# CAT 2023 Question Paper | Quant Slot 3

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

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 21 : Let $a_n=46+8 n$ and $b_n=98+4 n$ be two sequences for natural numbers $n $leq 100$. Then, the sum of all terms common to both the sequences is 1. 15000 2. 14900 3. 14602 4. 14798 ## 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 We have $a _ { n } = 46 + 8 n$and $b _ { m } = 98 + 4 m$ where n, m are positive integers ≤ 100. Let's find the smallest possible values of m , n where $a _ { n } = b _ { m }$ $46 + 8 n = 98 + 4 m$ $8 n - 4 m = 52$ $2 n - m = 13$ $n = 7 , m = 1$are smallest values of m, n where $a _ { n } = b _ { m }$. $a _ { 7 } = b _ { 1 } = 102$ Therefore, the common elements in the series will be of the form $102 + 8 k$. $a _ { 100 } = 846 ; b _ { 100 } = 498$ The largest natural number less than or equal to 498 and of the form 102 + 8k is 494. So the common terms of both the series are 102 , 110, 118, ..., 494 102, 102 + 8, 102 + 8$2), ..., 102 + 8(49)
So, there are 50 terms in this A.P
Sum of all the terms = $$frac { 102 + 494 } { 2 } $times 50 = 14,900$. The question is " Let $a_n=46+8 n$ and $b_n=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is " ##### Hence, the answer is '14900' Choice B 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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