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Manager  Joined: 09 May 2009
Posts: 139
Find the sum of all the four digit numbers which are formed  [#permalink]

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23 00:00

Difficulty:   25% (medium)

Question Stats: 73% (01:42) correct 27% (01:51) wrong based on 388 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, 05:38.
Last edited by Bunuel on 06 Nov 2012, 02:22, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 65785

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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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VP  Joined: 06 Sep 2013
Posts: 1491
Concentration: Finance
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

Hope it helps
Cheers!
J Manager  S
Joined: 12 Dec 2016
Posts: 79
Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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Doesn't 'sum of all' suggest that repetition is allowed ?
Current Student B
Joined: 20 Sep 2015
Posts: 16
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Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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

I have the same query. Experts, please clarify.
Math Expert V
Joined: 02 Sep 2009
Posts: 65785
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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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?
Math Expert V
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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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GMAT 2: 670 Q48 V34 Find the sum of all the four digit numbers which are formed  [#permalink]

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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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Posts: 1260
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

1256+6521=7777
7777/2=3888.5
3888.5*4!=93324
B
Director  D
Joined: 08 Aug 2017
Posts: 763
Re: Find the sum of all the four digit numbers which are formed  [#permalink]

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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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Joined: 20 Aug 2019
Posts: 46
Location: Malaysia
Concentration: Strategy, General Management
Schools: Mannheim "21 (A)
GMAT 1: 630 Q40 V36
GPA: 4
Find the sum of all the four digit numbers which are formed  [#permalink]

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Hi Bunuel , thanks for the good explanation as always. Regarding the formula below, can you confirm my understanding that it is not applicable if there is a "0" in one of the digits provided?

Based on a similar question from the link below, the calculation for this question can also be done as:
Total possible 4-digit numbers= 4*3*2*1= 24

Sum of digits at unit place= 24/4*(1+2+5+6)=84
Sum of digits at tens place= 24/4*(1+2+5+6)=84
Sum of digits at hundreds place= 24/4*(1+2+5+6)=84
Sum of digits at thousands place= 24/4*(1+2+5+6)=84

the sum of all possible 4 digit numbers that can be formed using all the digits of the number 1256
= 84* (1000+100+10+1)=93,324

https://gmatclub.com/forum/find-the-sum ... s#p2448163 Find the sum of all the four digit numbers which are formed   [#permalink] 28 Jan 2020, 22:37

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