Considering above graph If the number of students in category 1 grew by x% from Year I to Directions for questions 17 and 18: The bar graph shows the distribution of students in various categories in College A, in Year I (blue bar) and Year II (orange bar).

Year II, and the number of students in category 3 grew by y% from Year I to Year II, then what is x: y?

5/3

13/5

13/7

None of these

Let's calculate the ratio \( x : y \) based on the percentage growth values obtained earlier.

### Recap of Percentage Growth:
- \( x \) (growth in Category 1 - Freshman): \( 10\% \)
- \( y \) (growth in Category 3 - Junior): \( -4.17\% \)

### Ratio Calculation \( x : y \):
Since \( y \) is negative, it will affect the ratio calculation.

\[
x : y = \frac{10\%}{-4.17\%} = \frac{10}{-4.17}
\]

To make this more manageable, we convert the decimal to a fraction:

\[
\frac{10}{-4.17} \approx \frac{10}{-4.17} = -2.4 \approx -\frac{24}{10} = -\frac{12}{5}
\]

Since none of the given options are negative, and the question might be looking for positive comparisons or ratios, we typically consider the absolute values when given multiple-choice options.

### Let's Convert:
Taking the absolute values:

\[
|x : y| = \left|\frac{10}{4.17}\right| \approx \frac{10}{4.17} \approx \frac{12}{5}
\]

**This is approximately \( 12:5 \), which is close to \( 13:5 \), but not exactly.**

### Conclusion:
The correct answer is **"None of these,"** since none of the options match the exact calculated ratio. The closest option \( 13/5 \) doesn't match the exact calculated value, so it's not correct.

Would you like any further clarification or additional details?

### Related Questions:
1. How would the ratio change if the number of students in Category 1 had grown by 20% instead?
2. What would the ratio \( x : y \) be if the number of students in Category 3 had increased instead of decreased?
3. What is the impact of negative growth rates on ratios?
4. If you consider all four categories, which pair of categories would have the highest ratio of growth rates?
5. How would the interpretation change if we only consider positive growth rates?

### Tip:
When dealing with ratios, especially in percentage growth problems, ensure to consider whether the growth is positive or negative, as it significantly impacts the final ratio calculation.

Explore how to calculate the ratio x : y for percentage growth in College A categories based on the given bar graph data. Understand the impact of positive and negative growth rates on ratios and learn how to interpret these ratios effectively.

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