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 2IIM : Best Online CAT Coaching Sign up and sample 5 classesfor free Best CAT Coaching in Chennai Crash course - Early Bird discount Starts Sat, June 29th, 2019 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. Best Online CAT CoachingTake Scholarship TestSign up and sample 5 classesfor free Signup Now! Already have an Account? CAT Coaching in ChennaiEnroll at 29000/- Next Weekend Batch Starts Sat, June 29th, 2019 Best CAT Coaching in ChennaiEarly Bird discount of 7000 Personalised attention, Small batch sizes. 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, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 How to reach 2IIM? Phone:$91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com