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# General Rule regarding Remainder questions

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Intern
Joined: 25 Mar 2011
Posts: 26
General Rule regarding Remainder questions  [#permalink]

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18 Jan 2012, 15:04
1
This might be dumb, but I am not an expert on mathematical lingo. Far from it, actually.

Here's my question:

If a question states:

when positive integer n is divided by 25, the remainder is 13. what is the value of n?

so, we have

n/25 = Z + 13/25

In these problems, can we ALWAYS assume that Z => 1 ???

at first glance, n could be 13 ITSELF, then 38, 63, 88....

however, I feel that I should be safe in assuming n DOESN'T equal 13, otherwise you wouldn't technically have a remainder?

I am seeking validation on this mathematical principle.
Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: General Rule regarding Remainder questions  [#permalink]

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18 Jan 2012, 15:30
DJK wrote:
This might be dumb, but I am not an expert on mathematical lingo. Far from it, actually.

Here's my question:

If a question states:

when positive integer n is divided by 25, the remainder is 13. what is the value of n?

so, we have

n/25 = Z + 13/25

In these problems, can we ALWAYS assume that Z => 1 ???

at first glance, n could be 13 ITSELF, then 38, 63, 88....

however, I feel that I should be safe in assuming n DOESN'T equal 13, otherwise you wouldn't technically have a remainder?

I am seeking validation on this mathematical principle.

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).

According to the above "when positive integer n is divided by 25, the remainder is 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 --> $$5=0*6+5$$.

Also note that you shouldn't worry about negative numbers in divisibility questions, as every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

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

Also check theory on remainders: compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html

Hope it helps.
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Intern
Joined: 25 Mar 2011
Posts: 26
Re: General Rule regarding Remainder questions  [#permalink]

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18 Jan 2012, 15:38
Thanks, Banuel.

So, N could equal 13. I understand the formula and everything - I just thought that the Quotient has to be great than 0.

13/25 = remainder of 13 is all that I need to know.

Thanks for the links to extra practice!
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Joined: 09 Sep 2013
Posts: 15602
Re: General Rule regarding Remainder questions  [#permalink]

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17 Oct 2019, 03:34
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Re: General Rule regarding Remainder questions   [#permalink] 17 Oct 2019, 03:34