Let total no of students who took English be x
Then students who took math, science will also be x
Now let’s draw the Venn diagram
E U M U S = 345 – 43 (Neither of the subjects)
E U M U S = E + M + S – E ∩ M - E ∩ S - S ∩ M + E ∩ M ∩ S
=) 302 = 3x - 84 + 14
=) 302 + 84 – 14 = 3x
=) x = 372/3 = 124
Thus the total no of students who took English as a subject = 124
Consequently the Venn diagram becomes
Again,
The students who has taken only one subject = E U M U S - E ∩ M - E ∩ S - S ∩ M - E ∩ M ∩ S
= 302 - 16 - 14 - 14 - 12 = 246
The students who took English and Math but not science = only E + Only M + E ∩ M
= 80 + 82 + 16 = 178
Percent of students who took English and Math but not science = 178/302 x 100 = approx. 59 %
Correct Answer: 124, 246, 59%
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