Question 65

Sonal, a mathematician defines a number as 'connected by 6' if it is divisible by 6, or if the sum of digits is 6, or if 6 is one of the digits of the number.Other numbers are 'not connected by 6'. As per the definition, the number of integers, from 1-60 (both inclusive) which are not connected with 6 is

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For the number to be connected to 6 it has to be either 

(i) Divisible by 6 which are : 6,12,18,24,30,36,42,48,54,60

(ii) Has 6 as their digits which are : 6,16,26,36,46,56,60

(iii) Sum of digit has to be 6 which are : 6,15,24,33,42,51,60

Here we see that 6,24,36,42,60 are repeated. Overall there are 17 numbers that are connected to 6. Thus 60-17 = 43 is the required answer

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