At most 100 students at a certain school study Mathematics. If at most 50 students in the school study both Mathematics and English, find the maximum number of students studying neither Mathematics nor English?
(1) At least 80% of the students, study either Mathematics or English or both
(2) The total students in the School is 200.Solution:- We have only been given the max. possible number of students for 2 criteries i.e. students who study Math and students who study both Math and English.
Statement 1.The total students at the school will include, (students who study only math) + (students who study only english) + (students who study both) + (students who study none) = Total
We need the max for number of students who study neither but the value for total students is
unknown
So statement 1 is insufficient
Statement 2.We are given the total number of students but no other information
Clearly insufficient
Statement 1+2Statement 2 gives exactly what statement 1 is missing. When we combine both, we have a definite answer.
IMO Correct answer is C