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 350,000 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: If a, b, and c are positive integers, what is the remainder [#permalink]
04 Feb 2012, 02:55

Expert's post

3

This post was BOOKMARKED

Smita04 wrote:

If a , b , and c are positive integers, what is the remainder after b - a is divided by 3?

(1) a = c^3 (2) b = (c + 1)^3

If a , b , and c are positive integers, what is the remainder after b - a is divided by 3?

(1) a = c^3 --> no info about b. Not sufficient. (2) b = (c + 1)^3 --> no info about b. Not sufficient.

When taken together you can go with algebraic approach or plug-in method:

Algebraic approach:

(1)+(2) Important tip: x^3-y^3 can be factored as follows: \(x^3-y^3=(x-y)(x^2+xy+y^2)\). Apply this factoring to \(b-a\) --> \(b-a=(c + 1)^3-c^3=(c+1-c)(c^2+2c+1+c^2+c+c^2)=3c^2+3c+1=3(c^2+c)+1\) --> remainder upon division this expression by 3 is 1. Sufficient.

Answer: C.

Plug-in method approach:

(1)+(2) try some numbers for a and b: \(a=c^3=1\) --> \(b=(c+1)^3=8\) and --> \(b-a=(c + 1)^3-c^3=7\) --> remainder upon division 3 is 1; \(a=c^3=8\) --> \(b=(c+1)^3=27\) and --> \(b-a=(c + 1)^3-c^3=19\) --> remainder upon division 3 is 1; \(a=c^3=27\) --> \(b=(c+1)^3=64\) and --> \(b-a=(c + 1)^3-c^3=37\) --> remainder upon division 3 is 1; \(a=c^3=64\) --> \(b=(c+1)^3=125\) and --> \(b-a=(c + 1)^3-c^3=61\) --> remainder upon division 3 is 1; ... It seem that there is some kind of pattern and we can safely assume that in all other cases remainder will also be 1. Sufficient.

Re: If a, b, and c are positive integers, what is the remainder [#permalink]
10 Oct 2012, 14:07

(A) & (B) ruled out as we do not get complete info about a & b together, because in question we are supposed to find remainder when (b-a) is divided by 3.

lets take both together;

Given: a=c^3;b=(c+1)^3 ) ( for a,b,c all positive integer) so lets check at three points; @c=1, a=1,b=8 ; @ c=2, a=8, b= 27, @ c= 3 , a=27,b=64

8-1/3 R->1 27-8/3 R->1 64-27/3 R->1

Hence C is the answer _________________

" Make more efforts " Press Kudos if you liked my post

Re: If a, b, and c are positive integers, what is the remainder [#permalink]
10 Oct 2012, 15:01

1

This post received KUDOS

Bunuel wrote:

Smita04 wrote:

If a , b , and c are positive integers, what is the remainder after b - a is divided by 3?

(1) a = c^3 (2) b = (c + 1)^3

If a , b , and c are positive integers, what is the remainder after b - a is divided by 3?

(1) a = c^3 --> no info about b. Not sufficient. (2) b = (c + 1)^3 --> no info about b. Not sufficient.

When taken together you can go with algebraic approach or plug-in method:

Algebraic approach:

(1)+(2) Important tip: x^3-y^3 can be factored as follows: \(x^3-y^3=(x-y)(x^2+xy+y^2)\). Apply this factoring to \(b-a\) --> \(b-a=(c + 1)^3-c^3=(c+1-c)(c^2+2c+1+c^2+c+c^2)=3c^2+3c+1=3(c^2+c)+1\) --> remainder upon division this expression by 3 is 1. Sufficient.

Answer: C.

Plug-in method approach:

(1)+(2) try some numbers for a and b: \(a=c^3=1\) --> \(b=(c+1)^3=8\) and --> \(b-a=(c + 1)^3-c^3=7\) --> remainder upon division 3 is 1; \(a=c^3=8\) --> \(b=(c+1)^3=27\) and --> \(b-a=(c + 1)^3-c^3=19\) --> remainder upon division 3 is 1; \(a=c^3=27\) --> \(b=(c+1)^3=64\) and --> \(b-a=(c + 1)^3-c^3=37\) --> remainder upon division 3 is 1; \(a=c^3=64\) --> \(b=(c+1)^3=125\) and --> \(b-a=(c + 1)^3-c^3=61\) --> remainder upon division 3 is 1; ... It seem that there is some kind of pattern and we can safely assume that in all other cases remainder will also be 1. Sufficient.

Answer: C.

Hope it helps.

