Analyzing College Admission Data

The question asks to identify the number of years where the number of students admitted to the B.A. program is greater than 50% of the total number of students admitted across all programs in that year.

Student Admissions Data

Calculating Years: B.A. vs. 50% Total

We need to perform calculations for each year:

• Calculate the total number of students admitted.
• Calculate 50% of the total students.
• Compare this 50% value with the number of B.A. students.
• Count the years where B.A. students > 50% of Total students.

Year-wise Analysis

Year 2021

• Total Students = 150 + 25 + 50 + 45 + 75 = 345
• 50% of Total Students = $\frac{345}{2}$ = 172.5
• B.A. Students = 150
• Comparison: Is 150 > 172.5? No.

Year 2022

• Total Students = 225 + 40 + 45 + 62 + 70 = 442
• 50% of Total Students = $\frac{442}{2}$ = 221
• B.A. Students = 225
• Comparison: Is 225 > 221? Yes. (Count = 1)

Year 2023

• Total Students = 450 + 65 + 30 + 90 + 32 = 667
• 50% of Total Students = $\frac{667}{2}$ = 333.5
• B.A. Students = 450
• Comparison: Is 450 > 333.5? Yes. (Count = 2)

Year 2024

• Total Students = 470 + 73 + 35 + 105 + 70 = 753
• 50% of Total Students = $\frac{753}{2}$ = 376.5
• B.A. Students = 470
• Comparison: Is 470 > 376.5? Yes. (Count = 3)

Year 2025

• Total Students = 500 + 80 + 36 + 132 + 74 = 822
• 50% of Total Students = $\frac{822}{2}$ = 411
• B.A. Students = 500
• Comparison: Is 500 > 411? Yes. (Count = 4)

Final Result

The condition (B.A. students > 50% of Total students) is met in 4 years (2022, 2023, 2024, 2025).