GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Oct 2019, 21:31

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.

Close

Request Expert Reply

Confirm Cancel

What is the sum of all possible 3-digit numbers that can be constructe

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 27 Mar 2012
Posts: 14
What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post Updated on: 28 Aug 2019, 22:54
2
12
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

83% (01:19) correct 17% (01:23) wrong based on 250 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 ?

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

Originally posted by sugu86 on 26 Apr 2012, 00:59.
Last edited by Bunuel on 28 Aug 2019, 22:54, edited 2 times in total.
Edited the question
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 26 Apr 2012, 01:20
11
1
13
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.

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.

Answer: E.

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.
_________________
Most Helpful Community Reply
Intern
Intern
avatar
Joined: 21 Dec 2012
Posts: 6
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 20 Jan 2013, 17:33
13
3
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.

\(\frac{345+543}{2} = 444\)

\(444*3! = 444*6 = 2664\)
General Discussion
Intern
Intern
avatar
Joined: 02 Apr 2012
Posts: 3
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 02 Oct 2012, 08:59
6
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.
Manager
Manager
avatar
Joined: 31 May 2011
Posts: 199
GMAT ToolKit User
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 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
Intern
Intern
avatar
Joined: 02 Apr 2012
Posts: 3
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 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.
Manager
Manager
avatar
Joined: 04 Jan 2013
Posts: 68
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 21 Jan 2013, 03:08
2
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.

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.

Answer: E.

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 :-)

Posted from my mobile device
Manager
Manager
avatar
Joined: 28 Feb 2012
Posts: 103
Concentration: Strategy, International Business
Schools: INSEAD Jan '13
GPA: 3.9
WE: Marketing (Other)
GMAT ToolKit User
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 27 Aug 2013, 23:42
1
I like that approach because it has precise formula, but could you please clarify this part:

Bunuel wrote:

(n-1)!*(sum of the digits)*(111…..n times)[/b]



So when to use 111 and when to use different number? You stated 111.....n times, isn't it should be 3 times in our case?
_________________
If you found my post useful and/or interesting - you are welcome to give kudos!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 28 Aug 2013, 09:26
ziko wrote:
I like that approach because it has precise formula, but could you please clarify this part:

Bunuel wrote:

(n-1)!*(sum of the digits)*(111…..n times)[/b]



So when to use 111 and when to use different number? You stated 111.....n times, isn't it should be 3 times in our case?


111... n times mean that if we have 2 digits it should be 11, if 3 digits 111, if 4 digits it should be 1,111.

Similar questions to practice:
find-the-sum-of-all-the-four-digit-numbers-formed-using-the-103523.html
find-the-sum-of-all-the-four-digit-numbers-which-are-formed-88357.html
find-the-sum-of-all-3-digit-nos-that-can-be-formed-by-88864.html
if-the-three-unique-positive-digits-a-b-and-c-are-arranged-143836.html
what-is-the-sum-of-all-3-digit-positive-integers-that-can-be-78143.html
what-is-the-sum-of-all-4-digit-numbers-that-can-be-formed-94836.html
the-sum-of-the-digits-of-64-279-what-is-the-141460.html
there-are-24-different-four-digit-integers-than-can-be-141891.html
the-addition-problem-above-shows-four-of-the-24-different-in-104166.html

Hope it helps.
_________________
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 05 Apr 2018, 16:58
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 possible 3-digit numbers are:

345, 354, 435, 453, 543, 534

Summing just the units digits of these 6 numbers, we get:

5 + 5 + 4 + 4 + 3 + 3 = 10 + 8 + 6 = 24

The only answer with a units digit of 4 is 2,664.

Answer: E
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
S
Joined: 20 Aug 2017
Posts: 36
CAT Tests
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 22 Aug 2019, 11:25
6
when we need to find the sum of digits such as in this case we can either form cases because the number of digits are less.

else the concept to find the sum is

ABC.
when C is 3,4,5 so AB can be arranged in 2! ways.

the sum of digits is 3+4+5 and since it is in the units digits it takes a place value of 1.
so it becomes (3+4+5)*1*2!

similarly in 10s digit, we fix 3,4,5 and the rest of the digits can be arranged in 2! ways.

so the place value is 10 and sum becomes (3+4+5)*10*2!

similarly for hundreds place it becomes (3+4+5)*100*2!

to find the sum of all digits we add these three,
it becomes 100(3+4+5)2! + 10(3+4+5)2! + 1(3+4+5)2!
taking 2! and sum of digits as common.

2!(3+4+5)*111

we can also generalise a formula from this,
3,4,5 ----> no of digits(n) = 3

the formula becomes
(n-1)! (111....n times) ( sum of digits)

so here n = 3.
putting the values in the formula,
(3-1)! (111) (3+4+5).

This gives us the answer as 2664.

If you like my solution, do give me kudos!
_________________
---------------------------------------------------------------------------------------
Nobody can defeat you, until you yourself give up!

If you like my solution, do give kudos!
Manager
Manager
avatar
B
Joined: 20 Jul 2012
Posts: 116
GMAT 1: 650 Q47 V33
What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 22 Aug 2019, 13:40
HullDown wrote:
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 is used only once in each number?

A) 2664
B) 2550
C) 2320
D) 3567
E) 1456


Each no. 3, 4, 5 will occur twice at any place. So in all the places it will be 2*(3+4+5) = 24.
In the units place 4 will come and carry is 2. In the tens place it will be 24+2 = 26 so 6 and carry 2. then at hundredth place it will be again 24+2 = 26 so 6 and carry 2.

So the sum will be 2664
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1224
What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 22 Aug 2019, 13:57
1
HullDown wrote:
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 is used only once in each number?

A) 2664
B) 2550
C) 2320
D) 3567
E) 1456


add least and greatest:
345+543=888
888/2=444 average
444*3!=2664
SVP
SVP
User avatar
P
Joined: 03 Jun 2019
Posts: 1723
Location: India
Premium Member Reviews Badge CAT Tests
Re: What is the sum of all possible 3-digit numbers that can be constructe  [#permalink]

Show Tags

New post 22 Aug 2019, 18:02
HullDown wrote:
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 is used only once in each number?

A) 2664
B) 2550
C) 2320
D) 3567
E) 1456


Number of 3 digit numbers formed using 3,4,5 = 3! with each digit appearing twice at each place.

Sum of all 6 such numbers = 2*111*(3+4+5) = 222*12= 2664

IMO E

Posted from my mobile device
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
GMAT Club Bot
Re: What is the sum of all possible 3-digit numbers that can be constructe   [#permalink] 22 Aug 2019, 18:02
Display posts from previous: Sort by

What is the sum of all possible 3-digit numbers that can be constructe

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne