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

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Manager
Joined: 09 May 2009
Posts: 151
Find the sum of all the four digit numbers which are formed  [#permalink]

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Updated on: 06 Nov 2012, 03:22
1
20
00:00

Difficulty:

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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Joined: 02 Sep 2009
Posts: 59708

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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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Joined: 06 Sep 2013
Posts: 1545
Concentration: Finance
Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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30 Dec 2013, 08:27
1
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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03 Oct 2017, 23:08
3
Doesn't 'sum of all' suggest that repetition is allowed ?
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Joined: 20 Sep 2015
Posts: 16
Location: India
GMAT 1: 700 Q48 V37
Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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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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Posts: 59708
Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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11 Oct 2017, 21:00
1
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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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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Posts: 59708
Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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11 Oct 2017, 23:26
2
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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Find the sum of all the four digit numbers which are formed  [#permalink]

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