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

• A. 7
• B. 5
• C. 10
• D. 4

Answer 1

Answer: (B)

5

Answer 2

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 $e = 12, b = 3, d + f = 12, c + e = 17 \Rightarrow c = 5;$ $a + d = 11$ $a +d + f = 18 \Rightarrow f = 7 \quad \therefore d = 12 - 7 = 5$