Integers, when divided by 3 can leave a remainder of \(0, 1, or 2.\) Integers cubed, when divided by 3, will leave the same remainders, because \(0^3=0, 1^3=1,\) and \(2^3=8=6+2.\)

Therefore, when subtracting cubes of two consecutive integers, the result will always leave a remainder of 1: the remainders repeat themselves cyclically \(0,1,2,0,1,2,...\), so \(1-0=2-1=1\) and \(\,\,0-2=-3+1.\) _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If a, b, and c are positive integers, what is the remainder [#permalink]
24 Jun 2014, 23:52

Bunuel wrote:

Smita04 wrote:

If a , b , and c are positive integers, what is the remainder after b - a is divided by 3?

(1) a = c^3 (2) b = (c + 1)^3

If a , b , and c are positive integers, what is the remainder after b - a is divided by 3?

(1) a = c^3 --> no info about b. Not sufficient. (2) b = (c + 1)^3 --> no info about b. Not sufficient.

When taken together you can go with algebraic approach or plug-in method:

Algebraic approach:

(1)+(2) Important tip: x^3-y^3 can be factored as follows: \(x^3-y^3=(x-y)(x^2+xy+y^2)\). Apply this factoring to \(b-a\) --> \(b-a=(c + 1)^3-c^3=(c+1-c)(c^2+2c+1+c^2+c+c^2)=3c^2+3c+1=3(c^2+c)+1\) --> remainder upon division this expression by 3 is 1. Sufficient.

Answer: C.

Plug-in method approach:

(1)+(2) try some numbers for a and b: \(a=c^3=1\) --> \(b=(c+1)^3=8\) and --> \(b-a=(c + 1)^3-c^3=7\) --> remainder upon division 3 is 1; \(a=c^3=8\) --> \(b=(c+1)^3=27\) and --> \(b-a=(c + 1)^3-c^3=19\) --> remainder upon division 3 is 1; \(a=c^3=27\) --> \(b=(c+1)^3=64\) and --> \(b-a=(c + 1)^3-c^3=37\) --> remainder upon division 3 is 1; \(a=c^3=64\) --> \(b=(c+1)^3=125\) and --> \(b-a=(c + 1)^3-c^3=61\) --> remainder upon division 3 is 1; ... It seem that there is some kind of pattern and we can safely assume that in all other cases remainder will also be 1. Sufficient.

Answer: C.

Hope it helps.

Hi Bunuel, Would it be possible for you to provide OA to the question and adjust the difficulty level, so that we guys can actually have some appreciation for the question?

Thanks! _________________

Bored of all the GMAT and MBA stuff? Check this page out -Odds of meeting your spouse at MBA- it might give you something to laugh on or may be to be hopeful about...

Re: If a, b, and c are positive integers, what is the remainder [#permalink]
25 Jun 2014, 01:00

1

This post received KUDOS

Expert's post

neo656 wrote:

Bunuel wrote:

Smita04 wrote:

If a , b , and c are positive integers, what is the remainder after b - a is divided by 3?

(1) a = c^3 (2) b = (c + 1)^3

If a , b , and c are positive integers, what is the remainder after b - a is divided by 3?

(1) a = c^3 --> no info about b. Not sufficient. (2) b = (c + 1)^3 --> no info about b. Not sufficient.

When taken together you can go with algebraic approach or plug-in method:

Algebraic approach:

(1)+(2) Important tip: x^3-y^3 can be factored as follows: \(x^3-y^3=(x-y)(x^2+xy+y^2)\). Apply this factoring to \(b-a\) --> \(b-a=(c + 1)^3-c^3=(c+1-c)(c^2+2c+1+c^2+c+c^2)=3c^2+3c+1=3(c^2+c)+1\) --> remainder upon division this expression by 3 is 1. Sufficient.

Answer: C.

Plug-in method approach:

(1)+(2) try some numbers for a and b: \(a=c^3=1\) --> \(b=(c+1)^3=8\) and --> \(b-a=(c + 1)^3-c^3=7\) --> remainder upon division 3 is 1; \(a=c^3=8\) --> \(b=(c+1)^3=27\) and --> \(b-a=(c + 1)^3-c^3=19\) --> remainder upon division 3 is 1; \(a=c^3=27\) --> \(b=(c+1)^3=64\) and --> \(b-a=(c + 1)^3-c^3=37\) --> remainder upon division 3 is 1; \(a=c^3=64\) --> \(b=(c+1)^3=125\) and --> \(b-a=(c + 1)^3-c^3=61\) --> remainder upon division 3 is 1; ... It seem that there is some kind of pattern and we can safely assume that in all other cases remainder will also be 1. Sufficient.

Answer: C.

Hope it helps.

Hi Bunuel, Would it be possible for you to provide OA to the question and adjust the difficulty level, so that we guys can actually have some appreciation for the question?

Hello everyone! Researching, networking, and understanding the “feel” for a school are all part of the essential journey to a top MBA. Wouldn’t it be great... ...

As part of our focus on MBA applications next week, which includes a live QA for readers on Thursday with admissions expert Chioma Isiadinso, we asked our bloggers to...