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 MandarinThen the number of students who study Spanish but not Mandarin could be any number froma)20 to 110b)80 to 100c)50 to 80d)80 to 170Correct answer is option 'A'. Can you explain this answer?

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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

a)
20 to 110
b)
80 to 100
c)
50 to 80
d)
80 to 170

Correct answer is option 'A'. Can you explain this answer?

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290 students of MBA (International Business) in a reputed Business Sch...

Atleast 80 students study neither Spanish nor Mandarin.
Hence, maximum number of students who study atleast one language = 290 – 80 = 210

Minimum number of students who study both languages = 100 + 120 – 210 = 10

∴ Maximum number of students who study Spanish but not Mandarin = 120 – 10 = 110

Maximum number of students who study both languages = smaller value of 100 and 120 = 100

∴ Minimum number of students who study Spanish but not Mandarin = 120 – 100 = 20

Hence, the range could be any number from 20 to 110.

Hence, option (a).

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290 students of MBA (International Business) in a reputed Business Sch...

The given problem can be solved using set theory and logical deductions.

Let's represent the number of students studying Spanish as A, the number of students studying Mandarin as B, and the number of students studying neither Spanish nor Mandarin as C. We need to find the number of students who study Spanish but not Mandarin.

Given information:
(i) A = 120 (students studying Spanish)
(ii) B = 100 (students studying Mandarin)
(iii) C ≥ 80 (students studying neither Spanish nor Mandarin)

We can deduce the following from the given information:
(i) A ∪ B = A + B - A ∩ B (Using the principle of inclusion-exclusion)
(ii) A ∪ B = 120 + 100 - A ∩ B
(iii) A ∪ B = 220 - A ∩ B

Now, let's consider the maximum value of A ∩ B (the number of students studying both Spanish and Mandarin) that satisfies the given conditions.
(i) A = 120 (students studying Spanish)
(ii) B = 100 (students studying Mandarin)
(iii) C ≥ 80 (students studying neither Spanish nor Mandarin)

To find the maximum value of A ∩ B, we assume that all the students studying neither Spanish nor Mandarin (C) also study a foreign language. Therefore, C = 80.

Now, let's substitute the values in the equation A ∪ B = 220 - A ∩ B.
120 + 100 = 220 - A ∩ B
220 = 220 - A ∩ B
A ∩ B = 0

So, the maximum value of A ∩ B (the number of students studying both Spanish and Mandarin) is 0.

Now, let's consider the minimum value of A ∩ B that satisfies the given conditions.
(i) A = 120 (students studying Spanish)
(ii) B = 100 (students studying Mandarin)
(iii) C ≥ 80 (students studying neither Spanish nor Mandarin)

To find the minimum value of A ∩ B, we assume that none of the students studying neither Spanish nor Mandarin (C) study a foreign language. Therefore, C = 290 - 80 = 210.

Now, let's substitute the values in the equation A ∪ B = 220 - A ∩ B.
120 + 100 = 220 - A ∩ B
220 = 220 - A ∩ B
A ∩ B = 0

So, the minimum value of A ∩ B (the number of students studying both Spanish and Mandarin) is 0.

Therefore, the number of students who study Spanish but not Mandarin could be any number from 20 to 110 (since A can vary from 120 to 20).

Hence, the correct answer is option 'A' (20 to 110).

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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 MandarinThen the number of students who study Spanish but not Mandarin could be any number froma)20 to 110b)80 to 100c)50 to 80d)80 to 170Correct answer is option 'A'. Can you explain this answer?

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