Radio Tay Mindbender

[Johnamill]

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

[sedge47]

10 percent

[jonker]

I agree with sedge47. I think it's 10% minimum and 70% maximum but it took a lot of thought.

[Rain Man4500]

Can someone please explain the working out on this one?

Ta

[sedge47]

It's the amount by which the total for the 4 subjects exceeds 300. If the number came to exactly 300
then no student would have to study 4 subjects (easiest example to demonstrate this is 100/100/50/50).
If the number came to 400 then 100% would be taking 4 subjects. So the 300 figure is the highest at
which no student would have to be studying 4 subjects (another example of this is 75/75/75/75).
Since the total in the question comes to 310, 10% of students (at least) must be taking 4 subjects.

[jonker]

I went about it in a different way, but arrived at the same answer: if you take the total attendance shortfall in any three subjects, you'll see the attendance in the remaining course always exceeds that shortfall by 10%. That means if ALL the absentees from the chosen subjects attend the remaining course, there'll be 10% who were not absent from any of the other three.

This works in any combination.

[Rain Man4500]

I think I just about get Jonker's explanation but, Sedge - where does the figure 300 pop up from please?

Apologies for being a bit thick on this one!!!

Ta