CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

The question is about Minimum value of a function. A question which combines sequence and function. We need to find out the minimum value of the function when t is equal to 6. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 20: If f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+3t|, where x is an integer and t is a positive integer, find the minimum value of f(x) when t = 6?

1. 63
2. 36
3. 30
4. 25

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Functions: Combo of Series and Functions.

When t = 3,
f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+18|

Minimum value of this function will occur when x = -9 i.e. the middle term is at its minimum which is 0.
Therefore, f(-9) = 9 + 6 + 3 + 0 + 3 + 6 + 9
= 2 * 18
= 36

The question is "find the minimum value of f(x) when t = 6?"

Hence the answer is "36"

Choice B is the correct answer.