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Intersection

Let S =1, 2...

Question

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

A

10

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B

13

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C

17

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D

20

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Solution

The correct option is C 17
0 5,10,15, .....40
1 2,7, ....., 36
3 3, 8, ...........38
4 4,9, ......... 39

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