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# What is the SUM of all possible 3 digit numbers that can be

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CEO
Joined: 21 Jan 2007
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Location: New York City
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What is the SUM of all possible 3 digit numbers that can be [#permalink]  17 Oct 2007, 20:59
What is the SUM of all possible 3 digit numbers that can be constructed using the digits 3,4,5 and if each digit can be used only one in each number?

Can someone explain this in detail?
Manager
Joined: 17 Aug 2007
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Re: MGMAT Place Value [#permalink]  17 Oct 2007, 21:28
bmwhype2 wrote:
What is the SUM of all possible 3 digit numbers that can be constructed using the digits 3,4,5 and if each digit can be used only one in each number?

Can someone explain this in detail?

this is a good question.

There can be six numbers with 3 4 and 5 with no repetitions.
3!.

now in each place i.3 units, tens and hundreds each number would show up twice. So the total would be 2*(3+4+5) = 24.

So while adding the units place we get 24 so we keep 4 and 2 carries over.
while adding tens place we get 24 + 2 = 26 so we keep 6 and 2 carries over. While adding hundred's place we have 24 + 2 = 26.

so the sum is 2664 as the answer.
Director
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Re: MGMAT Place Value [#permalink]  17 Oct 2007, 21:33
bmwhype2 wrote:
What is the SUM of all possible 3 digit numbers that can be constructed using the digits 3,4,5 and if each digit can be used only one in each number?

Can someone explain this in detail?

= 3!
= 6 numbers

345
354
435
453
534
543

each number repets twice. so 2 (3+4+5) = 24 is the sum of unit/tens/hundred digits.

so total = 2664
Re: MGMAT Place Value   [#permalink] 17 Oct 2007, 21:33
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