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What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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Updated on: 30 Sep 2018, 04:13
Question Stats:
53% (02:17) correct 47% (02:16) wrong based on 227 sessions
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What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? A. 103324 B. 93324 C. 87645 D. 77678 E. 65432
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Originally posted by fitzpratik on 29 Sep 2018, 20:31.
Last edited by Bunuel on 30 Sep 2018, 04:13, edited 1 time in total.
Renamed the topic and edited the question.




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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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29 Sep 2018, 23:18
fitzpratik wrote: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
A. 103324
B. 93324
C. 87645
D. 77678
E. 65432 let us take 2 as the thousands digit the following combinations are possible 2345 2435 2354 2534 2453 2543 let us take sum of units digit 2*5 + 2*4 + 2*3 = 10+8+6 = 24 similarly when we take 3 as the thousands digit 2*5 + 2*2 + 2*4 = 10+4+8=22 when we take 4 as the thousands digit 2*5 + 2*2 + 2*3 = 10+4+6=20 when we take 5 as the thousands digit 2*2 + 2*3 + 2*4 = 4+6+8=18 sum of units digit = 84 similarly sum of tens digit = 84*10 sum of hundreds digit =84*100 sum of thousands digit = 84*1000 sum total = 84+84*10+84*100+84*1000 = 84(1111) = 93324 B




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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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01 Oct 2018, 21:55
The way I solved it was using the formula suggested by bunuel on the following link: https://gmatclub.com/forum/whatisthe ... 94836.html
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What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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05 Oct 2018, 08:40
I solved this question using another approach, Since there are 4! Or 24 Ways of arranging the digits without repetition, the sum of all the numbers formed should be a multiple of 24. Using POE I got OA.Although I got OA Bunuel is this reasoning applicable to questions of this sort? Thanks. Posted from my mobile device



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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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16 Nov 2018, 10:24
fitzpratik wrote: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
A. 103324
B. 93324
C. 87645
D. 77678
E. 65432 carcass gmatbusters VeritasKarishma Dear Experts, Kindly help with a solution on this one please. Thank you.



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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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16 Nov 2018, 11:24
fitzpratik wrote: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
A. 103324
B. 93324
C. 87645
D. 77678
E. 65432 add least and greatest: 2345+5432=7777 7777/2=3888.5=average 4! possible combinations=24 24*3888.5=93324 B



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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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16 Nov 2018, 19:14
Four digit numbers =4⋅3⋅2⋅1=24 ways we can form a four digit number. Since it's a 4 digit number, each digit will appear 6=24/4 times in each of units, tens, hundreds, and thousands place. Therefore, the sum of digits in the units place is 6(2+3+4+5)=85 Why they are adding 2+3+4+5?= Because each digit will come at those places. Similarly sum of digits at tens,hundreds,thousands place is 84 Required sum of all numbers =84+84⋅10+84⋅100+84⋅1000=93324 poojasingavi wrote: fitzpratik wrote: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
A. 103324
B. 93324
C. 87645
D. 77678
E. 65432 carcass gmatbusters VeritasKarishma Dear Experts, Kindly help with a solution on this one please. Thank you.
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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17 Nov 2018, 02:52
poojasingavi wrote: fitzpratik wrote: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
A. 103324
B. 93324
C. 87645
D. 77678
E. 65432 carcass gmatbusters VeritasKarishma Dear Experts, Kindly help with a solution on this one please. Thank you. Request to all forum users: I am one of the forum experts on the PS and CR forums. If you would like me to take a look at any question on these forums, please mention it on my thread (link given below): PS  https://gmatclub.com/forum/veritasprep ... 78042.htmlCR  https://gmatclub.com/forum/veritasprep ... 78026.htmlSince I receive 100s of mails everyday in my mailbox, unfortunately, it becomes very difficult to follow up on every query even if I am tagged on it. I do take a look at both my threads on a daily basis and hence will certainly get to your query if you mention on it. Thank you! Coming to the question: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? A few things to note here: The numbers will be of the form 2354, 3425 ... etc There will be a total of 4*3*2*1 = 24 numbers These will be made symmetrically. What this means is that in the 24 numbers, 2 will appear 6 times, 3 will appear 6 times, 4 will appear 6 times and 5 will appear 6 times (since all digits are equivalent) 2345 3245 ... 2354 3254 ... etc This will be true of digits in tens place, hundreds place and thousands place too. The sum of digits in units place = 6*2 + 6*3 + 6*4 + 6*5 = 6*(2 + 3 + 4 + 5) = 84 The sum of digits in tens places, hundreds places and thousands places will also be 84 each. The sum of all numbers then will be = 84 + 84*10 + 84*100 + 84*1000 = 93324 Answer (B)
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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17 Nov 2018, 03:57
fitzpratik wrote: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
A. 103324
B. 93324
C. 87645
D. 77678
E. 65432 GMATinsight : sir is there any direct formula to solve such questions?
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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17 Nov 2018, 19:59
Hi,
If we are not told can we assume that the numbers can repeat?



