CAT 2024 - Slot 3 Quant Question 8
This is a detailed step-by-step solution for CAT 2024 - Slot 3 Quant Question 8. Understand the concept, common mistakes, and expert tips to solve similar questions in CAT exam.
CAT 2024 Slot 3 - Quant
The expression on the right-hand side will have two critical points: 2 and – 2
For any value of x greater than equal to 2, the equation changes to x + 2 – (x – 2) = 4 the value of min{x, 2} would be 2, so we would want max {x, 2} to be 4 + 2 = 6
Therefore, x = 6 works.
For any value of x less than equal to – 2, the equation changes to – (x + 2) + (x – 2) = – 4 the value of max{x, 2} would be 2, so we would want min{x, 2} to be 6 again; this cannot be the case.
In general, subtracting the smaller (min) of the two values from the bigger (max) can not lead to a negative number. The max it can lead to is a 0
When x lies between – 2 and 2, the equation becomes 2x
The maximum function will give back 2, and the minimum function will give back x, with the right-hand side giving 2x
Solving this we would get 2 – x = 2x which is x = 2/3
Therefore, there are two real values of x for which the given equation holds.
Hence, 2 is the correct answer.
The graph of the function on the right hand side can be visualised as: