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?

- 25
- 20
- 35
- 45

45

Try upto 40 hours for free

Learn from the best!

Online Batches Available Now!

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?"**

Choice D is the correct answer.

CAT 2021

Enroll at

44,000/-

Online Classroom Batches Starting Now!

1. Digit Numbers | CAT Permutation and Combination | CAT Coaching Online

2. Numbers with Distinct Digits | CAT Permutation and Combination | CAT Coaching Online

3. Alphabetical Order | CAT Permutation and Combination | CAT Coaching Online

4. Geometric Progression | CAT Permutation and Combination | CAT Coaching Online

5. Bayes Theorem | CAT Permutation and Combination | CAT Coaching Online

2. Numbers with Distinct Digits | CAT Permutation and Combination | CAT Coaching Online

3. Alphabetical Order | CAT Permutation and Combination | CAT Coaching Online

4. Geometric Progression | CAT Permutation and Combination | CAT Coaching Online

5. Bayes Theorem | CAT Permutation and Combination | CAT Coaching Online

6. Rearranging Letters | CAT Permutation and Combination | CAT Coaching Online

7. Possible Integer Solutions | CAT Permutation and Combination | CAT Coaching Online

8. Rearrangement of Letters | CAT Permutation and Combination | CAT Coaching Online

9. Number Theory | CAT Permutation and Combination | CAT Coaching Online

10. Distribution | CAT Permutation and Combination | CAT Coaching Online

7. Possible Integer Solutions | CAT Permutation and Combination | CAT Coaching Online

8. Rearrangement of Letters | CAT Permutation and Combination | CAT Coaching Online

9. Number Theory | CAT Permutation and Combination | CAT Coaching Online

10. Distribution | CAT Permutation and Combination | CAT Coaching Online

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com