# CAT 2023 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 10

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 10 : The population of a town in 2020 was 100000 . The population decreased by $y $%$ from the year 2020 to 2021 , and increased by $x $%$ from the year 2021 to 2022, where $x$ and $y$ are two natural numbers. If population in 2022 was greater than the population in 2020 and the difference between $x$ and $y$ is 10 , then the lowest possible population of the town in 2021 was 1. 74000 2. 75000 3. 72000 4. 73000 ## 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 $100,000 \left$ 1 - $frac { 4 } { 100 } \right$ $left$ 1 + $frac { x } { 100 } \right$ > 100,000$ $$left$ 1 - $frac { 4 } { 100 } \right$ $left$ 1 + $frac { x } { 100 } \right$ > 1$ $$ 100 - y ) ( 100 + x ) > 10,000$
$x > y$. Why? Think $( 1 - k ) ( 1 + k ) = 1 - k ^ { 2 } < 1$
$$therefore x - y = 10 ; $Rightarrow x = y + 10$ $$ 100 - y$ ( 100 + y + 10 ) > 10000$
$- 100 y + 100 y - y ^ { 2 } + 1000 - 10 y > 0$
$y ^ { 2 } + 10 y - 1000 < 0$
$y ^ { 2 } + 2 $cdot 5 $cdot y + 25 - 1025 < 0$ $$ y + 5$ ^ { 2 } < 1025$
$$sqrt { 1025 } $cong 32.015$ $$ y + 5$ ^ { 2 } $leq 32 ^ { 2 }$ To calculate the minimum population in 2021, we need y to be as large as possible. largest $y = 32 - 5 = 27$ Minimum population in 2021 is $100,000 $left$ 1 - $frac { 27 } { 100 } \right$ = 73,000$. The question is " The population of a town in 2020 was 100000 . The population decreased by $y $%$ from the year 2020 to 2021 , and increased by $x \%$ from the year 2021 to 2022, where $x$ and $y$ are two natural numbers. If population in 2022 was greater than the population in 2020 and the difference between $x$ and $y$ is 10 , then the lowest possible population of the town in 2021 was " ##### The answer is '73000' Choice D 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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