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What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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18 Nov 2018, 01:37
bpdulog wrote: Hi,
If we are not told can we assume that the numbers can repeat? YES, No mentioned on repetition of digit means that repetition of digits is allowed. and therefore all above mentioned solutions are incorrect as they assumed that repetition of digits is not allowed. Here the solution should be smalled such number = 2222 Largest number = 5555 Sum of the pair of largest and smallest numbers = 2222+5555 = 7777 Total Such numbers = 4*4*4*4 = 256 Total suc pairs = 256/2 = 128 Sum of all pairs = 7777*128 = 995456
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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18 Nov 2018, 03:08
GMATinsight wrote: bpdulog wrote: Hi,
If we are not told can we assume that the numbers can repeat? YES, No mentioned on repetition of digit means that repetition of digits is allowed. and therefore all above mentioned solutions are incorrect as they assumed that repetition of digits is not allowed. Here the solution should be smalled such number = 2222 Largest number = 5555 Sum of the pair of largest and smallest numbers = 2222+5555 = 7777 Total Such numbers = 4*4*4*4 = 256 Total suc pairs = 256/2 = 128 Sum of all pairs = 7777*128 = 995456 GMATinsight : but sir your answer is not one of the given options? also what would be the solution in case repetition of digits is not allowed..
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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18 Nov 2018, 06:50
GMATinsight wrote: bpdulog wrote: Hi,
If we are not told can we assume that the numbers can repeat? YES, No mentioned on repetition of digit means that repetition of digits is allowed. and therefore all above mentioned solutions are incorrect as they assumed that repetition of digits is not allowed. Here the solution should be smalled such number = 2222 Largest number = 5555 Sum of the pair of largest and smallest numbers = 2222+5555 = 7777 Total Such numbers = 4*4*4*4 = 256 Total suc pairs = 256/2 = 128 Sum of all pairs = 7777*128 = 995456 If numbers cnt be repeated then in that case what will be the sum? Posted from my mobile device



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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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19 Nov 2018, 06:32
Archit3110 wrote: GMATinsight wrote: bpdulog wrote: Hi,
If we are not told can we assume that the numbers can repeat? YES, No mentioned on repetition of digit means that repetition of digits is allowed. and therefore all above mentioned solutions are incorrect as they assumed that repetition of digits is not allowed. Here the solution should be smalled such number = 2222 Largest number = 5555 Sum of the pair of largest and smallest numbers = 2222+5555 = 7777 Total Such numbers = 4*4*4*4 = 256 Total suc pairs = 256/2 = 128 Sum of all pairs = 7777*128 = 995456 GMATinsight : but sir your answer is not one of the given options? also what would be the solution in case repetition of digits is not allowed.. That means that either question couldn't explain properly that repetition of digits is not allowed or Options are incoorect. Probably the prior assumption is correct.
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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17 Dec 2018, 23:08
No of ways of arranging 4 digits = No of possible 4 digit numbers = 4! = 24. Each digit will appear for 6 times at each of thousandth, hundredth, tens and ones position. The sum of the digits at ones place = 6(2 + 3 + 4 + 5) = 84. Similarly, sum of digits at tens , hundredth, thousand place = 6(2 + 3 + 4 + 5) = 84. Sum of all possible numbers = 1000 x 84 + 100 x 84 + 10 x 84 +84 = 93324.




Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?
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