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What is the sum of all possible 3-digit numbers that can be
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07 Jan 2010, 04:07
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73% (00:36) correct 27% (00:20) wrong based on 48 sessions
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vitaliy 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?
My Q.: How we receive 24s in the final equalization (attached). thnx
Three digit number has the form: 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
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22 Mar 2015, 14:01
Bunuel wrote:
vitaliy 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?
My Q.: How we receive 24s in the final equalization (attached). thnx
Three digit number has the form: 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
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23 Mar 2015, 02:05
metskj127 wrote:
Bunuel wrote:
vitaliy 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?
My Q.: How we receive 24s in the final equalization (attached). thnx
Three digit number has the form: 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.
What is the sum of all possible 3-digit numbers that can be
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28 Dec 2018, 11:36
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?
add least and greatest numbers: 345+543=888 888/2=444 mean 444*3! total possibilities=2664 sum
Re: What is the sum of all possible 3-digit numbers that can be
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29 Dec 2018, 12:31
Bunuel wrote:
vitaliy 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?
My Q.: How we receive 24s in the final equalization (attached). thnx
Three digit number has the form: 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.
Hi Bunuel. This formula will break if zero is one of the digits to be used for forming 3 digit numbers. Can you provide an idea for such scenarios? Thanks.
Re: What is the sum of all possible 3-digit numbers that can be
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06 Jan 2019, 02:57
metskj127 wrote:
Bunuel 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?
Three digit number has the form: 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.
Hi Bunuel,
Thanks for the help. For the above equation, is 111 constant, or does that number increase to match n? Example, if n=5, would we use 11,111?
(n-1)!*(sum of the digits)*(11,111…..n times)[/b]
Yes, there should be n number of 1's. So, if n=5, it should be 11,111.[/quote]
Is this applicable only when the digits can't be repeated ? What id we were to form four digit numbers using 3,4,5 with any one being repeated ? Are there more formulae for such questions ?
gmatclubot
Re: What is the sum of all possible 3-digit numbers that can be &nbs
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06 Jan 2019, 02:57
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73% (00:36) correct 
