It is currently 24 Nov 2017, 06:23

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a, b, and c are positive integers, what is the remainder

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

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 29 Nov 2011
Posts: 81

Kudos [?]: 382 [1], given: 37

If a, b, and c are positive integers, what is the remainder [#permalink]

Show Tags

New post 03 Feb 2012, 21:45
1
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:01) correct 26% (01:27) wrong based on 342 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Jun 2014, 01:59, edited 2 times in total.
Edited the question and added the OA

Kudos [?]: 382 [1], given: 37

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42356

Kudos [?]: 133204 [2], given: 12439

Re: If a, b, and c are positive integers, what is the remainder [#permalink]

Show Tags

New post 04 Feb 2012, 03:55
2
This post received
KUDOS
Expert's post
5
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.

Answer: C.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133204 [2], given: 12439

Director
Director
User avatar
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 534

Kudos [?]: 361 [0], given: 75

Location: India
GPA: 3.82
WE: Account Management (Retail Banking)
Re: If a, b, and c are positive integers, what is the remainder [#permalink]

Show Tags

New post 10 Oct 2012, 15:07
(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

Kudos [?]: 361 [0], given: 75

1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1074 [1], given: 43

WE: Science (Education)
Re: If a, b, and c are positive integers, what is the remainder [#permalink]

Show Tags

New post 10 Oct 2012, 16:01
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.

Kudos [?]: 1074 [1], given: 43

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15499

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If a, b, and c are positive integers, what is the remainder [#permalink]

Show Tags

New post 04 Oct 2017, 07:14
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Re: If a, b, and c are positive integers, what is the remainder   [#permalink] 04 Oct 2017, 07:14
Display posts from previous: Sort by

If a, b, and c are positive integers, what is the remainder

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.