# CAT Quantitative Aptitude Questions | CAT Number Theory - Digits questions

###### CAT Questions | Number Theory | Greatest integer function CAT Questions

The question is about Greatest integer function. Another question on possible values. We need to find out the possible values of 'n' which satisfies of the equation of greatest integer function. Dealing with digits and base system of a number is a vital component in CAT Number Systems. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 6: [x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [$$frac{n}{11}\\$] = [$\frac{n}{13}\\$]. 1. 31 2. 25 3. 35 4. 40 ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2021Online Batches Available Now! ### Explanatory Answer ##### Method of solving this CAT Question from Number Theory - Digits: The greatest integer function is brilliant, it is not-intrusive$discrete) and takes you to a higher level (step function).

This is a classic case of brute-force counting.
When n = 1, 2, 3....10, both values will be equal to 0. 10 possibilities
When n = 13, 14, ....21, both values will be equal to 1. 9 possibilities
When n = 26, 27, ....32, both values will be equal to 2. 7 possibilities
When n = 39, 27, ....43, both values will be equal to 3. 5 possibilities
When n = 52, 53, 54, both values will be equal to 4. 3 possibilities
when n = 65, both will be equal to 5. 1 possibility

So, totally there are 1 + 3 + 5 + 7 + 9 + 10 = 35 possibilities.

The question is Find the number of positive integers n such that [$$frac{n}{11}\\$] = [$\frac{n}{13}\\$]. ##### Hence the answer is "35 possibilities" Choice C is the correct answer. ###### Prepare for CAT 2022 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Coaching | CAT Number Systems questions Videos On YouTube #### Other useful sources for Number System Questions | Number Theory HCF and LCM Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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