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?
(a) 10
(b) 13
(c) 17
(d) 20
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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?
(a) 10
(b) 13
(c) 17
(d) 20
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?
(a) 10
(b) 13
(c) 17
(d) 20
Answer is : (c) 17
We have, S = {1, 2, 3, 4, …, 40}
A is subset of S whose sum of two element of A is not divisible by 5.
Possible set A = {1, 2, 5, 6, 7, 11, 12, 16, 17, 21, 22, 26, 27, 31, 32, 36, 37}
∴ Maximum number of elements in A is 17.