integer n is divided [#permalink]

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22 Mar 2016, 02:44
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Re: What is the remainder when the positive integer n is divided [#permalink]

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26 Jan 2017, 18:34
Statement 1:
Options for n = 5, 10, 15, 20...
When 10 is divided by 6, the remainder is 4.
When 15 is divided by 6, the remainder is 3.
Since the remainder can be different values, INSUFFICIENT.

Statement 2:
Options for n = 12, 24, 36, 48...
When 12 is divided by 6, the remainder is 0.
When 24 is divided by 6, the remainder is 0.
When 36 is divided by 6, the remainder is is 0.
Since the remainder is the same in every case, SUFFICIENT.

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Re: What is the remainder when the positive integer n is divided [#permalink]

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31 Jan 2018, 01:21
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Re: What is the remainder when the positive integer n is divided   [#permalink] 31 Jan 2018, 01:21
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