Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Oct 2014, 16:31

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 29 Nov 2011
Posts: 81
Followers: 1

Kudos [?]: 72 [0], given: 37

If a, b, and c are positive integers, what is the remainder [#permalink] New post 03 Feb 2012, 20:45
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

81% (01:00) correct 19% (00:55) wrong based on 103 sessions
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, 00:59, edited 2 times in total.
Edited the question and added the OA
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23357
Followers: 3604

Kudos [?]: 28727 [1] , given: 2839

Re: If a, b, and c are positive integers, what is the remainder [#permalink] New post 04 Feb 2012, 02:55
1
This post received
KUDOS
Expert's post
1
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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
User avatar
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 564
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)
Followers: 13

Kudos [?]: 144 [0], given: 75

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

1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 73

Kudos [?]: 529 [1] , given: 43

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

BSchool Forum Moderator
User avatar
Status: Let's Get Ready to Rhumble...
Affiliations: GMATClub ...
Joined: 20 Apr 2014
Posts: 209
Location: Malaysia
Concentration: General Management, Strategy
GMAT 1: 760 Q50 V41
GPA: 3.2
WE: Project Management (Other)
Followers: 2

Kudos [?]: 35 [0], given: 417

GMAT ToolKit User
Re: If a, b, and c are positive integers, what is the remainder [#permalink] New post 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!
_________________

Was I helpful? Shower some kudos... :) Feeling sick with all that boring education or the stressful applications.?! Follow me I'll throw you some stressbusters.. ;)

LBS Research made easy - Check it out.
Check out for quick info about Tuck - Why Tuck? EA Round Pros & Cons. Admission Process and Tips.

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... :)

Raves, rants and war stories of First Year MBA Students

Received an offer? Congrats! You might want to 'Negotiate the Offer'.

Be a sport. Update your profile here.

"GMAT conquered. Let's talk about applications..."
Persistence is the key. And I'm gonna make through...

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23357
Followers: 3604

Kudos [?]: 28727 [1] , given: 2839

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

Thanks!


Added the OA. Thank you.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: If a, b, and c are positive integers, what is the remainder   [#permalink] 25 Jun 2014, 01:00
    Similar topics Author Replies Last post
Similar
Topics:
15 Experts publish their posts in the topic If a and b are positive integers, what is the remainder when kingflo 4 20 Jul 2013, 08:26
1 Experts publish their posts in the topic If N, C, and D are positive integers, what is the remainder kingb 4 06 Nov 2012, 17:35
2 Experts publish their posts in the topic If a, b, and c are positive integers, what is the remainder thevenus 3 10 Oct 2012, 13:56
13 Experts publish their posts in the topic If a and b are positive integers, what is the remainder when enigma123 8 26 Feb 2012, 15:30
a and b are positive integers. What is the remainder of of AJB77 2 25 Jun 2005, 18:53
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.