Question 114

# 290 students of MBA (International Business) in a reputed Business School have to study foreign language in Trimesters IV and V. Suppose the following information are given .i. 120 students study Spanishii. 100 students study Mandariniii. At least 80 students, who study a foreign language, study neither Spanish nor MandarinThen the number of students who study Spanish but not Mandarin could be any number from

Solution

It's given that 120 students study Spanish :         A + B = 120                                        ...(1)

Also 100 students study Mandarin :       B + C = 100                                        ...(2)

At least 80 students will not opt for any of these two languages i.e.

Spanish + Mandarin $$\leq$$ (290-80)

Spanish + Mandarin $$\leq$$ 210

A + B + C $$\leq$$ 210

Case 2: When B is minimum and A is maximum.

Solving for boundary condition  A + B + C = 210                                                             ...(3)

Solving equations (1)+(2)-(3)

B = 10

i.e. A = 120 - B = 120 - 10 =110 {Maximum possible value of A}

Case 2: When B is maximum and A is minimum.

Since B+C = 100 so, Maximum value B can attain is 100. Hence, the minimum value of A = 120 - B = 120 - 100 = 20 {Minimum possible value of A}

So we can say that the number of students who study Spanish but not Mandarin will be A [20 ,110].