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 500,000 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:

What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

26 Apr 2012, 00:59

1

This post received KUDOS

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

86% (01:49) correct
14% (00:42) wrong based on 182 sessions

HideShow timer Statistics

What is the sum of all possible 3-digit numbers that can be constructed using the digits 3, 4 and 5 if each digit can be used only once in each number ?

Re: What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

26 Apr 2012, 01:20

6

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

sugu86 wrote:

What is the sum of all possible 3-digit numbers that can be constructed using the digits 3, 4 and 5 if each digit can be used only once in each number ?

A) 2660 B) 2661 C) 2662 D) 2663 E) 2664

Thanks,

Suganth

What is the sum of all possible 3-digit numbers that can be constructed using the digits 3, 4 and 5 if each digit can be used only once in each number ? A. 2660 B. 2661 C. 2662 D. 2663 E. 2664

Any 3-digit number can be written as: 100a+10b+c.

# of three digit numbers with digits {3, 4, 5} is 3!=6.

These 6 numbers will have 6/3=2 times 3 as hundreds digit (a), 2 times 4 as as hundreds digit, 2 times 5 as hundreds digit.

Re: What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

02 Oct 2012, 08:59

2

This post received KUDOS

sugu86 wrote:

What is the sum of all possible 3-digit numbers that can be constructed using the digits 3, 4 and 5 if each digit can be used only once in each number ?

A. 2660 B. 2661 C. 2662 D. 2663 E. 2664

the unit digits of all possible 3-digit numbers are supposed to have a sum of 3 +3 +4+4+5+5=24, so the sum of numbers should have 4 as a unit digit - 2664 is the only possible option.

Re: What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

02 Oct 2012, 09:36

I think Bunuel got the basic way to solve this kind of question. if the number is 4 digit or the answer has 4 number with last number is 4 then U should follow Bunuel

Re: What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

06 Oct 2012, 19:53

thaihoang305 wrote:

I think Bunuel got the basic way to solve this kind of question. if the number is 4 digit or the answer has 4 number with last number is 4 then U should follow Bunuel

Many thanks to Bunuel for his very clear explanations, I am going through all problems with his explanations in forum's PS part. For this very problem I just wanted to find out the fastest way to solve as far as you need to take time into account as well.

I encountered the below question on MGAT 5th Edition FDP guide, and the last part (underlined) does not make sense to me.

What is the sum of all the possible three-digit numbers that can be constructed using the digits 3, 4, and 5 if each digit can be used only once in each number

The answer provided by the guide is below: (and I know how to solve the problem that results in the below answer, but that underlined part of the question threw me away):

Re: Unable to comprehend this question [#permalink]

Show Tags

07 Nov 2012, 15:00

Expert's post

megafan wrote:

I encountered the below question on MGAT 5th Edition FDP guide, and the last part (underlined) does not make sense to me.

What is the sum of all the possible three-digit numbers that can be constructed using the digits 3, 4, and 5 if each digit can be used only once in each number

The answer provided by the guide is below: (and I know how to solve the problem that results in the below answer, but that underlined part of the question threw me away):

Re: What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

20 Jan 2013, 17:33

5

This post received KUDOS

1

This post was BOOKMARKED

Another way to approach this problem is to recognize that the way the sequence increases from the min (345) is symmetrical to the way it decreases from the max (543). Therefore if you find the average of the min and max and multiply it by the number of possibilities (3! or 6) then you'll have your answer.

Re: What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

21 Jan 2013, 03:08

1

This post was BOOKMARKED

Bunuel wrote:

sugu86 wrote:

What is the sum of all possible 3-digit numbers that can be constructed using the digits 3, 4 and 5 if each digit can be used only once in each number ?

A) 2660 B) 2661 C) 2662 D) 2663 E) 2664

Thanks,

Suganth

What is the sum of all possible 3-digit numbers that can be constructed using the digits 3, 4 and 5 if each digit can be used only once in each number ? A. 2660 B. 2661 C. 2662 D. 2663 E. 2664

Any 3-digit number can be written as: 100a+10b+c.

# of three digit numbers with digits {3, 4, 5} is 3!=6.

These 6 numbers will have 6/3=2 times 3 as hundreds digit (a), 2 times 4 as as hundreds digit, 2 times 5 as hundreds digit.

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)

In our original question: n=3. sum of digits=3+4+5=12. --> (3-1)!*(12)*(111)=24*111=2664.

Hope it's clear.

wow on this type of a question i was only able to come up with the computation of possible number of ways of arranging 3 digits,but the rest part gave me problems

truly speaking @bunuel i am complete lost on this part( These 6 numbers will have 6/3=2 times 3 as hundreds digit (a), 2 times 4 as as hundreds digit, 2 times 5 as hundreds digit.

The same with tens and units digits.

100*(2*3+2*4+2*5)+10*(2*3+2*4+2*5)+(2*3+2*4+2*5)=100*24+10*24+24=24*111=2664.)...but i guess the formula would make it easier..you should add it in the topic of number theory in the gmat math book.. Rgrds

Re: What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

06 Sep 2014, 18:27

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: What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

26 Sep 2015, 20:01

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: What is the sum of all possible 3-digit numbers that can be [#permalink]

Show Tags

17 Apr 2016, 09:29

there are 6 ways to answer to arrange the 3 digits: 345, 354, 435, 453, 534, 543, with repetitions of 3+3+4+4+5+5 = 24 each time you go down. If you multiply the 24*100 for the hundred, 24*10 for the tens and 24 *1 for the single digits, then you can put it together like this: 24*100 + 24*10 + 24 = 2,400 + 240 + 24 = 2,664. this is the answer.

gmatclubot

Re: What is the sum of all possible 3-digit numbers that can be
[#permalink]
17 Apr 2016, 09:29

Last year when I attended a session of Chicago’s Booth Live , I felt pretty out of place. I was surrounded by professionals from all over the world from major...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...