# CAT 2023 Question Paper | Quant Slot 1

###### CAT Previous Year Paper | CAT Quant Questions | Question 20

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 20 : For some positive and distinct real numbers $x, y$ and $z$, if $$frac{1}{$sqrt{y}+\sqrt{z}}$ is the arithmetic mean of $\frac{1}{\sqrt{x}+\sqrt{z}}$ and $\frac{1}{\sqrt{x}+\sqrt{y}}$, then the relationship which will always hold true, is 1. $\sqrt{x}, \sqrt{y}$ and $\sqrt{z}$ are in arithmetic progression 2. $\sqrt{x}, \sqrt{z}$ and $\sqrt{y}$ are in arithmetic progression 3. $y, x$ and $z$ are in arithmetic progression 4. $x, y$ and $z$ are in arithmetic progression ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer Given: $\frac { 1 } { \sqrt { y } + \sqrt { z } } = \frac { \frac { 1 } { \sqrt { x } + \sqrt { z } } + \frac { 1 } { \sqrt { x } + \sqrt { y } } } { 2 }$ $\frac { 2 } { \sqrt { y } + \sqrt { z } } = \frac { 2 \sqrt { x } + \sqrt { z } + \sqrt { y } } {$ $sqrt { x } + \sqrt { z }$$ $sqrt { x } + $sqrt { y }$ }$ $$frac { 2$ $sqrt { x } + \sqrt { 2 }$$ $sqrt { x } + $sqrt { y }$ } {$ $sqrt { y } + $sqrt { 2 }$ } = 2 $sqrt { x } + \sqrt { 2 } + \sqrt { y }$ $\frac { 2 [ x + \sqrt { x }$ $sqrt { y } + \sqrt { z }$ + $sqrt { z } \sqrt { y } ] } { \sqrt { y } + \sqrt { z } } = 2 \sqrt { x } + \sqrt { z } + \sqrt { y }$ $\frac { 2 [ x + \sqrt { z } \sqrt { y } ] } { \sqrt { y } + \sqrt { z } } = \sqrt { z } + \sqrt { y }$ $2 x + 2 \sqrt { z } \sqrt { y } =$ $sqrt { z } + \sqrt { y }$ ^ { 2 }$ $2 x + 2 $sqrt { z } \sqrt { y } = z + y + 2 \sqrt { z } \sqrt { y }$ $2 x = z + y$ $x = \frac { z + y } { 2 }$ x is the Arithmetic Mean of z & y, therefore, z, x, y form an A.P. It goes without saying that y, x, z also forms an A.P. ##### The answer is '$y, x$ and $z$ are in arithmetic progression' 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? ###### 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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