Problem: 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
Rationale: explanation : numbers from 1 to 60 , which are divisible by 6 are : 6 , 1218 , 24 , 30 , 3642 , 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 3 such 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 . answer : d
annotated_formula: subtract(60, add(add(const_10, const_3), const_4))