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09 Oct 2019, 15:55
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Difficulty:
55%
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Question Stats:
50% (01:00) correct
50%
(03:26)
wrong
based on 6
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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
(A) 1332
(B) 1333
(C) 1336
(D) 1668
09 Oct 2019, 18:42
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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
Posted from my mobile device
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
Posted from my mobile device
