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1.Set Theory
medium
Let $S=\{1,2,3, \ldots, 40)$ 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
$20$
(KVPY-2012)
Solution
(c)
We have,
$S=\{1,2,3,4, \ldots, 40\}$
$A$ is subset of $S$ whose sum of two element of $A$ is not divisible by $5$ .
Possible set $A=\{1,2,5,6,7,11,12,16$, $17,21,22,26,27,31,32,36,37\}$
$\therefore$ Maximum number of elements in $A$ is $17 .$
Standard 11
Mathematics
