All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?
Choose the correct choice from the following options
A) 25 B) 20 C) 35 D) 45 E) 55
DETAILED SOLUTION   Any multiple of 6 will end in a zero. There are 25 such numbers. Beyond this, we can have zero as the middle digit of a 3-digit number.   This will be the case for numbers from 37 - 41, 73 - 77, 109 - 113 and 145 - 149. There are 20 such numbers.   Overall, there are 45 numbers that have a zero in them.   Correct Answer : 45
<result>D</result>
All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?