XAT 2011 Question 87

Question 87

There are 240 second year students in a B - School. The Finance area offers 3 electives in the second year. These are Financial Derivatives, Behavioural Finance, and Security Analysis. Four students have taken all the three electives, and 48 students have taken Financial Derivatives. There are twice as many students who study Financial Derivatives and Security Analysis but not Behavioural Finance, as those who study both Financial Derivatives and Behavioural Finance but not Security Analysis, and 4 times as many who study all the three. 124 students study Security Analysis. There are 59 students who could not muster courage to take up any of these subjects. The group of students who study both Financial Derivatives and Security Analysis but not Behavioural Finance, is exactly the same as the group made up of students who study both Behavioural Finance and Security Analysis. How many students study Behavioural Finance only?

Solution

Given : $$e = 4$$

$$FD = 48$$, => $$a + b + d + e = 48$$

$$d = 2b$$ and $$d = 4e$$

$$SA = 124$$, => $$d + e + f + g = 124$$

$$d = e + f$$ and $$h = 59$$

To find : $$c = ?$$

Solution : $$d = 4e = 4 \times 4 = 16$$

=> $$b = \frac{d}{2} = \frac{16}{2} = 8$$

=> $$f = d - e = 16 - 4 = 12$$

=> $$a = 48 - b - d - e = 48 - 8 - 16 - 4 = 20$$

=> $$g = 124 - d - e - f = 124 - 16 - 4 - 12 = 92$$

Now, we know that, $$a + b + c + d + e + f + g + h = 240$$

=> $$20 + 8 + c + 16 + 4 + 12 + 92 + 59 = 240$$

=> $$c + 211 = 240$$

=> $$c = 240 - 211 = 29$$



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