CAT 2023 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 1

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 1 : For a real number $x$, if $$frac{1}{2}, $frac{\log _3\left$2^x-9$right$}{$log _3 4}$, and $\frac{\log _5\left$2^x+$frac{17}{2}\right$}{$log _5 4}$ are in an arithmetic progression, then the common difference is 1. $\log _4 7$ 2. $\log _4\left$$frac{3}{2}\right$$ 3. $$log _4\left$$frac{7}{2}\right$$ 4. $$log _4\left$$frac{23}{2}\right$$ Best CAT Online Coaching Try upto 40 hours for free Learn from the best! 2IIM : Best Online CAT Coaching. Video Explanation Best CAT Coaching in Chennai CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! Explanatory Answer $$frac { 1 } { 2 } , \frac { \log _ { 3 } \left$ 2 ^ { x } - 9 $right$ } { $log _ { 3 } ^ { 4 } } , \frac { \log _ { 5 } \left$ 2 ^ { x } + $frac { 17 } { 2 } \right$ } { $log _ { 5 } ^ { 4 } }$are in AP. $\because \quad \frac { A } { B } = A$ $\frac { 1 } { 2 } , \left$ 2 ^ { x } - 9 $right$ , $left$ 2 ^ { x } + $frac { 17 } { 2 } \right$$are in A.P $2 , $left$ 2 ^ { x } - 9 $right$ , $left$ 2 ^ { x } + $frac { 17 } { 2 } \right$$are in A.P If $$log \log A , \log \log B , \log \log C$ all in $A . P$, then $A , B , C$ will be in $G . P$ $\therefore 2 , \left$ 2 ^ { x } - 9 $right$ , $left$ 2 ^ { x } + $frac { 17 } { 2 } \right$$are in G.P $$left$ 2 ^ { x } - 9 $right$ ^ { 2 } = 2 $times \left$ 2 ^ { x } + $frac { 17 } { 2 } \right$$ $2 ^ { 2 x } + 81 - 9 $times 2 ^ { x + 1 } = 2 ^ { x + 1 } + 17$ $2 ^ { 2 x } - 10 \times 2 ^ { x + 1 } + 64 = 0$ $\left$ 2 ^ { x } $right$ ^ { 2 } - 20 $left$ 2 ^ { x } $right$ + 64 = 0$ Let $y = 2 ^ { x }$ $y ^ { 2 } - 20 y + 64 = 0$ $y ^ { 2 } - 16 y - 4 y + 64 = 0$ $y = 16$ or $y = 4$ $2 ^ { x } = 16$ or $2 ^ { x } = 4$ $x = 4$ or $x = 2$ if $x = 2 ; $left$ 2 ^ { 2 } - 9 $right$ =$ - 5 )$
But, since the argument of the log can't be negative, $x = 4$
∴ The common ratio of the G.P is $$frac { 2 ^ { x } - 9 } { 2 } = $frac { 2 ^ { 4 } - 9 } { 2 } = \frac { 16 - 9 } { 2 } = \frac { 7 } { 2 }$ $\therefore$ The common difference of the $A P = \left$ $frac { 7 } { 2 } \right$$ The question is " For a real number $x$, if $$frac{1}{2}, \frac{\log _3\left$2^x-9$right$}{$log _3 4}$, and $\frac{\log _5\left$2^x+$frac{17}{2}\right$}{$log _5 4}$ are in an arithmetic progression, then the common difference is " The answer is '$\log _4\left$$frac{7}{2}\right$$' Choice C 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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