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 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

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β Β 

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

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

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

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β Spanish +Β Mandarin $$\leq$$ (290-80)

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β Spanish +Β Mandarin $$\leq$$ 210

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  A + B + CΒ $$\leq$$ 210

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

Solving for boundary conditionΒ  A + B + CΒ = 210Β Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β Β Β  Β  Β  Β  Β  Β Β Β  Β  Β  ...(3)

Solving equations (1)+(2)-(3)Β 

Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β B = 10Β 

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

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

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

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

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