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What is the sum of all the numbers formed by taking the digits 3, 5, 6

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Manager
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What is the sum of all the numbers formed by taking the digits 3, 5, 6  [#permalink]

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New post 25 Nov 2019, 05:04
7
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (02:42) correct 37% (02:15) wrong based on 27 sessions

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What is the sum of all the numbers formed by taking the digits 3, 5, 6, 7 and 8, exactly once?

(A) 5241698
(B) 5894162
(C) 6581426
(D) 7733256
(E) 7799158
Intern
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Re: What is the sum of all the numbers formed by taking the digits 3, 5, 6  [#permalink]

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New post 25 Nov 2019, 05:56
Shouldn’t the unit digit be 9? As if we add all the number it is 29!!

Can anyone explain it?

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Re: What is the sum of all the numbers formed by taking the digits 3, 5, 6  [#permalink]

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New post 02 Dec 2019, 01:02
1
I solved this haphazardly with guesswork;
just took average of first and last combination: (35678 * 87653) / 2 = 61665.5
and multiplied it: 5! * 61665.5 = 7399860
and picked D coz its closer
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What is the sum of all the numbers formed by taking the digits 3, 5, 6  [#permalink]

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New post 04 Dec 2019, 13:59
2
1
A good Q.
All the digits can be arranged in 5! ways = 120 ways.
This means all the digits will appear 120/5 = 24 times in each position.
Sum of all digits in units place = 24(3+5+6+7+8) = 24*29 = 696. So the unit's digit of the sum will be 6.
Carry 69 to the ten's place. ten's digit will be last digit of 696+69 which is 5.
So the last 2 digits will be 56.

Answer D
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Re: What is the sum of all the numbers formed by taking the digits 3, 5, 6  [#permalink]

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New post 05 Dec 2019, 02:48
Total of 5 X 4 X 3 X 2 X 1 = 120 numbers.
For unit place, we have 120/5 = 24 complete set of 3, 5, 6, 7, 8 for the total of 29 X 24 = 696

The sum is 696 (1 + 10 + 100 + 1000 + 10000) = 11111 * 696
I only need to determine that the sum starts with 7 and ends with 6.
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Re: What is the sum of all the numbers formed by taking the digits 3, 5, 6   [#permalink] 05 Dec 2019, 02:48
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