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 Pick:
A) 18
B) 22
C) 42
D) 43
E) 45
<gadget id="calculator">10 + 3</gadget>
<output>13</output>

<gadget id="calculator">13 + 4</gadget>
<output>17</output>

<gadget id="calculator">60 - 17</gadget>
<output>43</output>

<result>D</result>
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
subtract(60, add(add(const_10, const_3), const_4))
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