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Manager  Joined: 09 May 2009
Posts: 156
Find the sum of all the four digit numbers which are formed  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 75% (01:43) correct 25% (01:47) wrong based on 333 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

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GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58955

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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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##### General Discussion
SVP  Joined: 06 Sep 2013
Posts: 1553
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: 76
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 ?
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Give me kudos and see what happens to your GMAT score Intern  B
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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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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: 58955
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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Manager  S
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Posts: 76
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?
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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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Manager  G
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Posts: 107
Location: United States (MA)
GMAT 1: 560 Q39 V28 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: 1223
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  P
Joined: 09 Aug 2017
Posts: 557
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. Re: Find the sum of all the four digit numbers which are formed   [#permalink] 19 Sep 2019, 09:32
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