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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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New post Updated on: 06 Nov 2012, 03:22
1
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A
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  25% (medium)

Question Stats:

75% (01:43) correct 25% (01:47) wrong based on 341 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

Originally posted by xcusemeplz2009 on 23 Dec 2009, 06:38.
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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New post 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.

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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New post 30 Dec 2013, 08:27
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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
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Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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New post 03 Oct 2017, 23:08
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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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New post 11 Oct 2017, 21:00
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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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New post 11 Oct 2017, 23:26
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Find the sum of all the four digit numbers which are formed  [#permalink]

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New post 24 Nov 2018, 04:37
Could also be solved with estimation:

\(4*1000 + 4*2000 + 4*5000 + 6*6000=68000\) Just looking at the answer choices option B is the only possible solution.
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Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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New post 24 Nov 2018, 10:56
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


1256+6521=7777
7777/2=3888.5
3888.5*4!=93324
B
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Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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New post 19 Sep 2019, 09:32
I have made similar mistakes in other problems.
Until repetition is not specified in problem, it is safe to proceed considering non-repetition of digits/letters.
And this rule is valid throughout the GMAT.

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.
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Re: Find the sum of all the four digit numbers which are formed   [#permalink] 19 Sep 2019, 09:32
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