Question:medium

In the second year, students at a business school opt for exactly one of three electives: Systems, Operations, or HR.

The number of girls who opted for Operations plus the number of boys who opted for Systems is 37. Twenty-two students opted for the Operations elective. Twenty girls opted for the Systems and Operations electives put together. The number of students who opted for the Systems elective plus the number of boys who opted for the Operations elective is 37. Twenty-five students opted for the HR elective.

If 20% of the girls opt for the HR elective, then the total number of boys in the second year is

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Use the earlier result that girls in Systems plus girls in Operations is 20, and treat that as 80% of all girls, since the remaining 20% of girls are in HR.
Updated On: Jul 10, 2026
  • 54
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  • 51
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The Correct Option is D

Solution and Explanation

Step 1: Find the total number of girls.
From the earlier question, girls in Systems and Operations together number $6 + 14 = 20$. If 20% of all girls choose HR, the other 80% (namely Systems and Operations) make up this 20, so:
\[ \text{total girls} = \frac{20}{0.8} = 25 \]

Step 2: Split HR into girls and boys.
HR has 25 students in total. Since 20% of the 25 total girls choose HR:
\[ \text{girls in HR} = 0.2 \times 25 = 5 \]
So boys in HR $= 25 - 5 = 20$.

Step 3: Recall the boys already found in Systems and Operations.
From the earlier question, boys in Systems $= 23$ and boys in Operations $= 8$.

Step 4: Add up boys across all three electives.
\[ \text{total boys} = 23 + 8 + 20 = 51 \]
This matches the total-minus-girls approach exactly, confirming 51 is correct.

Final Answer:
The total number of boys in the second year is 51.\[ \boxed{51} \]
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