CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

The question is from Permutation and Combination. Another question which combines number theory with combinatorics. We need to find out how many numbers will contain zero when converted to base 6.This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 10: All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?

1. 25
2. 20
3. 35
4. 45

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: Remember, we are looking for numbers that have a zero in them, not numbers that end in a zero.

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.

The question is "All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?"

Hence the answer is "45"

Choice D is the correct answer.