Question

Let's evaluate both sums in Column A and Column B.

**Column A:**
\[ 0.5 + \frac{3}{4} \]

First, let's convert \(0.5\) to a fraction:
\[ 0.5 = \frac{1}{2} \]

Now we have:
\[ \frac{1}{2} + \frac{3}{4} \]

To add these fractions, we need a common denominator. The least common denominator (LCD) of \(2\) and \(4\) is \(4\):
\[ \frac{1}{2} = \frac{2}{4} \]

Now, we can add the fractions:
\[ \frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4} \]

So, the sum for Column A is:
\[ \frac{5}{4}, \text{ which is rational}. \]

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**Column B:**
\[ \sqrt{3} + \frac{2}{5} \]

The term \(\sqrt{3}\) is an irrational number. \( \frac{2}{5} \) is a rational number. The sum of a rational and an irrational number is always irrational. Therefore:
\[ \sqrt{3} + \frac{2}{5} \text{ is irrational}. \]

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Now we can summarize the results:
- Column A has the sum \( \frac{5}{4} \) (rational).
- Column B has the sum \( \sqrt{3} + \frac{2}{5} \) (irrational).

Reviewing the statements:
- Statement #1: Only Column A has a rational sum. **(True)**
- Statement #2: Only Column B has a rational sum. **(False)**
- Statement #3: Column A and Column B both have rational sums. **(False)**

Thus, the correct statement is: **Statement #1 is true.**

The final answer is:
Statement # (1) is true.