In a class of 80 students at least 40 participated in both cricket

It says that the total of students is 80. T=80. And at least 40 play both sports. B=>40


Statement 1

Students that play at least 1 sport =54. This includes students playing both also (but we dont need to know how may play 2 sports). Students playing neither is 80-54= 26 Sufficient.

Statement 2

35 students played at most 1 sport. This includes student playing 1 or neither sports. Students playing both then would be 45 (but this is irrelevant). We cannot know how many played neither. Not Sufficient.


ANSWER A

let us take
the number of students who participated only in cricket be "A"
the number of students who participated only in football be "B"
the number of students who participated in both be "C"
from the question we can get the total number of students in the class is "80"
number of students who participated in both cricket and football is at least 40
i.e., C>=40
we are asked to find out students participated in neither of the two game i.e., "80-(A+B+C)"


From Statement:1

It is mentioned that the number of students who play at least one game( Means more than or equal to 1 game) is 54
i.e. A+B+C =54
so the answer is "80-54"=26

Sufficient

From Statement:2

It is mentioned that 35 students participated in at most one game (means less than or equal to 1 game)
A+B=35
As we are not sure of C because from the given data C can be 40,41,42,43,44 or 45
So Insufficient

And the Answer is Option A

taking Venn diagram is easy to visualize the given data

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