Question

Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is

Options

• 7

• 5

• 10

• 4

Answer 1

5

Explanation:

C stands for set of students taking economics

a + b + c + d + e + f + g = 40; a + b + d + g = 16

b + c + e + g = 22; d + e + f + g = 26

b + g = 5; e + g = 14; g = 2

Go by backward substitution

e = 12, b = 3, d + f = 12, c + e = 17 ⇒ c = 5; a + d = 11

a + d + f = 18 ⇒ f = 7

∴ d = 12 – 7 = 5