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

It is currently 30 Aug 2014, 02:17

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

Find the sum of 4 digit numbers

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 278
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 20 [0], given: 282

Find the sum of 4 digit numbers [#permalink] New post 24 Aug 2012, 01:31
Find the sum of all the 4 digit numbers which are formed by the digits 1,2,5,6.

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

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

BSchool Thread Master
User avatar
Status: If you think you can, then eventually you WILL!
Joined: 05 Apr 2011
Posts: 429
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 57

Kudos [?]: 234 [0], given: 41

GMAT Tests User Premium Member
Re: Find the sum of 4 digit numbers [#permalink] New post 24 Aug 2012, 01:52
Find the sum of all the 4 digit numbers which are formed by the digits 1,2,5,6.

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

A 4 digit number abcd is written as 1000*a + 100*b + 10*c + d

Possible 4digit numbers starting with 1 in thousdands digit are
1256
1265
1526
1562
1625
1652
As, you will notice the pattern in the hundred's ten's and unit's digit then 2,5 and 6 each occur twice in hundred's ten's and unit's digit
So Sum of all the numbers in which 1 is in the thousand's digit is given by
1000*6*1 + 100*2*(2+5+6) + 10*2*(2+5+6) + 1*2*(2+5+6)
= 6000 + (2+5+6)*2*(100+10+1)
= 6000 + 13*2*111
= 8886

Similarly when 2 is in the thousand's digit then the sum of all the numbers will be
1000*6*2 + 100*2*(1+5+6) + 10*2*(1+5+6) + 1*2*(1+5+6)
= 12,000 + 12*2*111
=> Sum = 14664

Similarly when 5 is in the thousand's digit then the sum of all the numbers will be
1000*6*5 + 100*2*(1+2+6) + 10*2*(1+2+6) + 1*2*(1+2+6)
= 30,000 + 111*2*9
=> Sum =31,998

Similarly when 6 is in the thousand's digit then the sum of all the numbers will be
1000*6*6 + 100*2*(1+2+5) + 10*2*(1+2+5) + 1*2*(1+2+5)
= 36,000 + 111*2*8
=> Sum = 37,776

Total Sum = 8886 + 14664 + 31,998 + 37,776 = 93,324

ONe MOre way of doing this is taking all the sums together then we have
1000*6*(1+2+5+6) + 100*2*3*(1+2+5+6) + 10*2*3*(1+2+5+6) + 1*2*3*(1+2+5+6)
= (1+2+5+6) * (6000+600+60+6)
= 14 * 6666
= 93,324

So, Answer is B

Hope it helps!
_________________

ankit
you must believe

How to start GMAT preparations?
How to Improve Quant Score?
gmatclub topic tags
Check out my GMAT debrief
Thursdays with Ron link
Looking for a Quant tutor? Check out my post for the same!

Combined Formula Sheet :
Number Properties || Word Problems and PnC || Equations, Inequalities || Geometry

How to Solve :
Statistics || Reflection of a line || Remainder Problems

Manager
Manager
avatar
Joined: 24 Jul 2011
Posts: 77
Location: India
Concentration: Strategy, General Management
GMAT 1: 670 Q49 V33
WE: Asset Management (Manufacturing)
Followers: 2

Kudos [?]: 59 [0], given: 5

Re: Find the sum of 4 digit numbers [#permalink] New post 26 Aug 2012, 06:26
Here is the short cut :

4 digit number is in the form of abcd
total number formed by different 4 digit numbers = 4! = 24
This 24 numbers are formed in which one of the four digits, say a, take all four positions.
So, a takes unit position > 6 nos.
a takes tens position > 6 nos.
a takes hundreds position > 6 nos.
a takes thousands position > 6 nos.

This mean number all the four numbers takes unit position 6 numbers, tens - 6 numbers, hundreds - 6 numbers and thousands - 6 numbers.

so, sum of thousands position = ((1+2+5+6)*6)* 1000 = 84000
sum of hundreds position = ((1+2+5+6)*6)* 100 = 8400
sum of tens position = ((1+2+5+6)*6)* 10 = 840
sum of unit position = ((1+2+5+6)*6) = 84
-----------------------------------------------------------------------------------
Total = 93324
_________________

My mantra for cracking GMAT:
Everyone has inborn talent, however those who complement it with hard work we call them 'talented'.


+1 Kudos = Thank You Dear :)
Are you saying thank you?

Senior Manager
Senior Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 278
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Followers: 9

Kudos [?]: 20 [0], given: 282

Re: Find the sum of 4 digit numbers [#permalink] New post 26 Aug 2012, 07:06
premnath wrote:
Here is the short cut :

4 digit number is in the form of abcd
total number formed by different 4 digit numbers = 4! = 24
This 24 numbers are formed in which one of the four digits, say a, take all four positions.
So, a takes unit position > 6 nos.
a takes tens position > 6 nos.
a takes hundreds position > 6 nos.
a takes thousands position > 6 nos.

This mean number all the four numbers takes unit position 6 numbers, tens - 6 numbers, hundreds - 6 numbers and thousands - 6 numbers.

so, sum of thousands position = ((1+2+5+6)*6)* 1000 = 84000
sum of hundreds position = ((1+2+5+6)*6)* 100 = 8400
sum of tens position = ((1+2+5+6)*6)* 10 = 840
sum of unit position = ((1+2+5+6)*6) = 84
-----------------------------------------------------------------------------------
Total = 93324



Yes This is a simpler way to solve this.. nice job :)
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Re: Find the sum of 4 digit numbers   [#permalink] 26 Aug 2012, 07:06
    Similar topics Author Replies Last post
Similar
Topics:
The sum of the digits of a two digit number.. vomhorizon 4 14 Nov 2012, 07:34
8 Experts publish their posts in the topic Find the sum of all the four digit numbers formed using the ankitranjan 8 24 Oct 2010, 10:03
13 Experts publish their posts in the topic What is the sum of all 4-digit numbers that can be formed dimitri92 12 25 May 2010, 23:38
2 Experts publish their posts in the topic Find the sum of all the four digit numbers which are formed xcusemeplz2009 3 23 Dec 2009, 05:38
7 Experts publish their posts in the topic Sum of 3-digit numbers sdrandom1 14 28 Jun 2009, 18:01
Display posts from previous: Sort by

Find the sum of 4 digit numbers

  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®.