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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

06 Jan 2010, 13:26

Just like in multiplication, when one but not both numbers are negative, the answer will be negative. If both numbers are negative, the answer will be positive. In number theory, remainders are always positive. -11 divided by 5 equals -2 remainder 1.

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

06 Jan 2010, 14:09

handsomebrute wrote:

Just like in multiplication, when one but not both numbers are negative, the answer will be negative. If both numbers are negative, the answer will be positive. In number theory, remainders are always positive. -11 divided by 5 equals -2 remainder 1.

But according to the formula y=xq + r (q = quotient, r = remainder):

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

06 Jan 2010, 14:09

handsomebrute wrote:

Just like in multiplication, when one but not both numbers are negative, the answer will be negative. If both numbers are negative, the answer will be positive. In number theory, remainders are always positive. -11 divided by 5 equals -2 remainder 1.

I doubt this...

- 11 = 5 x (-2) + 1 ????

Guess remainder should be -1. It would then satisfy the equation above!

Cheers! JT
_________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

06 Jan 2010, 14:33

mrblack wrote:

jeeteshsingh wrote:

I doubt this...

- 11 = 5 x (-2) + 1 ????

Guess remainder should be -1. It would then satisfy the equation above!

Cheers! JT

Can you have negative remainders? Never heard of such a thing before...

No offence mate.. but I havent heard of anything as positive remainder (on a lighter note)

Usually we simply call them as remainders as long as I remember...
_________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

06 Jan 2010, 14:58

2

This post received KUDOS

OK... finally I got some insight on this..

There is way of calculating the remainder when dealing with Negative Numbers....

Say you have a Number 'N' which is to be divided by 'd'. On division you get a quotient 'q' and remainder 'r'

Now if N is +ve, then \(N = q*d + r\) where \(q*d \leq N \leq (q+1)*d\) and \(r = N - q*d\)

e.g. \(11 = 5*2 + 1\)

Now if N is negative, we have a change.... in this equation: \(q*d \leq N \leq (q+1)*d\)... mutliply by -ve throughout and see the change as: \(-(q+1)*d \leq -N \leq -(q)*d\)

Therefore remainder now would be: \(r = (-N) - (-(q+1)*d) = (q+1)*d -N\)

e.g. Let N = -11, d = 5... Hence \(-(3)*5 \leq -11 \leq -(2)*5\) Therefore \(q = 2\) Hence \(r = (2+1)*5-11 = 4\)

You can verify this as \(-11 = 5 * (-3) + 4\) Therefore quotient = -3 and remainder = 4! Hope it makes sence and is clear....

Cheers! JT
_________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

06 Jan 2010, 15:16

Reminder can be either positive or negative Example: If a and d are integers, with d non-zero, then a remainder is an integer r such that a = qd + r for some integer q, and with 0 ≤ |r| < |d|. When defined this way, there are two possible remainders. For example, the division of −42 by −5 can be expressed as either −42 = 9×(−5) + 3 as is usual for mathematicians, or −42 = 8×(−5) + (−2). So the remainder is then either 3 or −2.

the negative remainder is obtained from the positive one just by subtracting 5, which is d. This holds in general. When dividing by d, if the positive remainder is r1, and the negative one is r2, then r1 = r2 + d.

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

06 Jan 2010, 15:51

1

This post received KUDOS

dmetla wrote:

Reminder can be either positive or negative Example: If a and d are integers, with d non-zero, then a remainder is an integer r such that a = qd + r for some integer q, and with 0 ≤ |r| < |d|. When defined this way, there are two possible remainders. For example, the division of −42 by −5 can be expressed as either −42 = 9×(−5) + 3 as is usual for mathematicians, or −42 = 8×(−5) + (−2). So the remainder is then either 3 or −2.

the negative remainder is obtained from the positive one just by subtracting 5, which is d. This holds in general. When dividing by d, if the positive remainder is r1, and the negative one is r2, then r1 = r2 + d.

