Tough Percentage Puzzle

clartharlear

At college, 70% of the students studied Maths, 75% studied English, 85% studied French and 80% studied German.
What percentage at least must have studied all 4?

Initially, you’d think that it would be 70% AND 75% AND 85% AND 80%, which would give you 37.5%, but that doesn’t take into account that doing one subject doesn’t have any effect on whether any of the other subjects are done.

I’ve seen another solution here, but I don’t find it convincing, though I believe the numerical answer.
70 +75 + 85+ 80 = 310
310 ÷ 3 = 100 remainder 10
3 subjects each student, 10 at least 4

I’ve been trying to draw Venn diagrams and Karnaugh maps with 4 variables where the outcome is F = ABCD, but I don’t know how to work that with the percentages.

Help would be much appreciated!

orourkeda

http://www.britishblogs.co.uk/images/449592.jpg

The Thinker

Hi,
Probably a bit late with this, only spotted it today.
30% didn't study Maths
25% didn't study English
15% didn't study French
20% didn't study German

This leaves 10% of students who must have studied all 4 ???

betterlife

The Thinker wrote: »

Hi,
Probably a bit late with this, only spotted it today.
30% didn't study Maths
25% didn't study English
15% didn't study French
20% didn't study German

This leaves 10% of students who must have studied all 4 ???

You've got a point there.

clartharlear

The Thinker wrote: »

Hi,
Probably a bit late with this, only spotted it today.
30% didn't study Maths
25% didn't study English
15% didn't study French
20% didn't study German

This leaves 10% of students who must have studied all 4 ???

Yes, that's exactly it. Thanks and well done!