General Rule regarding Remainder questions : GMAT Quantitative Section
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 12:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# General Rule regarding Remainder questions

Author Message
TAGS:

### Hide Tags

Intern
Joined: 25 Mar 2011
Posts: 29
Followers: 0

Kudos [?]: 2 [0], given: 1

General Rule regarding Remainder questions [#permalink]

### Show Tags

18 Jan 2012, 15:04
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: 36567
Followers: 7081

Kudos [?]: 93195 [0], given: 10553

Re: General Rule regarding Remainder questions [#permalink]

### Show Tags

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.
_________________
Intern
Joined: 25 Mar 2011
Posts: 29
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: General Rule regarding Remainder questions [#permalink]

### Show Tags

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!
Re: General Rule regarding Remainder questions   [#permalink] 18 Jan 2012, 15:38
Similar topics Replies Last post
Similar
Topics:
1 General question regarding parenthesis. 8 09 May 2015, 09:07
1 General Question, regarding Geometry! 3 20 Sep 2012, 21:34
General Math Rule Question 2 10 Jan 2012, 17:01
2 Remainder question 12 21 Mar 2011, 11:40
Inequalities - General Rule (multiplying two inequalities) 3 24 Jul 2010, 00:07
Display posts from previous: Sort by