[Math] How to find the minimum percentage who have studied all four subjects

percentages

At college, 70% students studied Maths, 75% students studied English, 85% studied french and 80% studied german. What percentage at least must have studied all 4?

Best Answer

Consider two subjects first. Suppose a certain fraction take subject A and another fraction take B then we can imagine shading in a bar with those fractions:

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Then we are free to 'shift' these two colours so as to minimise the overlap.

Once you can solve this for two subjects then JiK has explained how to solve it for an arbitrary number.

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