The average of five consecutive odd number is 61. Then the difference between the highest and lowest numbers is

Options

A. 2
B. 5
C. 8
D. Cannot be determined

Answer

To solve the problem of finding the difference between the highest and lowest of five consecutive odd numbers, given that their average is 61, we can follow these steps:

### Step-by-Step Solution:

1. **Define the First Odd Number**:
Let the first odd number be represented as \( x \).

2. **List the Consecutive Odd Numbers**:
The five consecutive odd numbers can be expressed as:
- First number: \( x \)
- Second number: \( x + 2 \)
- Third number: \( x + 4 \)
- Fourth number: \( x + 6 \)
- Fifth number: \( x + 8 \)

3. **Calculate the Average**:
The average of these five numbers is given by the formula:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Number of items}} \]
The sum of the five numbers is:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 5x + 20 \]
Therefore, the average can be expressed as:
\[ \text{Average} = \frac{5x + 20}{5} = x + 4 \]

4. **Set the Average Equal to 61**:
Since the average is given as 61, we can set up the equation:
\[ x + 4 = 61 \]

5. **Solve for \( x \)**:
To find \( x \), we rearrange the equation:
\[ x = 61 - 4 = 57 \]

6. **Identify the Highest and Lowest Numbers**:
Now that we have \( x \):
- Lowest number: \( x = 57 \)
- Highest number: \( x + 8 = 57 + 8 = 65 \)

7. **Calculate the Difference**:
The difference between the highest and lowest numbers is:
\[ \text{Difference} = (x + 8) - x = 8 \]

### Final Answer:
The difference between the highest and lowest numbers is **8**.

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