The average of four consecutive odd numbers is 40. What is the largest number?

Options

A. 42
B. 45
C. 43
D. 44

Answer

To solve the problem step by step, we will determine the four consecutive odd numbers and find the largest one based on the given average.

### Step-by-Step Solution:

1. **Define the smallest odd number**:
Let the smallest odd number be represented as \( A \).

2. **Identify the consecutive odd numbers**:
The four consecutive odd numbers can be expressed as:
- First number: \( A \)
- Second number: \( A + 2 \)
- Third number: \( A + 4 \)
- Fourth number: \( A + 6 \)

3. **Set up the equation for the average**:
The average of these four numbers is given as 40. The formula for the average is:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Number of items}} \]
Therefore, we can write:
\[ \frac{A + (A + 2) + (A + 4) + (A + 6)}{4} = 40 \]

4. **Simplify the equation**:
Combine the terms in the numerator:
\[ \frac{A + A + 2 + A + 4 + A + 6}{4} = \frac{4A + 12}{4} = 40 \]

5. **Multiply both sides by 4**:
To eliminate the fraction, multiply both sides by 4:
\[ 4A + 12 = 160 \]

6. **Solve for \( A \)**:
Subtract 12 from both sides:
\[ 4A = 160 - 12 \]
\[ 4A = 148 \]
Now, divide by 4:
\[ A = \frac{148}{4} = 37 \]

7. **Determine the largest number**:
The largest of the four consecutive odd numbers is \( A + 6 \):
\[ A + 6 = 37 + 6 = 43 \]

### Final Answer:
The largest number is **43**.