`{:("Column A"," ","Column B"),("The last digit in the average of the numbers 13 and 23",,"The last digit in the average of the numbers 113 and 123"):}`

Options

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

Answer

To solve the problem, we need to find the last digit of the averages of the two sets of numbers provided in Column A and Column B. Let's break down the steps:

### Step 1: Calculate the average of the numbers in Column A
The numbers given in Column A are 13 and 23. The formula for the average of two numbers \( A \) and \( B \) is:

\[ \text{Average} = \frac{A + B}{2} \]

Substituting the values:

\[ \text{Average} = \frac{13 + 23}{2} \]

### Step 2: Perform the addition
Now, we add the numbers:

\[ 13 + 23 = 36 \]

### Step 3: Divide by 2 to find the average
Next, we divide the sum by 2:

\[ \text{Average} = \frac{36}{2} = 18 \]

### Step 4: Identify the last digit of the average in Column A
The last digit of 18 is:

\[ \text{Last digit} = 8 \]

### Step 5: Calculate the average of the numbers in Column B
Now, we move to Column B, where the numbers are 113 and 123. We will use the same formula for the average:

\[ \text{Average} = \frac{113 + 123}{2} \]

### Step 6: Perform the addition
Adding these numbers gives:

\[ 113 + 123 = 236 \]

### Step 7: Divide by 2 to find the average
Now, we divide the sum by 2:

\[ \text{Average} = \frac{236}{2} = 118 \]

### Step 8: Identify the last digit of the average in Column B
The last digit of 118 is:

\[ \text{Last digit} = 8 \]

### Final Comparison
Now we compare the last digits from both columns:

- Last digit from Column A: 8
- Last digit from Column B: 8

Since both last digits are equal, we conclude that:

**Both columns are equal.**