JEE MainMathematicsToughPermutations and Combinations

If a and b are any two numbers belonging to the set, then the number of pairs (a, b) such that product of a
and b is divisible by 3 is

Show answer and solution

S = \{ 1,2,3,\ldots.100\}

elements of S are of form

3n\:3,6,9

,.........

99 \rightarrow 33

number

3n + 1:1,4,7,

.......

100 \rightarrow 34

number

3n + 2:2,5,8,

.......

98 \rightarrow 33

number
If a b is to be divisible by 3 either a or b is divisible by 3 or both
a and b are to be divisible by

Source: Grass-G / M-08 Mathematics Paper 23 October.docx

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