Question

In a class 85% of the student received the highest grade in English Literature, 80% in Math, 75% in History, and 30% in Chemistry. About what percentage of the students could you say for sure that they received the highest grade in all 4 subjects?

Answer 1

i am pretty sure it is 67.5% cause
85/100 + 80/100+ 75/100+30/100= 270/400 and 240 divided by 400 is 0.675 0r 67.5%

Answer 2

I get 0% that we can say for sure got all four.
Here's how I work it out.

Between English (85%) and Mathematics (80%), the students total 165%, so there must be at least 65% who got the highest marks in both.
If we proceed this way, we can build a table of the minimum overlap between two subjects.
Subj Engl Math Hist Chem
Engl 85
Math 65___80
Hist 60___55___75
Chem 15___10___5____30

Proceeding in the same manner, we find that
Math+English=65%
History+English=60%
Total = 125%
So at least 25% have all three.

Students who excel in Chemistry (30%) can easily fit outside of the 25% who have all three, which means that we cannot say for sure that there is anyone who have all four.

We will suggest the chemistry teachers to work harder!!

Here's a Venn diagram for three subjects Maths, History and English.
http://img131.imageshack.us/img131/6307/1255641485.jpg