The average of seven consecutive odd numbers is 27. If the last number is removed from the list, then the average of the remaining numbers is:

Options

A. 26
B. 25
C. 24
D. 22

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We know that the average of seven consecutive odd numbers is 27. We need to find the average of the remaining six numbers after removing the last number.

### Step 2: Find the Seven Consecutive Odd Numbers
Since the average of the seven numbers is 27, and these numbers are consecutive odd numbers, we can determine the middle number (which is also the average). The middle number in a set of seven numbers is the fourth number.

- The fourth number (middle number) is 27.
- The numbers can be represented as:
- 4th number: 27
- 3rd number: 25 (27 - 2)
- 2nd number: 23 (25 - 2)
- 1st number: 21 (23 - 2)
- 5th number: 29 (27 + 2)
- 6th number: 31 (29 + 2)
- 7th number: 33 (31 + 2)

So, the seven consecutive odd numbers are: **21, 23, 25, 27, 29, 31, 33**.

### Step 3: Remove the Last Number
Now, we need to remove the last number, which is 33. The remaining numbers are:
- 21, 23, 25, 27, 29, 31

### Step 4: Calculate the Sum of the Remaining Numbers
Now, we will calculate the sum of the remaining six numbers:
- Sum = 21 + 23 + 25 + 27 + 29 + 31

Calculating the sum:
- 21 + 23 = 44
- 44 + 25 = 69
- 69 + 27 = 96
- 96 + 29 = 125
- 125 + 31 = 156

So, the sum of the remaining numbers is **156**.

### Step 5: Calculate the Average of the Remaining Numbers
To find the average of the remaining six numbers, we divide the sum by the number of remaining numbers:
- Average = Sum of remaining numbers / Number of remaining numbers
- Average = 156 / 6

Calculating the average:
- Average = 26

### Final Answer
The average of the remaining numbers after removing the last number is **26**.

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