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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Find the sum of 4 digit numbers [#permalink]
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+

Re: Find the sum of 4 digit numbers [#permalink]
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

Re: Find the sum of 4 digit numbers [#permalink]
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?

Re: Find the sum of 4 digit numbers [#permalink]
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+

gmatclubot

Re: Find the sum of 4 digit numbers
[#permalink]
26 Aug 2012, 07:06