# CAT 2023 Question Paper | Quant Slot 1

###### CAT Previous Year Paper | CAT Quant Questions | Question 22

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 22 : A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the $n^{$text {th }}$ day exceeds one million, then the lowest possible value of $n$ is ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer 1 Million = 106 Population on… Day 1: 2 Day 2: $2 ^ { 2 } + 3$ Day 3: $2 ^ { 3 } + 3 $cdot 2 + 3$ Day 4: $2 ^ { 4 } + 3 \cdot 2 ^ { 2 } + 3 \cdot 2 + 3$ Day n: $2 ^ { n } + 3 \left$ 2 ^ { n - 2 } + 2 ^ { n - 3 } + $cdots + 1 \right$$ = $2 ^ { n } + 3 $left$ 2 ^ { n - 1 } - 1 $right$$ = $2 ^ { n - 1 }$ 2 + 3 ) - 3$
= $2 ^ { n - 1 } ( 4 + 1 ) - 3$
= $2 ^ { n + 1 } + 2 ^ { n - 1 } - 3$
$10 ^ { 6 } = 2 ^ { 6 } $cdot 5 ^ { 6 }$ $10 ^ { 6 } > 2 ^ { 6 } $cdot 4 ^ { 6 }$ $10 ^ { 6 } > 2 ^ { 6 } \cdot 2 ^ { 12 }$ $10 ^ { 6 } > 2 ^ { 18 }$ Putting n = 18 in $2 ^ { n + 1 } + 2 ^ { n - 1 } - 3$, we get 655357, which is less than 106 On the 19th day the population will be more than double the population on the 18th day, which is more than 2 × 655357, which is definitely more than 106. ##### The answer is '19' ###### 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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