The question is from Permutation and Combination. Another question which combines number theory with combinatorics. We need to find out the number of five digits which can be formed with the given conditions. 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 8: From the digits 2, 3, 4, 5, 6 and 7, how many 5-digit numbers can be formed that have distinct digits and are multiples of 12?

- 36
- 60
- 84
- 72

60

The Best CAT Online Coaching Courses

Starts Sun, March 1st, 2020

Any multiple of 12 should be a multiple of 4 and 3.

First, let us look at the constraint for a number being a multiple of 3.

Sum of the digits should be a multiple of 3.

Sum of all numbers from 2 to 7 is 27.

So, if we have to drop a digit and still retain a multiple of 3, we should drop either 3 or 6.

So, the possible 5 digits are 2, 4, 5, 6, 7 or 2, 3, 4, 5, 7.

When the digits are 2, 4, 5, 6, 7.

The last two digits possible for the number to be a multiple of 4 are 24, 64, 52, 72, 56, 76.

For each of these combinations, there are 6 different numbers possible.

So, with this set of 5 digits we can have 36 different numbers.

When the digits are 2, 3, 4, 5, 7. The last two digits possible for the number to be a multiple of 4 are 32, 52, 72, 24.

For each of these combinations, there are 6 different numbers possible.

So, with this set of 5 digits we can have 24 different numbers.

Overall, there are 60 different 5-digit numbers possible.

The question is **"how many 5-digit numbers can be formed that have distinct digits and are multiples of 12?"**

Choice B is the correct answer.

CAT 2020

Enroll at 44,000/-

Next Weekend Batch Starts Sun, March 1st 2020

Register Online, get Rs 4000/- off

Attend a Demo Class

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