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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

Re: Nice question and a good way to solve.... [#permalink]
24 Oct 2010, 10:22

8

This post received KUDOS

2

This post was BOOKMARKED

We can form a total of 4! or 24 numbers.When we add all these numbers ,let us look at the contribution of of the digit 2 to the sum.

When 2 occurs in the thousand place in a particular number,its contribution in the total will be 2000.the number of numbers that can be formed with 2 in the thousand place is 3! i.e 6 numbers.Hence when 2 is in the thousands place its contribution to the sum is 3! * 2000

Similarly when 2 occurs in the hundreds place, its contribution to the sum is 3! * 200

Similarly when 2 occurs in the tenth place, its contribution to the sum is 3! * 20

Similarly when 2 occurs in the unit place, its contribution to the sum is 3! * 10

The total contribution of 2 to the sum is 3! *(2000+200+20+1)=3!*2222 In a similar manner ,the contribution of 3,4, and 5 to sum will respectively be 3!*3333,3!*4444 and 3!*5555

Hence total sum using the aove four digits 3!*(2222+3333+4444+5555) i.e 3! *(2+3+4+5) * 1111

Now we can generalize the above

If all the possible n digit numbers using n distinct digits are formed ,the sum of all the numbers so formed is equal to (n-1)! * ( sum of the n digits ) *( 1111...n times)

Re: Nice question and a good way to solve.... [#permalink]
24 Oct 2010, 10:24

1

This post received KUDOS

ankitranjan wrote:

Find the sum of all the four digit numbers formed using the digits 2,3,4 and 5 without repetition.

I will post OA and OE tomorrow.

If u find this post useful ,consider giving me KUDOS.

Along with the question, do post the options.

if you keep the digit 2 at the one's digit. The total numbers that can be formed is 3! = 6 => 2 occurs at one's digit 6 times. Similarly all the 4 numbers occurs at one's digit 6 times.

Similar all the 4 numbers occurs at all the 4 digits - one's,ten's, hundred's, thousand's- 6 times.

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).

Re: Find the sum of all the four digit numbers formed using the [#permalink]
27 Apr 2013, 07:21

Hi Bunuel, So in the below question if we apply the formula shouldn't we consider 4 as n? Find the sum of all the four digit numbers formed using the digits 2,3,4 and 5 without repetition. (4-1)*(2+3+4+5)*1111 Many thanks for your help. Aybige

Re: Find the sum of all the four digit numbers formed using the [#permalink]
28 Apr 2013, 02:28

Expert's post

aybige wrote:

Hi Bunuel, So in the below question if we apply the formula shouldn't we consider 4 as n? Find the sum of all the four digit numbers formed using the digits 2,3,4 and 5 without repetition. (4-1)!*(2+3+4+5)*1111 Many thanks for your help. Aybige

Correct, but you've missed factorial (!). It should be: (4-1)!*(2+3+4+5)*(1111)=93324. _________________

I´ve done an interview at Accepted.com quite a while ago and if any of you are interested, here is the link . I´m through my preparation of my second...

It’s here. Internship season. The key is on searching and applying for the jobs that you feel confident working on, not doing something out of pressure. Rotman has...