# CAT 2020 Question Paper | Quants Slot 3

###### CAT Previous Year Paper | CAT Quants Questions | Question 12

Do you get stumped by questions from Number Theory? A range of questions can be formed from Number theory. Sometimes the question could be super hard. But, When it comes to your CAT Preparation practicing tons of relevant questions matters a lot. Practice questions from CAT Previous Year Question Paper to get a fabulous CAT score.

Question 12 : Let m and n be natural numbers such that n is even and 0.2 < $$frac{m}{20}$, $\frac{n}{m}$, $\frac{n}{11}$ < 0.5. Then m - 2n equals 1. 4 2. 2 3. 1 4. 3 ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer 0.2 < $\frac{m}{20}$, $\frac{n}{m}$, $\frac{n}{11}$ < 0.5 $\frac{1}{5}$ < $\frac{m}{20}$, $\frac{n}{m}$, $\frac{n}{11}$ < $\frac{1}{2}$ $\frac{1}{5}$ < $\frac{m}{20}$ < $\frac{1}{2}$ Observe that if m = 4; $\frac{m}{20}$ = $\frac{4}{20}$ = $\frac{1}{5}$ In order for $\frac{m}{20}$to be greater than $\frac{1}{5}$, m > 4 Similarly, observe that if m = 10; $\frac{m}{20}$ = $\frac{10}{20}$ = $\frac{1}{2}$ In order for $\frac{m}{20}$to be lesser than $\frac{1}{2}$, m < 10 So, the possible values that m can take = {5, 6, 7, 8, 9} $\frac{1}{5}$ < $\frac{n}{11}$ < $\frac{1}{2}$ Observe that if n = 2.2; $\frac{n}{11}$ = $\frac{2.2}{11}$ = $\frac{1}{5}$ In order for $\frac{n}{11}$to be greater than $\frac{1}{5}$, n > 2.2 Similarly, observe that if n = 5.5; $\frac{n}{11}$ = $\frac{5.5}{11}$ = $\frac{1}{2}$ In order for $\frac{n}{11}$to be lesser than $\frac{1}{2}$, n < 5.5 So, the possible values that n can take = {3, 4, 5} We are told that n is even; n = 4. If n = 4; $\frac{n}{m}$ will be greater than $\frac{1}{5}$ if m is less than 20. Similarly at n = 4; $\frac{n}{m}$ will be lesser than $\frac{1}{2}$ if m is greater than 8. So, for n = 4; 8 ≤ m ≤ 20. m can only take one of the values in {5, 6, 7, 8, 9} Hence m = 9. m - 2n = 9 - 2$4) = 9 - 8 = 1.

The question is "Let m and n be natural numbers such that n is even and 0.2 < $$frac{m}{20}$, $\frac{n}{m}$, $\frac{n}{11}$ < 0.5. Then m - 2n equals" ##### Hence, the answer is, "1" ###### 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 2023 Classroom Batches Starting Now! @Gopalapuram ###### 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! ##### 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? Mobile:$91) 99626 48484 / 94459 38484
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