I think this is not correct because.....

in −42 = 8×(−5) + (−2)... you are dividing -42 with 8 and choosing -5 as quotient...but -5 x 8 gives -40 which is greater than -42 and hence is not as per the divisibility methodology....

If u have to divide 11 by 5, you would use 10 (5x2) and not 15 (5x3) as 10 is less 11.. Similarly, for -42 you should use -48 (i.e. 8x-6) as -48 is less than -42 but -40 is more than -42!

The eq −42 = 8×(−5) + (−2) is correct mathematically but fails to ascertain the quotient and remainder correctly...!

More over your first example (highlighted in red) is wrong.. as you are dividing -42 with -5 which means you dividing 42 with 5 and hence the situation of a negative number being divided is void!
_________________

Cheers! JT........... If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

Wiki definition of the remainder: If \(a\) and \(d\) are natural numbers, with \(d\) non-zero, it can be proven that there exist unique integers \(q\) and \(r\), such that \(a = qd + r\) and \(0\leq{r} < d\). The number \(q\) is called the quotient, while \(r\) is called the remainder.

GMAT Prep definition of the remainder: If \(a\) and \(d\) are positive integers, there exists unique integers \(q\) and \(r\), such that \(a = qd + r\) and \(0\leq{r}<d\). \(q\) is called a quotient and \(r\) is called a remainder.

Moreover many GMAT books say factor is a "positive divisor", \(d>0\).

I've never seen GMAT question asking the ramainder when dividend (\(a\)) is negative, but if we'll cancel this restriction (\(dividend=a<0\)), and only this restriction, meaning that we'll leave the other one (\(0\leq{r}<d\)), then division of \(-11\) by \(5\) will result:

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

06 Jan 2010, 19:51

Bunuel wrote:

Wiki definition of the remainder: If \(a\) and \(d\) are natural numbers, with \(d\) non-zero, it can be proven that there exist unique integers \(q\) and \(r\), such that \(a = qd + r\) and \(0\leq{r} < d\). The number \(q\) is called the quotient, while \(r\) is called the remainder.

GMAT Prep definition of the remainder: If \(a\) and \(d\) are positive integers, there exists unique integers \(q\) and \(r\), such that \(a = qd + r\) and \(0\leq{r}<d\). \(q\) is called a quotient and \(r\) is called a remainder.

Moreover many GMAT books say factor is a "positive divisor", \(d>0\).

I've never seen GMAT question asking the ramainder when dividend (\(a\)) is negative, but if we'll cancel this restriction (\(dividend=a<0\)), and only this restriction, meaning that we'll leave the other one (\(0\leq{r}<d\)), then division of \(-11\) by \(5\) will result:

Thanks for the lengthy response Bunuel. The wiki entry seems to imply that there could be a +ve or -ve remainder. Referring to my original question once more, it seems that -11/5 can be either:

Wiki definition of the remainder: If \(a\) and \(d\) are natural numbers, with \(d\) non-zero, it can be proven that there exist unique integers \(q\) and \(r\), such that \(a = qd + r\) and \(0\leq{r} < d\). The number \(q\) is called the quotient, while \(r\) is called the remainder.

GMAT Prep definition of the remainder: If \(a\) and \(d\) are positive integers, there exists unique integers \(q\) and \(r\), such that \(a = qd + r\) and \(0\leq{r}<d\). \(q\) is called a quotient and \(r\) is called a remainder.

Moreover many GMAT books say factor is a "positive divisor", \(d>0\).

I've never seen GMAT question asking the ramainder when dividend (\(a\)) is negative, but if we'll cancel this restriction (\(dividend=a<0\)), and only this restriction, meaning that we'll leave the other one (\(0\leq{r}<d\)), then division of \(-11\) by \(5\) will result:

Thanks for the lengthy response Bunuel. The wiki entry seems to imply that there could be a +ve or -ve remainder. Referring to my original question once more, it seems that -11/5 can be either:

-11 = (-3)*5 + 4 or -11 = (-2)*5 + (-1)

I think either case is valid.

