**Maths Set Theory Puzzle - 1 August**

In a school, there are four subjects. Seventy percent of students study English, seventy five percent of students study Science, eighty five percent of students study Mathematics and eighty percent of students study Spanish.

Can you calculate the percentage of students that study all four subjects?

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Can you calculate the percentage of students that study all four subjects? ... NO

ReplyDeleteAnswer is somewhere between 10% and 70%

70+75+85+80=310%

ReplyDeleteBy the "pigeonhole principle" if all students (100%) are studying 3 subjects we would have 3*100=300 . 10 less than 310 .That means that thera at least 10 students attending all 4 subjects.

ALTERNATIVE SOLUTION:

Let's take the complementary percentages.

If 70% study English thiw means 30% do not study English

25% do not study Science

15% do not study Mathematics

20% do not study Spanish

30+25+15+20=90. That means there is a 10% of students who do not "do not" study any of the 4 subjects. Meaning 10% study all subjects.