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If a subset of integers is chosen from between 1 to 3000
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Hovkial
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Joined: 23 Apr 2019
Status:PhD trained. Education research, management.
Posts: 823
If a subset of integers is chosen from between 1 to 3000 [#permalink] New post  09 Oct 2019, 14:55
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55% (hard)

Question Stats:

50% (01:00) correct 50% (03:26) wrong based on 6 sessions

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If a subset of integers is chosen from between 1 to 3000, such that no two integers add up to a multiple of nine, then what can be the maximum number of elements in the subset? Include both 1 and 3000.

(A) 1332

(B) 1333

(C) 1336

(D) 1668
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Peddi
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Joined: 20 Jul 2019
Posts: 63
Re: If a subset of integers is chosen from between 1 to 3000 [#permalink] New post  09 Oct 2019, 17:42
Take all integers of form 9k+1,9k+2, 9k+3, 9k+4
9k+1 --> 1,10,19 ... 2998 --> 334
9k+2 --> 2,11... 2999 --> 334
9k+3 --> 3,12 ... 3000 --> 334
9k+4 --> 4,13 ... 2992 --> 333
And include one multiple of 9 --> 1
Total = 334+334+334+333+1 = 1336

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