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{:("Column A","a and b are integers grea...

`{:("Column A","a and b are integers greater than zero", "Column B"),(a//b,,a^2):}`

A

If column A is larger

B

If column B is larger

C

If the columns are equal

D

If there is not enough information to decide

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to compare the two expressions given in Column A and Column B: - Column A: \( \frac{a}{b} \) - Column B: \( a^2 \) where \( a \) and \( b \) are positive integers (greater than zero). ### Step-by-Step Solution: 1. **Understanding the Expressions**: - We have two expressions: \( \frac{a}{b} \) (Column A) and \( a^2 \) (Column B). - We need to determine the relationship between these two expressions for different values of \( a \) and \( b \). 2. **Testing with Specific Values**: - Let's first test with \( a = 1 \) and \( b = 1 \): - Column A: \( \frac{1}{1} = 1 \) - Column B: \( 1^2 = 1 \) - Conclusion: For \( a = 1 \) and \( b = 1 \), both columns are equal. 3. **Testing with Different Values**: - Now, let’s try \( a = 5 \) and \( b = 2 \): - Column A: \( \frac{5}{2} = 2.5 \) - Column B: \( 5^2 = 25 \) - Conclusion: For \( a = 5 \) and \( b = 2 \), Column B is larger than Column A. 4. **Analyzing the Results**: - From the first test, we found that both columns were equal. - From the second test, we found that Column B was larger than Column A. - This indicates that the relationship between the two columns can change depending on the values of \( a \) and \( b \). 5. **Conclusion**: - Since we have found cases where the two columns are equal and cases where one is larger than the other, we cannot definitively say which column is larger in general. - Therefore, the correct answer is that there is not enough information to decide which column is greater. ### Final Answer: The answer is **D: There is not enough information to decide**.
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