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

Options

A. 4
B. 6
C. 9
D. 8

Answer

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

### Step-by-Step Solution:

1. **Understanding the Average**:
The average of a set of numbers is the sum of the numbers divided by the count of the numbers. Here, we have five consecutive odd numbers, and their average is given as 61.

2. **Finding the Middle Number**:
For five consecutive odd numbers, the average is also the middle number. Therefore, the middle number is 61.

3. **Identifying the Consecutive Odd Numbers**:
Since 61 is the middle number, we can find the other four consecutive odd numbers:
- The number before 61: 61 - 2 = 59
- The number before that: 59 - 2 = 57
- The number after 61: 61 + 2 = 63
- The number after that: 63 + 2 = 65

So, the five consecutive odd numbers are: 57, 59, 61, 63, and 65.

4. **Finding the Highest and Lowest Numbers**:
From the list of numbers, the lowest number is 57 and the highest number is 65.

5. **Calculating the Difference**:
To find the difference between the highest and lowest numbers, we subtract the lowest number from the highest number:
\[ \text{Difference} = \text{Highest} - \text{Lowest} = 65 - 57 = 8 \]

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

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