# CAT 2023 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 4

CAT 2023 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 4 : If $x$ is a positive real number such that $x^8+$left$$frac{1}{x}$right$^8=47$, then the value of $x^9+$left$$frac{1}{x}\right$^9$ is 1. $40 $sqrt{5}$ 2. $36 \sqrt{5}$ 3. $30 \sqrt{5}$ 4. $34 \sqrt{5}$ ## 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 $x ^ { 8 } + \frac { 1 } { x ^ { 8 } } = 47$ $\left$ x ^ { 4 } + $frac { 1 } { x ^ { 4 } } \right$ ^ { 2 } = x ^ { 8 } + $frac { 1 } { x ^ { 8 } } + 2 = 47 + 2 = 49$ $\left$ x ^ { 4 } + $frac { 1 } { x ^ { 4 } } \right$ = 7$ $$left$ x ^ { 2 } + $frac { 1 } { x ^ { 2 } } \right$ ^ { 2 } = x ^ { 4 } + $frac { 1 } { x ^ { 4 } } + 2 = 7 + 2 = 9$ $\left$ x ^ { 2 } + $frac { 1 } { x ^ { 2 } } \right$ = 3$ $$left$ x + $frac { 1 } { x } \right$ ^ { 2 } = x ^ { 2 } + $frac { 1 } { x ^ { 2 } } + 2 = 3 + 2 = 5$ $\left$ x + $frac { 1 } { x } \right$ = $sqrt { 5 }$ $\left$ x + $frac { 1 } { x } \right$ ^ { 3 } = x ^ { 3 } + $frac { 1 } { x ^ { 3 } } + 3 \times x \times \frac { 1 } { x } \left$ x + $frac { 1 } { x } \right$$ $$ $sqrt { 5 } ) ^ { 3 } = x ^ { 3 } + $frac { 1 } { x ^ { 3 } } + 3 \sqrt { 5 }$ $x ^ { 3 } + \frac { 1 } { x ^ { 3 } } = 5 \sqrt { 5 } - 3 \sqrt { 5 } = 2 \sqrt { 5 }$ $\left$ x ^ { 3 } + $frac { 1 } { x ^ { 3 } } \right$ ^ { 3 } = x ^ { 9 } + $frac { 1 } { x ^ { 9 } } + 3 \times x ^ { 3 } \times \frac { 1 } { x ^ { 3 } } \left$ x ^ { 3 } + $frac { 1 } { x ^ { 3 } } \right$$ $$ 2 $sqrt { 5 } ) ^ { 3 } = x ^ { 9 } + $frac { 1 } { x ^ { 9 } } + 3$ 2 $sqrt { 5 }$$ $x ^ { 9 } + $frac { 1 } { x ^ { 9 } } = 40 \sqrt { 5 } - 6 \sqrt { 5 } = 34 \sqrt { 5 }$ The question is " If $x$ is a positive real number such that $x^8+\left$$frac{1}{x}\right$^8=47$, then the value of $x^9+$left$$frac{1}{x}\right$^9$ is " ##### Hence, the answer is '$34 $sqrt{5}$' Choice D is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## CAT Questions | Verbal Ability for CAT ##### 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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