set theory

in a fourth yearof a school there were156 students who took both science and maths they all pass atleast one subject and 75 pass both subjects. if twice as many pass science as pass maths, how many pass only maths?
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1 Answer

The Venn diagram shows the geometric regions associated with the described sets (math=maths).

KEY: SO=science only, MO=math only; SM=science & math; PASS=those that passed; PSM=those that passed both subjects; PS=passed science only; PM=passed math only; NONE=those that neither took nor passed science or math.

PSM=75

PS+PM+PSM=156 (NONE=0), PS+PM=156-75=81; PS=81-PM

PS+PSM=2(PM+PSM) (twice as many passed science as passed math),  PS=2PM+PSM=2PM+75;

Substitute for PS: 81-PM=2PM+75, 3PM=6, PM=2.

So, two passed math only.

by Top Rated User (1.2m points)

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