Find the sum of all the four digit numbers which are formed : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 05 Dec 2016, 13:44

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Find the sum of all the four digit numbers which are formed

Author Message
TAGS:

Hide Tags

Manager
Joined: 09 May 2009
Posts: 203
Followers: 1

Kudos [?]: 218 [1] , given: 13

Find the sum of all the four digit numbers which are formed [#permalink]

Show Tags

23 Dec 2009, 05:38
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

77% (02:21) correct 23% (01:44) wrong based on 231 sessions

HideShow timer Statistics

Find the sum of all the four digit numbers which are formed by digits 1, 2, 5, 6

A. 933510
B. 93324
C. 65120
D. 8400
[Reveal] Spoiler: OA

_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Last edited by Bunuel on 06 Nov 2012, 02:22, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 35867
Followers: 6840

Kudos [?]: 89958 [5] , given: 10384

Show Tags

23 Dec 2009, 06:16
5
KUDOS
Expert's post
4
This post was
BOOKMARKED
xcusemeplz2009 wrote:
find the sum of all the four digit numbers which are formed by digits 1,2,5,6

a)933510
b)93324
c)65120
d)8400

The answer choices make the solution easy:

There are 4!=24 four digit numbers which are formed by digits 1, 2, 5, 6.

Obviously 24/4=6 numbers will end with 1; 6 numbers will end with 2, 6 numbers with 5 and 6 numbers with 6.

6*1+6*2+6*5+6*6=6*14=84, which means that the sum of all these 24 numbers must end by 4, only answer choice with 4 at the end is B.

But if we were not given such an easy answer choices, the solution would be:

We have 24 numbers of the of the form: 1000a+100b+10c+d, where a, b, c and d can take any value from the set {1, 2, 5, 6} and there will be 6 numbers with same digit (a, b, c, d) at the thousands, hundreds, tens and units digits.

(1000*6a+1000*6b+1000*6c+1000*6d)+(100*6a+100*6b+100*6c+100*6d)+(10*6a+10*6b+10*6c+10*6d)+(6a+6b+6c+6d)=(6a+6b+6c+6d)(1111)=
=6(a+b+c+d)(1111)=6*14*1111=93324

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)
_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 414 [0], given: 11

Show Tags

20 Dec 2012, 04:36
Hi Bunnuel?,
If it's not mention that repetitions is allowed, do I have to assume that repetitions are not allowed?
_________________

Impossible is nothing to God.

Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 60

Kudos [?]: 581 [0], given: 355

Re: Find the sum of all the four digit numbers which are formed [#permalink]

Show Tags

30 Dec 2013, 07:27
xcusemeplz2009 wrote:
Find the sum of all the four digit numbers which are formed by digits 1, 2, 5, 6

A. 933510
B. 93324
C. 65120
D. 8400

3!*1111*(14) will have units digit 4

Hope it helps
Cheers!
J
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12876
Followers: 559

Kudos [?]: 158 [1] , given: 0

Re: Find the sum of all the four digit numbers which are formed [#permalink]

Show Tags

25 May 2015, 02:41
1
KUDOS
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 Club Legend
Joined: 09 Sep 2013
Posts: 12876
Followers: 559

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

Re: Find the sum of all the four digit numbers which are formed [#permalink]

Show Tags

15 Jun 2016, 15:26
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.
_________________
Re: Find the sum of all the four digit numbers which are formed   [#permalink] 15 Jun 2016, 15:26
Similar topics Replies Last post
Similar
Topics:
16 What is the sum of all four digit integers formed using the digits 1, 7 24 Feb 2016, 03:18
10 How many distinct four-digit numbers can be formed by the 11 02 Jan 2014, 12:09
21 Find the sum of all the four digit numbers formed using the 8 24 Oct 2010, 10:03
61 What is the sum of all 4-digit numbers that can be formed 17 25 May 2010, 23:38
22 Find the sum of all 3-digit nos that can be formed by 1, 2 10 07 Jan 2010, 01:17
Display posts from previous: Sort by