The sum of 5 consecutive odd numbers of Set A is 125. What will be the sum of Set B containing 4 consecutive odd numbers, if the smallest odd number of Set B is 16 more than the highest odd number of Set A?

Options

A. 156
B. 184
C. 192
D. 202

Answer

To solve the problem, we will break it down into steps.

### Step 1: Define the first set of odd numbers (Set A)
Let the first odd number of Set A be \( x \). The five consecutive odd numbers in Set A can be expressed as:
- First: \( x \)
- Second: \( x + 2 \)
- Third: \( x + 4 \)
- Fourth: \( x + 6 \)
- Fifth: \( x + 8 \)

### Step 2: Set up the equation for the sum of Set A
The sum of these five consecutive odd numbers is given as 125:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 125 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 5x + (2 + 4 + 6 + 8) = 125 \]
\[ 5x + 20 = 125 \]

### Step 4: Solve for \( x \)
Subtract 20 from both sides:
\[ 5x = 125 - 20 \]
\[ 5x = 105 \]
Now, divide by 5:
\[ x = \frac{105}{5} = 21 \]

### Step 5: Find the highest number in Set A
The highest number in Set A is:
\[ x + 8 = 21 + 8 = 29 \]

### Step 6: Define the first number of Set B
According to the problem, the smallest odd number in Set B is 16 more than the highest odd number of Set A:
\[ \text{Smallest number in Set B} = 29 + 16 = 45 \]

### Step 7: Define the four consecutive odd numbers in Set B
The four consecutive odd numbers in Set B are:
- First: \( 45 \)
- Second: \( 45 + 2 = 47 \)
- Third: \( 45 + 4 = 49 \)
- Fourth: \( 45 + 6 = 51 \)

### Step 8: Calculate the sum of Set B
Now, we add these four numbers together:
\[ 45 + 47 + 49 + 51 \]

Calculating step-by-step:
1. \( 45 + 47 = 92 \)
2. \( 49 + 51 = 100 \)
3. Now add these two results together:
\[ 92 + 100 = 192 \]

### Final Answer
The sum of Set B is \( 192 \).

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