The average of four consecutive even numbers a, b, c and d is 33. Find the product of b and d.

Options

A. A)1236
B. B)1252
C. C)1152
D. D)1156

Answer

To solve the problem, we need to find the product of two consecutive even numbers, b and d, given that the average of four consecutive even numbers a, b, c, and d is 33.

### Step-by-Step Solution:

1. **Understanding Consecutive Even Numbers**:
Let the four consecutive even numbers be represented as:
- a = x (the smallest even number)
- b = x + 2 (the next even number)
- c = x + 4 (the next even number)
- d = x + 6 (the largest even number)

2. **Setting Up the Average**:
The average of these four numbers is given by the formula:
\[ \text{Average} = \frac{a + b + c + d}{4} \]
Substituting the values of a, b, c, and d, we get:
\[ \frac{x + (x + 2) + (x + 4) + (x + 6)}{4} = 33 \]

3. **Simplifying the Equation**:
Combine the terms in the numerator:
\[ \frac{4x + 12}{4} = 33 \]
Simplifying further:
\[ 4x + 12 = 132 \]

4. **Solving for x**:
Subtract 12 from both sides:
\[ 4x = 120 \]
Divide by 4:
\[ x = 30 \]

5. **Finding the Values of a, b, c, and d**:
Now we can find the values of a, b, c, and d:
- a = 30
- b = 32
- c = 34
- d = 36

6. **Calculating the Product of b and d**:
Now we need to find the product of b and d:
\[ b \times d = 32 \times 36 \]

7. **Performing the Multiplication**:
To calculate \(32 \times 36\):
\[ 32 \times 36 = 1152 \]

### Final Answer:
The product of b and d is **1152**.