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What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?

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Joined: 17 Oct 2016
Posts: 99
Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GMAT 2: 680 Q48 V35
GPA: 3.05
WE: Pharmaceuticals (Health Care)
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What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?  [#permalink]

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New post Updated on: 30 Sep 2018, 04:13
3
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

61% (02:01) correct 39% (02:13) wrong based on 56 sessions

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What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?

A. 103324

B. 93324

C. 87645

D. 77678

E. 65432

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Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

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Originally posted by fitzpratik on 29 Sep 2018, 20:31.
Last edited by Bunuel on 30 Sep 2018, 04:13, edited 1 time in total.
Renamed the topic and edited the question.
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?  [#permalink]

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New post 29 Sep 2018, 23:18
2
fitzpratik wrote:
What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?

A. 103324

B. 93324

C. 87645

D. 77678

E. 65432


let us take 2 as the thousands digit
the following combinations are possible
2345
2435
2354
2534
2453
2543

let us take sum of units digit
2*5 + 2*4 + 2*3 = 10+8+6 = 24

similarly
when we take 3 as the thousands digit
2*5 + 2*2 + 2*4 = 10+4+8=22

when we take 4 as the thousands digit
2*5 + 2*2 + 2*3 = 10+4+6=20

when we take 5 as the thousands digit
2*2 + 2*3 + 2*4 = 4+6+8=18

sum of units digit = 84

similarly sum of tens digit = 84*10
sum of hundreds digit =84*100
sum of thousands digit = 84*1000

sum total = 84+84*10+84*100+84*1000 = 84(1111) = 93324
B
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Joined: 17 Oct 2016
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Concentration: General Management, Healthcare
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Re: What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?  [#permalink]

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New post 01 Oct 2018, 21:55
The way I solved it was using the formula suggested by bunuel

on the following link:
https://gmatclub.com/forum/what-is-the- ... 94836.html
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What is the sum of all the 4 digit numbers formed by digits 2,3,4,5?  [#permalink]

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New post 05 Oct 2018, 08:40
1
I solved this question using another approach,
Since there are 4! Or 24 Ways of arranging the digits without repetition, the sum of all the numbers formed should be a multiple of 24. Using POE I got OA.Although I got OA Bunuel is this reasoning applicable to questions of this sort? Thanks.

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What is the sum of all the 4 digit numbers formed by digits 2,3,4,5? &nbs [#permalink] 05 Oct 2018, 08:40
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