# CAT 2021 Question Paper | Quant Slot 3

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

CAT 2021 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 : For a real number a, if $$frac{$log _{15} a+\log _{32} a}{\left$$log _{15} a\right$$left$$log _{32} a\right$}=$ = 4 then a must lie in the range 1. 4 < a < 5 2. 3 < a < 4 3. a > 5 4. 2 < a < 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 $$frac { \log _ { 15 } ^ { a } + \log _ { 32 } ^ { a } } { \left$ $log _ { 15 } ^ { a } \times \log _ { 32 } ^ { a } \right$ }$ = 4 $$frac { 1 } { \log _ { 32 } ^ { a } } + \frac { 1 } { \log _ { 15 } ^ { a } }$= 4 $\log _ { a } ^ { 32 } + \log _ { a } ^ { 15 }$= 4 $\log _ { a } ^ {$ 32 $times 15$ }$ = 4 a4 = 32 × 15 = 480 We know that, 44 = 256 and 54 = 625 256 < 480 < 625 44 < a4 < 54 4 < a < 5 The question is " For a real number a, if $$frac{\log _{15} a+\log _{32} a}{\left$$log _{15} a\right$$left$$log _{32} a\right$}=$ = 4 then a must lie in the range " ##### Hence, the answer is '4 < a < 5' 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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