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:

In short, if we divide N by d, with a quotient Q and remainder R, then N = d*Q + R

Here, we divide a by 9, get some unknown quotient (call it x) and a remainder of 4. That gives us: a = 9x + 4 Then, we divide b by 9, get some unknown quotient (call it y) and a remainder of 7. That gives us: b = 9y + 7

Then, a − 2b = (9x + 4) − 2*(9y + 7) = 9x + 4 − 18y − 14 = 9x − 18y − 10 That's what we are going to divide by 9. Well, the part (9x − 18y) is a multiple of 9, so 9 goes into that with no remainder. It's hard to tell what the remainder is if we divide -10 by 9: here's a way to think of it. Take any multiple of 9, any at all, subtract 10, and find the remainder when you divide by 9.

18 - 10 = 8 --- remainder = 8 54 = 10 = 44 --- divide by 9, and the remainder = 8

So, the remainder when (a − 2b) is divided by 9 is 8.

In short, if we divide N by d, with a quotient Q and remainder R, then N = d*Q + R

Here, we divide a by 9, get some unknown quotient (call it x) and a remainder of 4. That gives us: a = 9x + 4 Then, we divide b by 9, get some unknown quotient (call it y) and a remainder of 7. That gives us: b = 9y + 7

Then, a − 2b = (9x + 4) − 2*(9y + 7) = 9x + 4 − 18y − 14 = 9x − 18y − 10 That's what we are going to divide by 9. Well, the part (9x − 18y) is a multiple of 9, so 9 goes into that with no remainder. It's hard to tell what the remainder is if we divide -10 by 9: here's a way to think of it. Take any multiple of 9, any at all, subtract 10, and find the remainder when you divide by 9.

18 - 10 = 8 --- remainder = 8 54 = 10 = 44 --- divide by 9, and the remainder = 8

So, the remainder when (a − 2b) is divided by 9 is 8.

In short, if we divide N by d, with a quotient Q and remainder R, then N = d*Q + R

Here, we divide a by 9, get some unknown quotient (call it x) and a remainder of 4. That gives us: a = 9x + 4 Then, we divide b by 9, get some unknown quotient (call it y) and a remainder of 7. That gives us: b = 9y + 7

Then, a − 2b = (9x + 4) − 2*(9y + 7) = 9x + 4 − 18y − 14 = 9x − 18y − 10 That's what we are going to divide by 9. Well, the part (9x − 18y) is a multiple of 9, so 9 goes into that with no remainder. It's hard to tell what the remainder is if we divide -10 by 9: here's a way to think of it. Take any multiple of 9, any at all, subtract 10, and find the remainder when you divide by 9.

18 - 10 = 8 --- remainder = 8 54 = 10 = 44 --- divide by 9, and the remainder = 8

So, the remainder when (a − 2b) is divided by 9 is 8.

Does all this make sense? Mike

Hi Mike, I tried to solve this problem by taking values a=13 and b=16. Therefore a-2b=13-32=-19 -19 divided by 9 leaves a remainder of -1. I am not sure whether a negative number can be a remainder. Please help.

Re: The positive integers a and b leave remainders of 4 and 7 [#permalink]

Show Tags

09 Aug 2014, 11:15

Another way might be 'substitution'? e.g a = 13 ; b = 16 => a-2b = -10 or a = 22; b = 25 => a-2b = -28 Division by 9 yields -1. I feel that answer should be |1|. Nevertheless, going by equations above :- a-2b = 9(x-2y) - 10 (a-2b)/9 = (x-2y) - 10/9 ; it all boils to 10/9. isn't it?

In short, if we divide N by d, with a quotient Q and remainder R, then N = d*Q + R

Here, we divide a by 9, get some unknown quotient (call it x) and a remainder of 4. That gives us: a = 9x + 4 Then, we divide b by 9, get some unknown quotient (call it y) and a remainder of 7. That gives us: b = 9y + 7

Then, a − 2b = (9x + 4) − 2*(9y + 7) = 9x + 4 − 18y − 14 = 9x − 18y − 10 That's what we are going to divide by 9. Well, the part (9x − 18y) is a multiple of 9, so 9 goes into that with no remainder. It's hard to tell what the remainder is if we divide -10 by 9: here's a way to think of it. Take any multiple of 9, any at all, subtract 10, and find the remainder when you divide by 9.

18 - 10 = 8 --- remainder = 8 54 = 10 = 44 --- divide by 9, and the remainder = 8

So, the remainder when (a − 2b) is divided by 9 is 8.

Does all this make sense? Mike

Hi Mike, I tried to solve this problem by taking values a=13 and b=16. Therefore a-2b=13-32=-19 -19 divided by 9 leaves a remainder of -1. I am not sure whether a negative number can be a remainder. Please help.

the remainder cannot be negative. \(0\leq remainder<divisor\)
_________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: The positive integers a and b leave remainders of 4 and 7 [#permalink]

Show Tags

09 Aug 2014, 11:34

1

This post received KUDOS

kishgau wrote:

Another way might be 'substitution'? e.g a = 13 ; b = 16 => a-2b = -10 or a = 22; b = 25 => a-2b = -28 Division by 9 yields -1. I feel that answer should be |1|. Nevertheless, going by equations above :- a-2b = 9(x-2y) - 10 (a-2b)/9 = (x-2y) - 10/9 ; it all boils to 10/9. isn't it?

to -10/9 that have remainder -1+9=8
_________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: The positive integers a and b leave remainders of 4 and 7 [#permalink]

Show Tags

09 Aug 2014, 23:16

This question led me to multiple thread where the -ve remainder is debated. Some have quoted wiki that doesn't have any reservation about a -ve remainder. However, as per GMAT prep, remainder is always >0.

There may be another way to look at this. If we draw number line, plot -10 on the line and take an intercept of |-9| , it would leave one unit distance before -10. I don't think we'd take two intercepts and then count the distance between -18 and -10.

This concept looks weird but as long as GMAT feels it right, I'd go with that.

Re: The positive integers a and b leave remainders of 4 and 7 [#permalink]

Show Tags

20 Jun 2016, 11:25

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.
_________________

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...