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KVPY2012MathematicsSets and Relations

Let S= 1,2,3, . ., 40 and let A be a subset of S such that no two elements in A have their sum divisible by 5 . What is the maximum number of elements possible in A ?

Options

  1. A10
  2. B13
  3. C17
  4. D20

Correct answer

C. 17

Step-by-step solution

A = 1,2,6,7,11,12,16,17,21,22,26,27,31,32,36,37 & One of the element which is multiple of 5 B = 3,4,8,9,13,14,18,19,23,24,28,29,33,34,38,39 & One of the element which is multiple of 5

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