What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
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What is the sum of all the 4 digit numbers formed by digits 2, 3, 4, 5 if repetition is not allowed??A. 103324B. 93324C. 87645D. 77678
E. 65432
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Originally posted by fitzpratik on 29 Sep 2018, 19:31.
Last edited by Bunuel on 04 Jun 2021, 05:59, edited 2 times 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? [#permalink]
fitzpratik wrote:
What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?A. 103324B. 93324C. 87645D. 77678
E. 65432
add least and greatest: 2345+5432=77777777/2=3888.5=average4! possible combinations=2424*3888.5=93324B
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
fitzpratik wrote:
What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?A. 103324B. 93324C. 87645D. 77678
E. 65432
let us take 2 as the thousands digit the following combinations are possible 234524352354253424532543let us take sum of units digit2*5 + 2*4 + 2*3 = 10+8+6 = 24similarly when we take 3 as the thousands digit 2*5 + 2*2 + 2*4 = 10+4+8=22when we take 4 as the thousands digit 2*5 + 2*2 + 2*3 = 10+4+6=20when we take 5 as the thousands digit2*2 + 2*3 + 2*4 = 4+6+8=18sum of units digit = 84similarly sum of tens digit = 84*10sum of hundreds digit =84*100sum of thousands digit = 84*1000sum total = 84+84*10+84*100+84*1000 = 84(1111) = 93324B
Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
The way I solved it was using the formula suggested by bunuelon the following link:
//gmatclub.com/forum/what-is-the- ... 94836.html
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
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.
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
fitzpratik wrote:
What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?A. 103324B. 93324C. 87645D. 77678
E. 65432
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
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)=85Why 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 84Required 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. 103324B. 93324C. 87645D. 77678
E. 65432
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
poojasingavi wrote:
fitzpratik wrote:
What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?A. 103324B. 93324C. 87645D. 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 - //gmatclub.com/forum/veritas-prep ... 78042.html
CR - //gmatclub.com/forum/veritas-prep ... 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 ... etcThere will be a total of 4*3*2*1 = 24 numbersThese 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)23453245...23543254...etcThis 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) = 84The 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 = 93324Answer (B) _________________
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
fitzpratik wrote:
What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?A. 103324B. 93324C. 87645D. 77678
E. 65432
GMATinsight : sir is there any direct formula to solve such questions?
Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
Hi,
If we are not told can we assume that the numbers can repeat?
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
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 = 2222Largest number = 5555Sum of the pair of largest and smallest numbers = 2222+5555 = 7777Total Such numbers = 4*4*4*4 = 256Total suc pairs = 256/2 = 128Sum 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? [#permalink]
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 = 2222Largest number = 5555Sum of the pair of largest and smallest numbers = 2222+5555 = 7777Total Such numbers = 4*4*4*4 = 256Total suc pairs = 256/2 = 128Sum 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? [#permalink]
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 = 2222Largest number = 5555Sum of the pair of largest and smallest numbers = 2222+5555 = 7777Total Such numbers = 4*4*4*4 = 256Total suc pairs = 256/2 = 128Sum 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? [#permalink]
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 = 2222Largest number = 5555Sum of the pair of largest and smallest numbers = 2222+5555 = 7777Total Such numbers = 4*4*4*4 = 256Total suc pairs = 256/2 = 128Sum 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? [#permalink]
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.
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
fitzpratik wrote:
What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?A. 103324B. 93324C. 87645D. 77678
E. 65432
Bunuel: How do we know that in this question digits can be repeated or not
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
Given the answer choices, the question stem should include the red portion below:
fitzpratik wrote:
What is the sum of all the 4-digit numbers that can be formed from the digits 2, 3, 4, and 5, if repetition is not allowed?A. 103324B. 93324C. 87645D. 77678
E. 65432
Total number of integers = number of ways to arrange the four digits = 4! = 24The middle values in the set are as follows:...3425, 3452, 3524, 3542, 4235, 4253, 4325, 4352...
Notice that every colored pair sums to 7777:3542+4235 = 7777
3524+4253 = 7777
3452+4325 = 7777
3425+4352 = 7777Since the 24 integers are composed of 12 such pairs, we get:Sum of the set = 12*7777 = 93324 _________________
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
fitzpratik wrote:
What is the sum of all the 4 digit numbers formed by digits 2, 3, 4, 5 if repetition is not allowed??A. 103324B. 93324C. 87645D. 77678
E. 65432
IMO B
There's a formula for such questions n= total number of digits given =4H= highest number formed by the digitsL=lowest number formed by the digitsSUM =(H+L)*n! /2put those values Sum=24/2*(2345+5432) =93324
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? [#permalink]
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