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 7. 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 21: In the previous question if t = 7, for how many values of x, f(x) will be minimum?

1. 1
2. 2
3. 4
4. 8

Explanatory Answer

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

When t = 7,
f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+21|
This expression has two middle terms: |x+9|, |x+12|

The value of f(x) will be minimized when the sum of the two middle terms are minimized
=) |x+9|+ |x+12| should be minimum
This happens when -12 ≤ x ≤ -9, Note that for x = -12, -11, -10, -9 the value of the sum of the middle terms = 3.

Therefore, for all 4 values of x, f(x) will have minimum value.

The question is "In the previous question if t = 7, for how many values of x, f(x) will be minimum?"

Hence the answer is "4"

Choice C is the correct answer.