# CAT 2023 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 21

CAT 2023 Quant was dominated by Algebra followed by Arithmetic. 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 21 : If $p^2+q^2-29=2 p q-20=52-2 p q$, then the difference between the maximum and minimum possible value of $$left$p^3-q^3$right)$ is 1. 486 2. 189 3. 378 4. 243 ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer $p ^ { 2 } + q ^ { 2 } - 29 = 2 p q - 20 = 52 - 2 p q$ $2 p q - 20 = 52 - 2 p q$ $4 p q = 72$ $p q = 18$ $p ^ { 2 } + q ^ { 2 } - 29 = 2 p q - 20$ $p ^ { 2 } + q ^ { 2 } - 2 p q = 29 - 20$ $$ p - q ) ^ { 2 } = 3 ^ { 2 }$
$p - q = $pm 3$ $$ p - q ) ^ { 3 } = p ^ { 3 } - q ^ { 3 } - 3 p q ( p - q )$
$p ^ { 3 } - q ^ { 3 } = ( p - q ) ^ { 3 } + 3 p q ( p - q )$
The maximum value of $p ^ { 3 } - q ^ { 3 }$ occurs when $p - q = 3$
$p ^ { 3 } - q ^ { 3 } = 3 ^ { 3 } + 3 ( 18 ) 3 = 3 ^ { 3 } ( 1 + 6 ) = 27 $times 7 = 189$ The minimum value of $p ^ { 3 } - q ^ { 3 }$ occurs when $p - q = - 3$ $p ^ { 3 } - q ^ { 3 } =$ - 3 ) ^ { 3 } + 3 ( 18 ) ( - 3 ) = - 189$
The difference between the maximum and minimum values $= 189 - ( - 189 ) = 2 ( 189 ) = 378$

The question is " If $p^2+q^2-29=2 p q-20=52-2 p q$, then the difference between the maximum and minimum possible value of $$left$p^3-q^3$right)$ is " ##### Hence, the answer is '378' 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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