Explanatory Answer

Method of solving this CAT Quantitative Ability Question from Permutation, Combination and Probability question

(a) For a number to be divisible by 3, the sum of its digitshas to be divisible by 3.

Given : 1000 ≤ n ≤ 1200...(1)

Again, for every digit of n to be odd, the four digits canbe selected from 1, 3, 5, 7 and 9. Again with (1), the firsttwo digits of n can be 1 & 1 only.

So the sum of the remaining two digits has to be divisibleby 3. Thus the possible digits can be 19, 73, 79, 13 and55.

These can be organised in 2 + 2 + 2 + 2 + 1 = 9 ways.

Hence, 9 elements of S are divisible by 3.