GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 11 Nov 2019, 15:51

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

General Rule regarding Remainder questions

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

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

Show Tags

New post 18 Jan 2012, 16:04
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
User avatar
V
Joined: 02 Sep 2009
Posts: 58954
Re: General Rule regarding Remainder questions  [#permalink]

Show Tags

New post 18 Jan 2012, 16:30
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
Intern
avatar
Joined: 25 Mar 2011
Posts: 26
Re: General Rule regarding Remainder questions  [#permalink]

Show Tags

New post 18 Jan 2012, 16:38
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!
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13554
Re: General Rule regarding Remainder questions  [#permalink]

Show Tags

New post 17 Oct 2019, 04:34
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: General Rule regarding Remainder questions   [#permalink] 17 Oct 2019, 04:34
Display posts from previous: Sort by

General Rule regarding Remainder questions

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne