Algebra for CAT Preparation – Finding smallest value in a maximum function

Tuesday, March 24th, 2015


A common type of question that gets asked in CAT is when you are given a maximum function and you are supposed to find out the minimum value of the function. Actually, the concept would remain the same even if you are given a minimum function and you are supposed to find out the maximum value of the function.

To solve such kind of questions, all you need to do is to find out the point of intersection of the individual values. More often than not, that would lead to the answer. Let us look at a question that has appeared in CAT before.

Let g(x) = max (5 − x, x + 2). The smallest possible value of g(x) is
A] 4.0
B] 4.5
C] 1.5
D] None of these.

Watch the video given below for better understanding of the same.

To solve such kind of questions, in most cases, all you need to do is to equate the two values inside the function
=> 5 – x = x + 2
=> x = 3/2 = 1.5
Please note that 1.5 is not the answer to the question.
To find out the answer to the question, we need to find out the value of g(1.5)
When we put x = 1.5, we get g(x) = max (5 – 1.5, 1.5 + 2) = max (3.5, 3.5) = 3.5
So, our answer is 3.5 Option D – None of these

I would strongly recommend that you watch the video for better understanding of the solution of the question. Do check out my Online CAT Coaching and CAT Preparation course which has 500+ video tutorials for CAT.

Other posts related to Quantitative Aptitude – Algebra

Quadratic Equations
Basic Functions and Modifications of Graphs
How to Solve Number of Integral Solutions Questions for CAT Exam
Problems on Ages with complete solutions, answers, and tricks to solve
An introductions to functions (Algebra) for CAT Exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam

CAT Questions related to Quantitative Aptitude – Algebra

All questions from CAT Exam Quantitative Aptitude – Algebra
Quantitative Aptitude – Algebra – Functions
       Quantitative Aptitude – Algebra – Functions – Question: If f(ab) = f(a)f(b) for all positive integers a and b, then the        largest possible value of f(1) is
Quantitative Aptitude – Algebra – Logarithms
       Quantitative Aptitude – Algebra – Logarithms – Question: If x is a real number such that log(base 3)5 = log(base 5)(2 +        x), then which of the following is true?
Quantitative Aptitude – Algebra – Quadratic Equations
       Quantitative Aptitude – Algebra – Quadratic Equations – Question: If x + 1 = x^2 and x > 0, then 2x^4 is
Quantitative Aptitude – Algebra – Maxima Minima
       Quantitative Aptitude – Algebra – Maxima Minima – Question: If a, b, c, and d are integers such that a + b + c + d =        30, then the minimum possible value of (a – b)^2 + (a – c)^2 + (a – d)^2 is
Quantitative Aptitude – Algebra – Inequalities
       Quantitative Aptitude – Algebra – Inequalities – Question: The number of solutions (x, y, z) to the equation x – y – z
Quantitative Aptitude – Algebra – Polynomials
       Quantitative Aptitude – Algebra – Polynomials – Question: If 9^(2x – 1) – 81^(x-1) = 1944, then x is
Quantitative Aptitude – Algebra – Simple Equations
       Quantitative Aptitude – Algebra – Simple Equations – Question : If a and b are integers of opposite signs such that (a +        3)^2 : b^2 = 9 : 1 and (a – 1)^2 : (b – 1)^2 = 4 : 1, then the ratio a^2 : b^2 is

Do let me know what you think about this via the comment section.

Algebra for CAT Preparation – Finding smallest value in a maximum function

4.9 (97.38%) 122 votes



If you Like this post then share it!


Comments are closed.