CMI2022-A: 5

Question

As part of a class activity, students in a class of $50$ were asked to keep track of the total number of hours that they spent looking at the screen of some digital device on a specific day. It was found that the average screentime for the class was $4$ hours. What is the maximum possible number of students with at least $16$ hours of screentime?

• A. $11$

• B. $12$

• C. $13$

• D. $14$

Answer 1

Given that students in a class of 50 and average screen time is 4 hours.

$\frac{S_1+S_2+...S_{50}}{50}=4$

Therefore the total screen time (${S_1+S_2+...S_{50}}$) = 50x4=200

Question asking that, minimum number of students with atleast 16 hours of screen time.

this is Pigeon hole Principle based question where  $n= 200$  & $k=16$

so it will be $ \left \lfloor n/k\right \rfloor$ will $ \left \lfloor 200/16\right \rfloor$  $=$ $12$

referecnce : https://www.math.uvic.ca/faculty/gmacgill/guide/pigeonhole.pdf

Comments

is it ceil or floor of $\frac{200}{16}$?

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Oh ohk sir got it ..  Maximum 12 students with atleast 16 hours we can have ..