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Most of us would tend to add up the number of students taking each course and try figure out the least common inclusion. I don't know if it can be done this way. I think this problem needs an indirect approach for solution. Think about exclusions instead of inclusions. When we say 70% students take Maths, it also means 30% do not take Maths. By the same rule, 25% do not take English, 15% do not take French and 20% do not take German. If we add up these exclusions (assuming these non-takers are mutually exclusive to maximize their count) we get a figure of 90%. So there is a possibility that 90% students do not take at least one of the subjects. It may be highly unlikely on a probability perspective, but still is mathematically possible. The more important point here is that it is mathematically impossible to increase the number of non-takers with the given data. So the answer will be AT LEAST 10% of the students must have taken all four subjects.

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