# CAT 2022 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 11

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 11 : If $$left$$sqrt{$frac{7}{5}}\right$^{3 x-y}=$frac{875}{2401}$ and $\left$$frac{4 a}{b}\right$^{6 x-y}=$left$$frac{2 a}{b}\right$^{y-6 x}$, for all non-zero real values of $a$ and $b$, then the value of $x+y$ is ## 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 $$left$ $sqrt { \frac { 7 } { 5 } } \right$ ^ { 3 x - y } = $frac { 875 } { 2401 }$ $\left$ $sqrt { \frac { 7 } { 5 } } \right$ ^ { 3 x - y } = $left$ $frac { 7 } { 5 } \right$ ^ { $frac { 3 x - y } { 2 } } = \frac { 125 } { 343 } = \left$ $frac { 5 } { 7 } \right$ ^ { 3 } = $left$ $frac { 7 } { 5 } \right$ ^ { - 3 }$ 3x - y = -6 $$left$ $frac { 4 a } { b } \right$ ^ { 6 x - y } = $left$ $frac { 2 a } { b } \right$ ^ { y - 6 x }$ $$ 2 ) ^ { 6 x - y } = $left$ $frac { 2 a } { b } $right$ ^ { 2 y - 12 x }$ Let R = $$frac { 2 a } { b }$, Since a and b are real numbers, R is also real. $$ 2$ ^ { 6 x - y } = $left$ R ^ { - 2 } $right) ^ { 6 x - y }$ R = $$frac { 1 } { \sqrt { 2 } }$, But $\frac { 1 } { \sqrt { 2 } }$ is not real. Hence, the given equation can be satisfied only when the powers zero. That is 6x - y = 0 y = 6x 3x - y = -6 x = 2 y = 12 x + y = 2 + 12 = 14 ##### The answer is '14' ###### 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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