Q1: Mr. X, a mathematician, defines a number as 'connected with 6 if it is divisible by 6 or if the sum of its digits is 6, or if 6 is one of the digits of the number. Other numbers are all 'not connected with 6'. As per this definition, the number of integers from 1 to 60 (both inclusive) which are not connected with 6 is

ANS:D - 43

Explanation: Numbers from 1 to 60, which are divisible by 6 are : 6,12,18, 24, 30, 36,42, 48, 54, 60. There are 10 such numbers. Numbers from 1 to 60, the sum of whose digits is 6 are : 6, 15, 24, 33, 42, 51, 60. There are 7 such numbers of which 4 are common to the above ones. So, there are 3such uncommon numbers. Numbers from 1 to 60, which have 6 as one of the digits are 6, 16, 26, 36, 46, 56, 60. Clearly, there are 4 such uncommon numbers. So, numbers 'not connected with 6' = 60 - (10 + 3 + 4) = 43.