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# Find the sum of all the four digit numbers which are formed

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Manager
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Find the sum of all the four digit numbers which are formed [#permalink]

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23 Dec 2009, 06:38
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78% (02:19) correct 22% (01:40) wrong based on 245 sessions

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Find the sum of all the four digit numbers which are formed by digits 1, 2, 5, 6

A. 933510
B. 93324
C. 65120
D. 8400
[Reveal] Spoiler: OA

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Last edited by Bunuel on 06 Nov 2012, 03:22, edited 1 time in total.
Renamed the topic and edited the question.
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23 Dec 2009, 07:16
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xcusemeplz2009 wrote:
find the sum of all the four digit numbers which are formed by digits 1,2,5,6

a)933510
b)93324
c)65120
d)8400

The answer choices make the solution easy:

There are 4!=24 four digit numbers which are formed by digits 1, 2, 5, 6.

Obviously 24/4=6 numbers will end with 1; 6 numbers will end with 2, 6 numbers with 5 and 6 numbers with 6.

6*1+6*2+6*5+6*6=6*14=84, which means that the sum of all these 24 numbers must end by 4, only answer choice with 4 at the end is B.

But if we were not given such an easy answer choices, the solution would be:

We have 24 numbers of the of the form: 1000a+100b+10c+d, where a, b, c and d can take any value from the set {1, 2, 5, 6} and there will be 6 numbers with same digit (a, b, c, d) at the thousands, hundreds, tens and units digits.

(1000*6a+1000*6b+1000*6c+1000*6d)+(100*6a+100*6b+100*6c+100*6d)+(10*6a+10*6b+10*6c+10*6d)+(6a+6b+6c+6d)=(6a+6b+6c+6d)(1111)=
=6(a+b+c+d)(1111)=6*14*1111=93324

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)
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20 Dec 2012, 05:36
Hi Bunnuel?,
If it's not mention that repetitions is allowed, do I have to assume that repetitions are not allowed?
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Re: Find the sum of all the four digit numbers which are formed [#permalink]

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30 Dec 2013, 08:27
xcusemeplz2009 wrote:
Find the sum of all the four digit numbers which are formed by digits 1, 2, 5, 6

A. 933510
B. 93324
C. 65120
D. 8400

3!*1111*(14) will have units digit 4

Hope it helps
Cheers!
J
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Re: Find the sum of all the four digit numbers which are formed [#permalink]

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25 May 2015, 03:41
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Hello from the GMAT Club BumpBot!

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Re: Find the sum of all the four digit numbers which are formed [#permalink]

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15 Jun 2016, 16:26
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).

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Re: Find the sum of all the four digit numbers which are formed   [#permalink] 15 Jun 2016, 16:26
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