# CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

###### CAT Questions | Algebra | Inequalities - Max and Min Values

The question is about maximum and minimun value. Our task is to maximize and minimize the given inequality. Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.

Question 24: What are the maximum and minimum possible values for $$frac{|x+y|}{|x|+|y|}\\$ + $\frac{|z+y|}{|z|+|y|}\\$ + $\frac{|z+x|}{|x|+|z|}\\$? 1. 3 and 1 2. 3 and 0 3. 4 and 0 4. 4 and 1 ## 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 ##### Method of solving this CAT Question from Algebra - Inequalities : The Question might seem very simple, but there is a catch!! We know that |x + y| < |x| + |y|. So, each of these fractions lies between 0 and 1. So, all three added together should go from 0 to 3? Is that the case? Is 2IIM running questions that are this simple? When would this be 3? If x, y and z all have the same sign. Each fraction would be 1 and we would get 3 overall. Spot on! So, the maximum value is 3. When can this go to zero. When x=-y this fraction goes to 0. When x and y have opposite signs, the first term would go to zero. Likewise for the second and third terms as well. So, what is the catch. Among x, y, and z at least two will have the same sign. So, of the three terms maximum of two can go to zero. One will be +1. So, the minimum total overall = 1$not 0)

The question is "What are the maximum and minimum possible values for $$frac{|x+y|}{|x|+|y|}\\$ + $\frac{|z+y|}{|z|+|y|}\\$ + $\frac{|z+x|}{|x|+|z|}\\$?" ##### Hence the answer is "3 and 1" Choice A is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### 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 Online Preparation | CAT Algebra Videos On YouTube #### Other useful sources for Algebra Questions | Inequalities Sample Questions ##### 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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