Find the sum of all 3-digit nos that can be formed by 1, 2 : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 08 Dec 2016, 11:43
GMAT Club Tests

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Find the sum of all 3-digit nos that can be formed by 1, 2

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

Hide Tags

Manager
Manager
avatar
Joined: 25 Nov 2009
Posts: 54
Location: India
Followers: 0

Kudos [?]: 53 [0], given: 8

Find the sum of all 3-digit nos that can be formed by 1, 2 [#permalink]

Show Tags

New post 07 Jan 2010, 01:17
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

75% (01:30) correct 25% (00:46) wrong based on 24 sessions

HideShow timer Statistics

Find the sum of all 3-digit nos that can be formed by 1, 2 and 3

(Ref: Kaplan. I didn't understand the explanation there. Can u pl help?)
Kaplan GMAT Prep Discount CodesMagoosh Discount CodesEconomist GMAT Tutor Discount Codes
2 KUDOS received
Intern
Intern
avatar
Joined: 20 Dec 2009
Posts: 14
Followers: 1

Kudos [?]: 28 [2] , given: 5

Re: Sum of all 3-digit nos with 1, 2 & 3 [#permalink]

Show Tags

New post 07 Jan 2010, 01:56
2
This post received
KUDOS
3
This post was
BOOKMARKED
As nothing has been mentioned in the question, we'll assume that repetition of numbers are allowed.
Hence the total number of 3 digit numbers that can be formed from 1,2,3 = 3*3*3
= 27.

Now out of these 27 numbers each of the digits 1,2,3 will occur at each of the hundred's, ten's and unit's position 9 times. e.g. starting from all the numbers having 1 in hundred position we have the following numbers -
111
112
113
121
122
123
131
132
133
Similar would be the sequence for numbers starting with 2 and 3 and if we count we'll find that 1,2,3 occurs at hundreds position 9 times each; at tens position 9 times each and at units position 9 times each.
Hence the sum of all these 27 numbers =
[(1+2+3) * 100 + (1+2+3) * 10 + (1+2+3) * 1 ] * 9
= 6 * 111 * 9 = 54 * 111 = 5994.
Hope this clarifies or else I will elaborate it more.
Thanks!
1 KUDOS received
Manager
Manager
avatar
Joined: 25 Nov 2009
Posts: 54
Location: India
Followers: 0

Kudos [?]: 53 [1] , given: 8

Re: Sum of all 3-digit nos with 1, 2 & 3 [#permalink]

Show Tags

New post 07 Jan 2010, 03:29
1
This post received
KUDOS
Hey thnx. It helps.

But thr's another explanation:

No of such 3-digit nos = 27 (which is Ok)
1st no = 111, Last no = 333 (these r also Ok)
Hence their average = (111 + 333)/2 = 222
(couldn't understand how this formula is applied. I thought this holds true for an AP series only)
So, Sum = Number of nos X Average of the nos
= 27 X 222 = 5994
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 02 Aug 2009
Posts: 4139
Followers: 306

Kudos [?]: 3250 [0], given: 100

Re: Sum of all 3-digit nos with 1, 2 & 3 [#permalink]

Show Tags

New post 07 Jan 2010, 03:46
hi sudip what i can of think as a way is... total nos=3*3*3=27.....
so sum will have 27 nos .... so each no 1,2,3 will be used (27/3)9 times in each digits place (hundreds,tens and ones)
...units digit=9*(1+2+3)=54, so 4..
tens digit=9*(1+2+3)=54(+5)=9, so 9.."+5" is the carried tens digit from 54 of step 1
hundreds digit=9*(1+2+3)=54(+5)=59, so the no is 5994..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Manager
Manager
avatar
Joined: 25 Nov 2009
Posts: 54
Location: India
Followers: 0

Kudos [?]: 53 [0], given: 8

Re: Sum of all 3-digit nos with 1, 2 & 3 (no repeat) [#permalink]

Show Tags

New post 08 Jan 2010, 00:53
Thnx.

By the way, what happens to the same problem if we are not allowed to repeat any of the digits in any particular no formed from by the digits (i.e. 111 or 221 or 133 etc are not to be considered)?
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 02 Aug 2009
Posts: 4139
Followers: 306

Kudos [?]: 3250 [0], given: 100

Re: Sum of all 3-digit nos with 1, 2 & 3 [#permalink]

Show Tags

New post 08 Jan 2010, 02:26
if the digits are not to be repeated..
total nos=3*2*1=6.. so each no 2 times..
no is =(3+2+1)*2*100+(3+2+1)*2*10+ (3+2+1)*2*1=1200+120+12=1332
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35912
Followers: 6853

Kudos [?]: 90055 [0], given: 10402

Re: Sum of all 3-digit nos with 1, 2 & 3 [#permalink]

Show Tags

New post 09 Jan 2010, 15:22
Expert's post
7
This post was
BOOKMARKED
sudip135 wrote:
Q. Find the sum of all 3-digit nos that can be formed by 1, 2 and 3 (Ref: Kaplan. I didn't understand the explanation there. Can u pl help?)


GMAT will tell you in advance whether repetition is allowed or not. Or the wording will make it obvious.

Actually there is the direct formula for this kind of problems. Of course it's better to understand the concept, then to memorize the formula but in case someone is interested here it is:

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).
_________________

New to the Math Forum?
Please read this: 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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12895
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: Find the sum of all 3-digit nos that can be formed by 1, 2 [#permalink]

Show Tags

New post 16 Jul 2014, 23:25
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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12895
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: Find the sum of all 3-digit nos that can be formed by 1, 2 [#permalink]

Show Tags

New post 14 Aug 2015, 06:10
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

Manager
Manager
User avatar
Joined: 10 Jun 2015
Posts: 128
Followers: 1

Kudos [?]: 25 [0], given: 0

Re: Find the sum of all 3-digit nos that can be formed by 1, 2 [#permalink]

Show Tags

New post 14 Aug 2015, 23:36
jusjmkol740 wrote:
Find the sum of all 3-digit nos that can be formed by 1, 2 and 3

(Ref: Kaplan. I didn't understand the explanation there. Can u pl help?)

with digits 1, 2, 3 you can form 3*3*3=27 distinct three digit numbers.
If you observe the unit digits, it is a repetition of 1,2, and 3, each digit repeating 9 times
The sum of 1,2, and 3 is 6. Therefore, when you add all 27 unit digits you get 9*6=54
If you add the ten's digits, again you get 54
If you add the hundred's digits, again you get 54
Now, you can mentally add
the answer is 5994.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12895
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: Find the sum of all 3-digit nos that can be formed by 1, 2 [#permalink]

Show Tags

New post 23 Oct 2016, 20:36
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: Find the sum of all 3-digit nos that can be formed by 1, 2   [#permalink] 23 Oct 2016, 20:36
    Similar topics Author Replies Last post
Similar
Topics:
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
11 Experts publish their posts in the topic What is the sum of all possible 3-digit numbers that can be Bunuel 5 07 Jan 2010, 04:07
20 What is the sum of all 3 digit positive integers that can be formed us R2I4D 7 30 Dec 2009, 02:29
52 Experts publish their posts in the topic What is the sum of all 3 digit positive integers that can be formed sdrandom1 21 28 Jun 2009, 18:01
115 Experts publish their posts in the topic What is the sum of all 3 digit positive integers that can be asimov 20 29 Apr 2009, 00:06
Display posts from previous: Sort by

Find the sum of all 3-digit nos that can be formed by 1, 2

  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 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®.