Let T be the set of integers {2, 12, 22, 32 ..., 542, 552} and S be a
subset of T such that the sum of no two elements of S is divisible by 3.
The maximum possible number of elements in S is

1) 18
2) 19
3) 20
4) 21

• Option 3 )20
  From 2 to 552 there are 56 numbers. Numbers of the form 3n are 12, 42, 72, … 552, i.e. 19 numbers 3n + 1 are 22, 52, 82, … 532, i.e. 18 numbers. 3n + 2 are 2, 32, … 542, i.e. 19 numbers. In order that sum of any 2 numbers is not divisible by 3. Choose 19 numbers of the form 3n + 2 and 1 number of the form 3n. Hence, there are 20 numbers possible
• 11 years agoHelpfull: Yes(1) No(0)