The sum of four consecutive even integers is 1092. The greatest of them is

Options

A. (a) 270
B. (b) 300
C. (c) 276
D. (d) 302

Answer

To solve the problem of finding the greatest of four consecutive even integers whose sum is 1092, we can follow these steps:

### Step-by-Step Solution:

1. **Define the First Integer**:
Let the first even integer be \( x \).

2. **Define the Next Three Integers**:
Since we are dealing with consecutive even integers, the next three integers can be expressed as:
- Second integer: \( x + 2 \)
- Third integer: \( x + 4 \)
- Fourth integer: \( x + 6 \)

3. **Set Up the Equation**:
The sum of these four integers is given as 1092. Therefore, we can write the equation:
\[ x + (x + 2) + (x + 4) + (x + 6) = 1092 \]

4. **Combine Like Terms**:
Simplifying the left side of the equation:
\[ 4x + 12 = 1092 \]

5. **Isolate the Variable**:
To find \( x \), first subtract 12 from both sides:
\[ 4x = 1092 - 12 \]
\[ 4x = 1080 \]

6. **Solve for \( x \)**:
Now, divide both sides by 4:
\[ x = \frac{1080}{4} \]
\[ x = 270 \]

7. **Find the Greatest Integer**:
The greatest of the four integers is:
\[ x + 6 = 270 + 6 = 276 \]

### Final Answer:
The greatest of the four consecutive even integers is **276**.

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