question_answer

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

Correct Answer: B

Solution :

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