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# How many three-digit numbers are composed of three distinct digits suc

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Math Expert
Joined: 02 Sep 2009
Posts: 59589
How many three-digit numbers are composed of three distinct digits suc  [#permalink]

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14 Mar 2019, 03:11
00:00

Difficulty:

75% (hard)

Question Stats:

27% (01:52) correct 73% (03:00) wrong based on 22 sessions

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How many positive three-digit numbers are composed of three distinct digits such that one digit is the average of the other two?

(A) 96
(B) 104
(C) 112
(D) 120
(E) 256

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Joined: 06 Feb 2019
Posts: 8
Re: How many three-digit numbers are composed of three distinct digits suc  [#permalink]

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17 Mar 2019, 20:53
1
Pick 3 single digit numbers such that the gap between them are the same, which can be 1, 2, 3, or 4. That way, the middle will be the average of the other two. Remember to subtract the numbers that begin with 0 since we want three digit numbers.

0,1,2; 1,2,3 ... 7,8,9 = 8 groups
0,2,4; ... 5,7,9 = 6 groups
0,3,6; ... 3,6,9 = 4 groups
0,4,8; 1,5,9 = 2 groups

So 20 different groupings of numbers, each with 3! ways to arrange them or 120. Subtract the 8 numbers that began with 0 since those are two digit numbers, and you get 112

Ans C
Re: How many three-digit numbers are composed of three distinct digits suc   [#permalink] 17 Mar 2019, 20:53
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