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

It is currently 25 Sep 2018, 10:51

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

1,234 1,243 1,324 ... ... +4,321 _______

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
VP
VP
avatar
Joined: 06 Jun 2004
Posts: 1020
Location: CA
1,234 1,243 1,324 ... ... +4,321 _______   [#permalink]

Show Tags

New post 20 Dec 2005, 00:44
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

1,234
1,243
1,324
...
...
+4,321
_______

The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1, 2 3, and 4 exactly once in each integer. What is the sume of these 24 integers?

(A) 24,000
(B) 26,664
(C) 40,440
(D) 60,000
(E) 66,660

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 4906
Location: Singapore
  [#permalink]

Show Tags

New post 20 Dec 2005, 01:05
Keeping 1 in the thousands place, we can have 6 arrangements for 2,3 and 4:

1234
1243
1324
1342
1432
1423

Keeping 2 in the thousands place, we can have 6 arrangements as well for 1,3,4
This time round, in the ones, tens and hundreds and thousands position, we will have 1,3,4 occuring twice in their respective positions.

Therefore, if we add the 24 numbers, we will have 1,2,3,4 occuring 6 times in their respective places.

For ones position, we will have 1,2,3,4 occuring 6 times. This gives us 6+12+18+24 = 60. So we keep 0 and carry 6 to the tens position.

For tens position, we will have 1,2,3,4 occuring 6 times. This gives us 60+6 = 66. Keep 6 and carry 6 to the hundreds positions.

For hundreds position, the sum is now 60+6 = 66. Keep 6 and carry 6 to thousands positions.

For thousands position, the sum is 66 with no carry over.

The sum of the 24 numbers is therefore 66,660 (E)
Director
Director
avatar
Joined: 09 Jul 2005
Posts: 566
  [#permalink]

Show Tags

New post 20 Dec 2005, 02:59
Each column sums 60. the answer should be E.
Senior Manager
Senior Manager
User avatar
Joined: 15 Apr 2005
Posts: 410
Location: India, Chennai
Re: PS: Addition  [#permalink]

Show Tags

New post 20 Dec 2005, 03:24
There are 6 different numbers with 1 in the thousands place, and similarly 6 different numbers for 2,3 and 4.

So approximately we will have
6 * 1000 = 6000 +
6 * 2000 = 12000 +
6 * 3000 = 18000 +
6 * 4000 = 24000
= 60000

We have just counted for the thousand's digit. So if we have to count the hundreds digit, tens and unit digit, it should be obvious that the number is > 60000. Hence E.
Manager
Manager
avatar
Joined: 12 Nov 2005
Posts: 77
  [#permalink]

Show Tags

New post 20 Dec 2005, 10:31
1
The answer is 66660.

If one can remember, here's the formula for that.

The sum of all the numbers formed from n digits is

(n-1)! *(Sum of Digits)*(111...n times)

Here in this case, n =(1,2,3,4)
Therefore Sum = (4-1)!* (1+2+3+4)*(1111) .....
= 6*10*1111
=66660
Intern
Intern
avatar
Joined: 26 Sep 2005
Posts: 3
Location: Rochester Hills,MI
  [#permalink]

Show Tags

New post 20 Dec 2005, 13:05
1
This is when you don't remember formulae.
My approach is from units place... when you look at the given answers all the number have different digits in tens place.
So attack from units end
There are 24 numbers with these numbers arranged ==> there are 6
numbers with each digit in units place.
1 * 6 = 06
2 * 6 = 12
3 * 6 = 18
4 * 6 = 24
=======
60

the last 2 digits should be 60 ====> E
I don't know if this is the right approach... Please correct me, if I am deviating
Thanks in advance
Senior Manager
Senior Manager
avatar
Joined: 03 Nov 2005
Posts: 346
Location: Chicago, IL
  [#permalink]

Show Tags

New post 20 Dec 2005, 13:34
1234
1324
1432

2134
2314
2431

.......
4231

There are 12 possible combinations with 1,2,3,4 where each digit is used 3 times in each place. The sum =1+2+3+4=10

So, sum=3*10*1000+3*10*100+3*10+10+ 3*10=33330
To find the sum of 24 numbers, multiply by 2=66660
_________________

Hard work is the main determinant of success

Senior Manager
Senior Manager
avatar
Joined: 11 Nov 2005
Posts: 313
Location: London
  [#permalink]

Show Tags

New post 20 Dec 2005, 15:35
I liked the method of 'krisrini' simple and easy to follow!

good work
Director
Director
avatar
Joined: 14 Sep 2005
Posts: 955
Location: South Korea
  [#permalink]

Show Tags

New post 21 Dec 2005, 02:11
This is interesting.


The sum of the following

1234
1324
1432
2134
2314
2431
...
4231

is same as the sum of the following;

1111
1111
1111
1111
1111
1111
2222
2222
2222
2222
2222
2222
3333
3333
3333
3333
3333
3333
4444
4444
4444
4444
4444
4444

Obviously, it's 66,660.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Auge um Auge, Zahn um Zahn :twisted: !

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8179
Premium Member
Re: 1,234 1,243 1,324 ... ... +4,321 _______   [#permalink]

Show Tags

New post 04 Sep 2018, 08:39
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: 1,234 1,243 1,324 ... ... +4,321 _______ &nbs [#permalink] 04 Sep 2018, 08:39
Display posts from previous: Sort by

1,234 1,243 1,324 ... ... +4,321 _______

  post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

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®.