Question

There are 240 second year students in a B-School. The Finance area offers 3 electives: Financial Derivatives (FD), Behavioural Finance (BF), and Security Analysis (SA). - 4 students have taken all three electives. - 48 students have taken FD. - The number of students who study FD and SA but not BF is twice the number of students who study FD and BF but not SA, and 4 times the number of students who study all three. - 124 students study SA. - 59 students do not take any of these subjects. - The number of students who study FD and SA but not BF is equal to the number of students who study BF and SA but not FD. Question: How many students study Behavioural Finance (BF) only?

• A. 29
• B. 30
• C. 32
• D. 35
• E. None of the above

Hint:

For Venn diagram word problems, always assign variables to each exclusive region (FD only, BF only, overlaps, etc.). Use the conditions step by step to solve systematically. Pay close attention to “only” vs “including all three,” as this is where most mistakes happen.

Answer 1

The Correct Option is A

Step 1: Define Venn regions.
Let us denote: \[ a = \text{FD only}, \quad b = \text{FD $\cap$ BF only}, \quad c = \text{BF only}, \quad d = \text{FD $\cap$ SA only}, \] \[ e = \text{FD $\cap$ BF $\cap$ SA}, \quad f = \text{BF $\cap$ SA only}, \quad g = \text{SA only}, \quad h = \text{none}. \]

Step 2: Use given values.
- Students in all three: $e = 4$.
- Total FD students: $48 \Rightarrow a + b + d + e = 48$.
- Total SA students: $124 \Rightarrow d + e + f + g = 124$.
- Students with none: $h = 59$. Also, given relationships: - FD $\cap$ SA only = $d = 2b$ and also $d = 4e$. Since $e = 4$, $\Rightarrow d = 16$. - Condition: FD $\cap$ SA only = BF $\cap$ SA only $\Rightarrow d = f$. So, $f = 16$.

Step 3: Calculate other regions.
From FD total: \[ a + b + d + e = 48 \quad \Rightarrow \quad a + b + 16 + 4 = 48 \] \[ a + b = 28 \] From SA total: \[ d + e + f + g = 124 \quad \Rightarrow \quad 16 + 4 + 16 + g = 124 \] \[ g = 88 \]

Step 4: Use total population.
Total students = 240. So: \[ a + b + c + d + e + f + g + h = 240 \] \[ (a+b) + c + 16 + 4 + 16 + 88 + 59 = 240 \] \[ 28 + c + 183 = 240 \] \[ c = 29 \]

Step 5: Final Answer.
Hence, the number of students who study Behavioural Finance only is: \[ \boxed{29} \]