Average of 8 consecutive odd numbers is 10. What will be the average of smallest 4 numbers out of 8 numbers?

Options

A. A)7
B. B)8
C. C)6
D. D)4

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Define the 8 consecutive odd numbers
Let's denote the average of the 8 consecutive odd numbers as 10. Since these are consecutive odd numbers, we can express them in terms of a variable \( A \) (the middle number). The numbers can be represented as:
- \( A - 7 \)
- \( A - 5 \)
- \( A - 3 \)
- \( A - 1 \)
- \( A + 1 \)
- \( A + 3 \)
- \( A + 5 \)
- \( A + 7 \)

### Step 2: Set up the equation for the average
The average of these 8 numbers is given by:
\[ \text{Average} = \frac{(A - 7) + (A - 5) + (A - 3) + (A - 1) + (A + 1) + (A + 3) + (A + 5) + (A + 7)}{8} \]
Simplifying the numerator:
\[ = \frac{8A}{8} = A \]
Since the average is given as 10, we have:
\[ A = 10 \]

### Step 3: Find the 8 consecutive odd numbers
Now substituting \( A \) back into our expressions for the numbers:
- \( 10 - 7 = 3 \)
- \( 10 - 5 = 5 \)
- \( 10 - 3 = 7 \)
- \( 10 - 1 = 9 \)
- \( 10 + 1 = 11 \)
- \( 10 + 3 = 13 \)
- \( 10 + 5 = 15 \)
- \( 10 + 7 = 17 \)

Thus, the 8 consecutive odd numbers are: **3, 5, 7, 9, 11, 13, 15, 17**.

### Step 4: Identify the smallest 4 numbers
The smallest 4 numbers from the list are:
- 3
- 5
- 7
- 9

### Step 5: Calculate the average of the smallest 4 numbers
Now we will calculate the average of these smallest 4 numbers:
\[ \text{Average} = \frac{3 + 5 + 7 + 9}{4} \]
Calculating the sum:
\[ 3 + 5 + 7 + 9 = 24 \]
Then, dividing by 4:
\[ \text{Average} = \frac{24}{4} = 6 \]

### Final Answer
The average of the smallest 4 numbers is **6**.

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