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

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

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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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Re: permutation [#permalink]

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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.

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

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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


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

B is the answer

Hope it helps
Cheers!
J :)

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Doesn't 'sum of all' suggest that repetition is allowed ?
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Re: Find the sum of all the four digit numbers which are formed [#permalink]

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New post 11 Oct 2017, 19:45
zvazviri wrote:
Doesn't 'sum of all' suggest that repetition is allowed ?


I have the same query. Experts, please clarify.

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

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gumnamibaba wrote:
zvazviri wrote:
Doesn't 'sum of all' suggest that repetition is allowed ?


I have the same query. Experts, please clarify.


No it does not. Ideally it should have been clarified more precisely but it's assumed that we are adding the numbers which could be constructed by re-arranging the numbers 1, 2, 5, and 6.
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Re: Find the sum of all the four digit numbers which are formed [#permalink]

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New post 11 Oct 2017, 23:23
Bunuel wrote:
gumnamibaba wrote:
zvazviri wrote:
Doesn't 'sum of all' suggest that repetition is allowed ?


I have the same query. Experts, please clarify.


No it does not. Ideally it should have been clarified more precisely but it's assumed that we are adding the numbers which could be constructed by re-arranging the numbers 1, 2, 5, and 6.


Given this ambiguity, it's safe to say this is not an OG problem, and I would not see problems worded similarly on the test?
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Re: Find the sum of all the four digit numbers which are formed [#permalink]

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zvazviri wrote:
Given this ambiguity, it's safe to say this is not an OG problem, and I would not see problems worded similarly on the test?


Yes, this is not a proper GMAT problem not only because of the wording. Notice that it has 4 options not 5.
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Re: Find the sum of all the four digit numbers which are formed   [#permalink] 11 Oct 2017, 23:26
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