# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Sequence and Series Questions | Question 20

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Question 20 :Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is

1. $$frac{1}{6}$ 2. $\frac{3}{6}$ 3. $\frac{3}{2}$ 4. $\frac{5}{2}$ ## ⏰ Last Intake for CAT '21 Crash course! Buy now for just Rs. 8000. Valid until 27th Sep #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2021Online Batches Available Now! ### Explanatory Answer ##### Method of solving this CAT Question from Sequence and Series Since x, y, z are in GP , Common ratio$r) = $$frac{y}{x}$ = $\frac{z}{y}$ => xz = y2 5x, 16y and 12z are in AP 16y – 5x = 12z- 16y 32y = 12z + 5x Consider the terms in GP to be of the form $\frac{a}{r}$, a, ar Replacing the values in the equation, 32y = 12yr + $\frac{5y}{r}$ 32r = 12r2 - 5 12r2 – 32r + 5 = 0 12r2 – 30r – 2r+5 = 0 6r$2r -5) – 1(2r-5) = 0
(6r-1)(2r-5) = 0
r= $$frac{1}{6}$ 𝑜𝑟 $\frac{5}{2}$ Since its given that x < y < z r must be of a number > 1 Only r = $\frac{5}{2}$ satisfies that condition The question is "Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is" ##### Hence, the answer is $\frac{5}{2}$ Choice D is the correct answer. ###### ⏰ Last Intake for CAT '21 Crash course! Buy now for just Rs. 8000. Valid until 27th Sep ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ##### 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? Phone:$91) 44 4505 8484
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