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# CAT 2018 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Progressions and Series Questions | Question 29

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Question 29 : The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u = $$frac{$x+y$}{2}$ and v = $\frac{$y+z$}{2}$. If x ≥ z, then the minimum possible value of x is [TITA] ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Progressions and Series Given that AM$x, y, z) = 80
So, x + y + z = 80 × 3 = 240 ----- (1)
Also, AM (x, y, z, u, v) = 75
So, x + y + z + u + v = 75 × 5 = 375 ----- (2)
Equation (2) – (1), we get
u + v = 375 - 240 = 135
Its also given that, u = $$frac{x + y}{2}$ and v = $\frac{y + z}{2}$ So, u + v = $\frac{x + y + z}{2}$ + $\frac{y}{2}$ $\frac{240}{2}$ + $\frac{y}{2}$ = 135 => y = 30 Substituting this value in$1), we get x + z = 210
It’s given that x ≥ z
x would take the minimum value when x = z
=> 2x = 210
=> x (min) = 105

The question is "The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u = $$frac{$x+y$}{2}$ and v = $\frac{$y+z$}{2}$. If x ≥ z, then the minimum possible value of x is [TITA]" ##### Hence, the answer is 105 ###### 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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