Wiki is not a best source for Math but even its definition: \(0\leq{r} < d\), so \(0\leq{r}\), remainder must be positive. But again I wouldn't worry about this issue for GMAT.
_________________

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

07 Jul 2010, 08:35

Bunuel wrote:

Wiki definition of the remainder: If \(a\) and \(d\) are natural numbers, with \(d\) non-zero, it can be proven that there exist unique integers \(q\) and \(r\), such that \(a = qd + r\) and \(0\leq{r} < d\). The number \(q\) is called the quotient, while \(r\) is called the remainder.

GMAT Prep definition of the remainder: If \(a\) and \(d\) are positive integers, there exists unique integers \(q\) and \(r\), such that \(a = qd + r\) and \(0\leq{r}<d\). \(q\) is called a quotient and \(r\) is called a remainder.

Moreover many GMAT books say factor is a "positive divisor", \(d>0\).

I've never seen GMAT question asking the ramainder when dividend (\(a\)) is negative, but if we'll cancel this restriction (\(dividend=a<0\)), and only this restriction, meaning that we'll leave the other one (\(0\leq{r}<d\)), then division of \(-11\) by \(5\) will result:

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

12 Sep 2014, 03:32

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.
_________________

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

02 May 2015, 11:57

This is what I think and according to the reminder theory :

when a=b*c => reminder of a/x i same as reminder of (b*c)/x moreover it same as reminder of (reminder of b/x * reminder ofc/x)/x

I will try to ilsitrate with the example. actualy this concept I saw on the forum somewhere posted by EvaJager I think.

-11 = -1 *11 => R of -1*11/5 is Rof (R of-1/5 * R of 11/5)/5

now R of -1/5 is -1 and R of 11/5 is 1 => R of -1*1/5 is just R of-1/5 which is -1. since we cant really have negative reminder we need to add the negative

reminder back to the divisor 5, or 5-1 = 4, so 4 is the reminder

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

17 Sep 2016, 09:38

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.
_________________

As always, questions like CMT 3,4 are often on the exam in a more developed form. Take a look at below and you’ll see the type of question that’s really common these days. This one, too, is a 5051-evel problem that is equivalent to CMT 4(A). You must get used to these. You need to know how variable approaches and CMT are related.

(ex 1) (integer) If x and y are postive integers, what is the remainder when 100x+y is divided by 11? 1) x=22 2) y=1 ==> If you change the original condition and the prolem, you all ways get the remainder of 1 if you divide 100x by 11 regardless of the value of x. Thus, you only need to know y. Therefore, the answer is . This is a typical 5051 level problem. (CMT 4(A)) Answer: A
_________________

Re: Finding the remainder when dividing negative numbers [#permalink]

Show Tags

21 Sep 2016, 21:14

MathRevolution wrote:

As always, questions like CMT 3,4 are often on the exam in a more developed form. Take a look at below and you’ll see the type of question that’s really common these days. This one, too, is a 5051-evel problem that is equivalent to CMT 4(A). You must get used to these. You need to know how variable approaches and CMT are related.

(ex 1) (integer) If x and y are postive integers, what is the remainder when 100x+y is divided by 11? 1) x=22 2) y=1 ==> If you change the original condition and the prolem, you all ways get the remainder of 1 if you divide 100x by 11 regardless of the value of x. Thus, you only need to know y. Therefore, the answer is . This is a typical 5051 level problem. (CMT 4(A)) Answer: A

Is it B or A? I am getting C.

St 1:

y can be anything

St 2:

For 101---- r=2 For 201 ----r=3

gmatclubot

Re: Finding the remainder when dividing negative numbers
[#permalink]
21 Sep 2016, 21:14

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...