Learn from 5 time CAT 100%iler | Best CAT Online Coaching | CAT Preparation

CAT 2018 Question Paper | Quants Slot 2

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

× CAT Questions
CAT Quantitative Aptitude
Geometry HCF and LCM Factors Remainders Factorials Digits Ratios,Mixtures;Averages Percents; Profits; SICI Speed & Time; Races Logarithms and Exponents Pipes,Cisterns; Work,Time Set Theory Coordinate Geometry Mensuration Trigonometry Linear & Quadratic Equations Functions Inequalities Polynomials Progressions Permutation Probability
CAT Verbal
Para Jumble Sentence Correction Sentence Elimination Paragraph Completion Reading Comprehension Critical Reasoning Word Usage Para Summary Text Completion

CAT Online Coaching

CAT Questions

The CAT Exam is known for trapping students with their tricky questions from Sequences and Series. However, you do not have to worry if you are an avid fan of CAT Previous Year paper. If not, then 2IIM's CAT Question Bank is the place to start. It provides you with the most recent CAT Previous Year paper with detailed solution with video explaination. Now try this question and see if you are able to solve this.

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 Solution

Explanatory Answer

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 2022
Limited 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]"