The average of four consecutive even number A, B, C and D respectively is 25. What is the product of A & C ?

Options

A. 528
B. 616
C. 624
D. 572

Answer

To solve the problem, we need to find the product of two consecutive even numbers A and C, given that the average of four consecutive even numbers A, B, C, and D is 25. Let's break down the steps:

### Step-by-Step Solution:

1. **Define the Consecutive Even Numbers**:
Let the first even number be \( A \). Since we are dealing with consecutive even numbers, we can express the other numbers as:
- \( B = A + 2 \)
- \( C = A + 4 \)
- \( D = A + 6 \)

2. **Set Up the Average Equation**:
The average of these four numbers is given by the formula:
\[ \text{Average} = \frac{A + B + C + D}{4} \]
Substituting the expressions for B, C, and D:
\[ \text{Average} = \frac{A + (A + 2) + (A + 4) + (A + 6)}{4} \]

3. **Simplify the Equation**:
Combine the terms in the numerator:
\[ = \frac{4A + 12}{4} \]
This simplifies to:
\[ = A + 3 \]

4. **Set the Average Equal to 25**:
According to the problem, the average is 25:
\[ A + 3 = 25 \]

5. **Solve for A**:
Subtract 3 from both sides:
\[ A = 25 - 3 \]
\[ A = 22 \]

6. **Find C**:
Now, we can find C:
\[ C = A + 4 = 22 + 4 = 26 \]

7. **Calculate the Product of A and C**:
Now we need to find the product of A and C:
\[ A \times C = 22 \times 26 \]

8. **Perform the Multiplication**:
Calculate \( 22 \times 26 \):
\[ 22 \times 26 = 572 \]

### Final Answer:
The product of A and C is \( 572 \).