# CAT 2022 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 6

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 6 : Let $r$ be a real number and $f(x)=$left${\begin{array}{cl}2 x-r & \text { if } x \geq r \\ r & \text { if } x\lt r\end{array}\right.$. Then, the equation $f$x$=f(f(x))$ holds for all real values of $x$ where

1. $x $leq r$ 2. $x $geq r$ 3. $x \gt r$ 4. $x \neq r$ ## 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 Observe that f$r$ = 2r - r = r
Therefore, f(f(r)) = f(r) = r
For any x < r,
f(x) = r
f(f(x)) = f(f(r)) = r
For any x > r,
(let’s assume that x = kr, where k is some number greater than 1)
f(x) = f(kr) = 2kr - r = (2k - 1)r
Since k is greater than 1, (2k - 1) is greater than k.
This means that every time we put an input that is greater than r, the output is greater than the input.
So, for any x > r,
f(f(x)) $$neq$ f$f(r))
Therefore, for f(f(x)) = f(x) to be satisfied, the necessary condition is, $x $leq r$. ##### The answer is '$x $leq r$' Choice A is the correct answer. ###### Prepare for CAT 2023 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 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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