Analysis of Male Students with Low Income Across Colleges

The question asks to identify the college with the fewest male students from a low-income group, assuming all colleges have the same total student population. Let the total number of students in each college be N.

Data Extraction and Calculation Approach

We need to calculate the number (or proportion relative to N) of male students with low income for each college. The formula is:

Number of Males (Low Income) = (Total Students) $ \times $ (Percentage Low Income / 100) $ \times $ (Male Ratio / (Male Ratio + Female Ratio))_{Low Income}

Since N is constant, we compare the product: (Percentage Low Income / 100) $ \times $ (Male Ratio / (Male Ratio + Female Ratio)) for each college.

College-wise Calculations

• College A:
  • Low Income Percentage: 35% = 0.35
  • Male:Female Ratio (Low Income): 5:6
  • Fraction of Males (Low Income): $ \frac{5}{5+6} = \frac{5}{11} $
  • Relative Number: $ 0.35 \times \frac{5}{11} = \frac{35}{100} \times \frac{5}{11} = \frac{7}{20} \times \frac{5}{11} = \frac{35}{220} = \frac{7}{44} $
  • Approximate Value: $ \approx 0.1591 $
• College B:
  • Low Income Percentage: 25% = 0.25
  • Male:Female Ratio (Low Income): 3:5
  • Fraction of Males (Low Income): $ \frac{3}{3+5} = \frac{3}{8} $
  • Relative Number: $ 0.25 \times \frac{3}{8} = \frac{1}{4} \times \frac{3}{8} = \frac{3}{32} $
  • Approximate Value: $ = 0.09375 $
• College C:
  • Low Income Percentage: 24% = 0.24
  • Male:Female Ratio (Low Income): 1:2
  • Fraction of Males (Low Income): $ \frac{1}{1+2} = \frac{1}{3} $
  • Relative Number: $ 0.24 \times \frac{1}{3} = \frac{24}{100} \times \frac{1}{3} = \frac{8}{100} = \frac{2}{25} $
  • Approximate Value: $ = 0.08 $
• College D:
  • Low Income Percentage: 19% = 0.19
  • Male:Female Ratio (Low Income): 3:2
  • Fraction of Males (Low Income): $ \frac{3}{3+2} = \frac{3}{5} $
  • Relative Number: $ 0.19 \times \frac{3}{5} = \frac{19}{100} \times \frac{3}{5} = \frac{57}{500} $
  • Approximate Value: $ = 0.114 $
• College E:
  • Low Income Percentage: 15% = 0.15
  • Male:Female Ratio (Low Income): 5:3
  • Fraction of Males (Low Income): $ \frac{5}{5+3} = \frac{5}{8} $
  • Relative Number: $ 0.15 \times \frac{5}{8} = \frac{15}{100} \times \frac{5}{8} = \frac{3}{20} \times \frac{5}{8} = \frac{15}{160} = \frac{3}{32} $
  • Approximate Value: $ = 0.09375 $

Comparison and Conclusion

Comparing the calculated relative numbers (or fractions) for male students with low income:

• College A: $ \frac{7}{44} \approx 0.1591 $
• College B: $ \frac{3}{32} = 0.09375 $
• College C: $ \frac{2}{25} = 0.08 $
• College D: $ \frac{57}{500} = 0.114 $
• College E: $ \frac{3}{32} = 0.09375 $

The smallest value is 0.08, which corresponds to College C.

Therefore, College C has the least number of male students with low income.