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The arithmetic mean of the nine numbers in the set {9, 99, 999, 9999,

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Joined: 02 Sep 2009
Posts: 59588
The arithmetic mean of the nine numbers in the set {9, 99, 999, 9999,  [#permalink]

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18 Mar 2019, 23:49
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:16) correct 24% (02:17) wrong based on 21 sessions

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The arithmetic mean of the nine numbers in the set {9, 99, 999, 9999, ..., 999999999} is a 9-digit number M, all of whose digits are distinct. The number M does not contain the digit

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

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Re: The arithmetic mean of the nine numbers in the set {9, 99, 999, 9999,  [#permalink]

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19 Mar 2019, 00:02
Bunuel wrote:
The arithmetic mean of the nine numbers in the set {9, 99, 999, 9999, ..., 999999999} is a 9-digit number M, all of whose digits are distinct. The number M does not contain the digit

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

So the mean will be =(9 + 99 +999 +.......+ 999999999)/9
=9(1+11+111+..........+111111111)/9
= 1 + 11+ 111+ ......+ 111111111
= 123456789

[ The unit digit contains 9 digits 111111111 .So when the series is added the unit digit of the sum will be 9 ,tens digit will be 8,..so on]

So M will no have the number 0. Ans A)
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Re: The arithmetic mean of the nine numbers in the set {9, 99, 999, 9999,  [#permalink]

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19 Mar 2019, 03:35
Bunuel wrote:
The arithmetic mean of the nine numbers in the set {9, 99, 999, 9999, ..., 999999999} is a 9-digit number M, all of whose digits are distinct. The number M does not contain the digit

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

avg

9*(1+11+111+1111+11111+111111+1111111+11111111+111111111)/9
missing digit is 0
IMO A
Re: The arithmetic mean of the nine numbers in the set {9, 99, 999, 9999,   [#permalink] 19 Mar 2019, 03:35
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