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

It is currently 24 Jul 2014, 19:57

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 the three unique positive digits A,B, and C are arranged

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 310
Location: Bangladesh
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Followers: 7

Kudos [?]: 91 [1] , given: 46

If the three unique positive digits A,B, and C are arranged [#permalink] New post 09 Dec 2012, 08:59
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

46% (02:20) correct 54% (01:03) wrong based on 67 sessions
If the three unique positive digits A,B, and C are arranged in all possible sequences (ABC,ACB,BAC,ETC....),then the sum of all the resulting three -digit integers must be divisible by each of the following EXCEPT?

(A) 2
(B) 3
(C) 6
(D) 11
(E) 37
[Reveal] Spoiler: OA
Expert Post
1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 123

Kudos [?]: 569 [1] , given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 09 Dec 2012, 19:16
1
This post received
KUDOS
Expert's post
The 6 numbers are:
ABC, ACB, BCA, BAC, CAB, CBA.
Adding these would give 200A+200B+200C+20A+20B+20C+2(A+B+C).
or 222(A+B+C).
Among the answer choices , the sum is not divisible by 37.
Hence the answer.
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Manager
Manager
avatar
Joined: 04 Nov 2012
Posts: 90
Location: United States
Concentration: Finance, International Business
GMAT 1: Q44 V38
GPA: 3.7
WE: Science (Pharmaceuticals and Biotech)
Followers: 1

Kudos [?]: 33 [0], given: 82

Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 09 Dec 2012, 20:06
Marcab wrote:
The 6 numbers are:
ABC, ACB, BCA, BAC, CAB, CBA.
Adding these would give 200A+200B+200C+20A+20B+20C+2(A+B+C).
or 222(A+B+C).
Among the answer choices , the sum is not divisible by 37.
Hence the answer.


Clever approach. Apparently the post is wrong then as it says the non-divisor is 11 (answer D).
_________________

kudos are appreciated

Manager
Manager
avatar
Joined: 26 Jul 2011
Posts: 131
Location: India
WE: Marketing (Manufacturing)
Followers: 1

Kudos [?]: 27 [0], given: 15

Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 09 Dec 2012, 21:42
The answer indeed is 11. However I reached there by actually doing the permutations of digits 1, 2, 3 and adding them up and checking for the divisibility furthur. I am sure there should be some other approach
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 123

Kudos [?]: 569 [0], given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 09 Dec 2012, 21:49
Expert's post
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18729
Followers: 3240

Kudos [?]: 22363 [1] , given: 2615

Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 10 Dec 2012, 00:50
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Marcab wrote:
If the three unique positive digits A,B, and C are arranged in all possible sequences (ABC,ACB,BAC,ETC....),then the sum of all the resulting three -digit integers must be divisible by each of the following EXCEPT?

(A) 2
(B) 3
(C) 6
(D) 11
(E) 37

The 6 numbers are:
ABC, ACB, BCA, BAC, CAB, CBA.
Adding these would give 200A+200B+200C+20A+20B+20C+2(A+B+C).
or 222(A+B+C).
Among the answer choices , the sum is not divisible by 37.
Hence the answer.


222 is not divisible by 11 but it is divisible by 37, thus the answer is D, not E.

Generally:

1. Sum of all the numbers which can be formed by using the n digits without repetition is: (n-1)!*(sum \ of \ the \ digits)*(111... \ n \ times).

2. Sum of all the numbers which can be formed by using the n digits (repetition being allowed) is: n^{n-1}*(sum \ of \ the \ digits)*(111... \ n \ times).

Similar questions to prctice:
the-addition-problem-above-shows-four-of-the-24-different-in-104166.html
what-is-the-sum-of-all-3-digit-positive-integers-that-can-be-78143.html
find-the-sum-of-all-the-four-digit-numbers-formed-using-the-103523.html
what-is-the-sum-of-all-4-digit-numbers-that-can-be-formed-94836.html
what-is-the-sum-of-all-3-digit-positive-integers-that-can-be-78143.html
find-the-sum-of-all-the-four-digit-numbers-which-are-formed-88357.html
find-the-sum-of-all-3-digit-nos-that-can-be-formed-by-88864.html
there-are-24-different-four-digit-integers-than-can-be-141891.html

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

Manager
Manager
avatar
Joined: 26 Jul 2011
Posts: 131
Location: India
WE: Marketing (Manufacturing)
Followers: 1

Kudos [?]: 27 [0], given: 15

Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 10 Dec 2012, 02:10
Mine is a random approach...the question here is "Except" kind off so one can pick any number. I picked 123 and listed all the possible permutations

123
132
231
213
312
321

Which sums up to 1332. one can see that the number "1332" is clearly divisible by 3 and 2 and hence 6. also it is not divisible by 11. for 37 I actually divided the number by 37 and found it as divisible. and hence answer is D....Bunuels' formula is an excellent way to do with..
Intern
Intern
User avatar
Joined: 24 Apr 2012
Posts: 48
Followers: 0

Kudos [?]: 12 [0], given: 1

Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 10 Dec 2012, 03:38
Ans: There would be six combinations of numbers, let A=x, B=y, C=z. Now ABC= 100x+10y+z and if we add all the six numbers we get 222(x+y+z). We check that 222 is divisible by all of the options except 37. The answer is (E).
_________________

www.mnemoniceducation.com

TURN ON YOUR MINDS!!!

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18729
Followers: 3240

Kudos [?]: 22363 [0], given: 2615

Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 10 Dec 2012, 03:41
Expert's post
priyamne wrote:
Ans: There would be six combinations of numbers, let A=x, B=y, C=z. Now ABC= 100x+10y+z and if we add all the six numbers we get 222(x+y+z). We check that 222 is divisible by all of the options except 37. The answer is (E).


222 IS divisible by 37: 37*6=222. Check here: if-the-three-unique-positive-digits-a-b-and-c-are-arranged-143836.html#p1152825
_________________

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

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1729
Followers: 165

Kudos [?]: 33 [0], given: 0

Premium Member
Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 18 Jun 2014, 07:13
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

Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 651
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 147 [0], given: 161

Re: If the three unique positive digits A,B, and C are arranged [#permalink] New post 19 Jun 2014, 01:45
ratinarace wrote:
Mine is a random approach...the question here is "Except" kind off so one can pick any number. I picked 123 and listed all the possible permutations

123
132
231
213
312
321

Which sums up to 1332. one can see that the number "1332" is clearly divisible by 3 and 2 and hence 6. also it is not divisible by 11. for 37 I actually divided the number by 37 and found it as divisible. and hence answer is D....Bunuels' formula is an excellent way to do with..



Did in the same way; shortened the addition part

Picked up first two & so on as below..

255 + 466 + 933

= 1332

Fails divisibility check of 11

Answer = D
_________________

Kindly press "Kudos" to appreciate

Re: If the three unique positive digits A,B, and C are arranged   [#permalink] 19 Jun 2014, 01:45
    Similar topics Author Replies Last post
Similar
Topics:
Averages of three sets A,B and C containing positive numbers ps_dahiya 2 19 Jul 2006, 14:30
There are three events A,B, and C, are they mutually sparky 8 09 Jun 2005, 12:37
If the units digit of the three-digit positive integer k is pb_india 3 18 Jan 2005, 19:44
If the units digit of the three-digit positive integer k is NEWKID 2 06 Nov 2004, 09:29
If the units digit of the three-digit positive integer k is Antmavel 3 16 Oct 2004, 23:06
Display posts from previous: Sort by

If the three unique positive digits A,B, and C are arranged

  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®.