A class of 120 students in Prayagraj takes Physics, Chemistry and Maths tuition. The note gives each subject's total and the diagram gives the overlaps. How many students take none of the three?

Question

Accepted Answer

12. Physics only = 45 - 10 - 12 - 6 = 17, Chemistry only = 50 - 10 - 8 - 6 = 26, Maths only = 55 - 12 - 8 - 6 = 29. At least one = 17 + 26 + 29 + 10 + 12 + 8 + 6 = 108, so none = 120 - 108 = 12. 0 subtracts the overlaps once from 45 + 50 + 55 = 150, 6 forgets to add the centre back, and 18 counts the centre once too many.

A class of 120 students in Prayagraj takes Physics, Chemistry and Maths tuition. The note gives each subject's total and the diagram gives the overlaps. How many students take none of the three?

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