If sum of six consecutive odd numbers is 168, then find the largest of these numbers.

Options

A. 23
B. 27
C. 31
D. 33

Answer

To find the largest of six consecutive odd numbers whose sum is 168, we can follow these steps:

### Step 1: Define the first odd number
Let the first odd number be \( x \).

### Step 2: Express the consecutive odd numbers
The six consecutive odd numbers can be expressed as:
- First number: \( x \)
- Second number: \( x + 2 \)
- Third number: \( x + 4 \)
- Fourth number: \( x + 6 \)
- Fifth number: \( x + 8 \)
- Sixth number: \( x + 10 \)

### Step 3: Set up the equation for the sum
According to the problem, the sum of these six consecutive odd numbers is 168. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) = 168 \]

### Step 4: Simplify the equation
Combining like terms, we have:
\[ 6x + (2 + 4 + 6 + 8 + 10) = 168 \]
Calculating the sum of the constants:
\[ 2 + 4 + 6 + 8 + 10 = 30 \]
Thus, the equation becomes:
\[ 6x + 30 = 168 \]

### Step 5: Solve for \( x \)
Subtract 30 from both sides:
\[ 6x = 168 - 30 \]
\[ 6x = 138 \]
Now, divide both sides by 6:
\[ x = \frac{138}{6} \]
Calculating this gives:
\[ x = 23 \]

### Step 6: Find the largest odd number
The largest of the six consecutive odd numbers is the sixth number, which is:
\[ x + 10 = 23 + 10 = 33 \]

### Final Answer
Thus, the largest of these six consecutive odd numbers is **33**.

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