Question

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

• A. 54
• B. 53
• C. 52
• D. 51

Hint:

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.

Answer 1

The Correct Option is D

Step 1: Recall the earlier result.
From the previous question, girls in Systems = 6 and girls in Operations = 14, so girls in Systems and Operations together number \(6 + 14 = 20\). Also, from the previous question the second year has 76 students in total.

Step 2: Use the 20% condition on girls.
We are told 20% of all girls opt for HR. That means the remaining 80% of girls are split between Systems and Operations, which we already found to be 20 girls. So:
\[ 0.8 \times (\text{total girls}) = 20 \]

Step 3: Solve for the total number of girls.
\[ \text{total girls} = \frac{20}{0.8} = 25 \]

Step 4: Subtract to get the number of boys.
The second year has 76 students in all (from the previous question), and 25 of them are girls, so the rest are boys:
\[ \text{boys} = 76 - 25 = 51 \]
The nearby wrong options (54, 53, 52) come from rounding the division 20 divided by 0.8 incorrectly or subtracting from the wrong total, so it is worth keeping the fraction exact: 20 divided by 0.8 is exactly 25, not a rounded value.

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