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 Spanish
ii. 100 students study Mandarin
iii. At least 80 students, who study a foreign language, study neither Spanish nor Mandarin
Then the number of students who study Spanish but not Mandarin could be any number from
It's given that 120 students study Spanish :Â Â Â Â Â A + B = 120Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(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.   Â
                           Spanish + Mandarin $$\leq$$ (290-80)
                           Spanish + Mandarin $$\leq$$ 210
                            A + B + C $$\leq$$ 210
Case 2:Â When B is minimum and A is maximum.Â
Solving for boundary condition A + B + C = 210                                 ...(3)
Solving equations (1)+(2)-(3)Â
                                  B = 10Â
                      i.e. A = 120 - B = 120 - 10 =110 {Maximum possible value of A}
Case 2:Â When B is maximum and A is minimum.Â
Since B+C = 100 so, Maximum value B can attain is 100. Hence, the minimum value of A = 120 - B = 120 - 100 = 20Â {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].
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