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

It is currently 27 Jul 2014, 20:52

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

What is the sum of all possible 3-digit numbers that can be

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18790
Followers: 3258

Kudos [?]: 22555 [2] , given: 2630

What is the sum of all possible 3-digit numbers that can be [#permalink] New post 07 Jan 2010, 04:07
2
This post received
KUDOS
Expert's post
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

67% (01:22) correct 33% (00:43) wrong based on 2 sessions
vitaliy wrote:
What is the sum of all possible 3-digit numbers that can be constructed using the digits 3,4 and 5, if each digit can be used only once in each number?


My Q.: How we receive 24s in the final equalization (attached). thnx


Three digit number has the form: 100a+10b+c.

# of three digit numbers with digits {3,4,5} is 3!=6.

These 6 numbers will have 6/3=2 times 3 as hundreds digit (a), 2 times 4 as as hundreds digit, 2 times 5 as hundreds digit.

The same with tens and units digits.

100*(2*3+2*4+2*5)+10*(2*3+2*4+2*5)+(2*3+2*4+2*5)=100*24+10*24+24=2664.

Generally the sum of all the numbers which can be formed by using the n distinct digits, is given by the formula:

(n-1)!*(sum of the digits)*(111…..n times)


In our original question: n=3. sum of digits=3+4+5=12. --> (3-1)!*(12)*(111)=24*111=2664.

Hope it's clear.
_________________

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

2 KUDOS received
Intern
Intern
avatar
Joined: 20 Dec 2009
Posts: 14
Followers: 1

Kudos [?]: 14 [2] , given: 5

Re: What is the sum of all possible 3-digit numbers that can be [#permalink] New post 07 Jan 2010, 04:40
2
This post received
KUDOS
@Vitality - Hope you have understood the solution given by Bunuel.
Now coming to your Qs - how we received 24?

Since each of the 3 digits - 3,4,5 appear twice at each position, hence we have multiplied the sum of these 3 digits i.e 12 by 2.

Sum @hundreds position = (3+4+5) * 100 * 2 = 12 * 2 * 100 = 24 *100
Sum @tens position = (3+4+5) * 10 * 2 = 12 * 2 *10 = 24 * 10
Sum @units position = (3+4+5) * 1 * 2 = 12 * 2 = 24
Total = 2400 + 240 + 24 = 2664.
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1770
Followers: 165

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

Premium Member
Re: What is the sum of all possible 3-digit numbers that can be [#permalink] New post 16 Jul 2014, 23:42
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

Re: What is the sum of all possible 3-digit numbers that can be   [#permalink] 16 Jul 2014, 23:42
    Similar topics Author Replies Last post
Similar
Topics:
8 Experts publish their posts in the topic What is the sum of all possible 3-digit numbers that can be sugu86 11 25 Apr 2012, 23:59
2 Experts publish their posts in the topic What is the sum of all the possible 3 digit numbers that can VeritasPrepKarishma 4 05 Jul 2011, 20:16
28 Experts publish their posts in the topic What is the sum of all 3 digit positive integers that can be asimov 17 29 Apr 2009, 00:06
What is the SUM of all possible 3 digit numbers that can be bmwhype2 2 17 Oct 2007, 20:59
What is the sum of the 3 digit numbers that can be formed krishrads 5 02 Jun 2005, 02:52
Display posts from previous: Sort by

What is the sum of all possible 3-digit numbers that can be

  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®.