Average of 5 consecutive even numbers is 42. Which number is the largest of the 5 numbers?

Options

A. a)44
B. b)46
C. c)42
D. d)48

Answer

To solve the problem, we need to find the largest of 5 consecutive even numbers whose average is 42.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that the average of 5 consecutive even numbers is given as 42.

2. **Using the Average**:
The average of a set of numbers is calculated by dividing the sum of the numbers by the count of the numbers. Here, we have 5 numbers, so we can express the average as:
\[ \text{Average} = \frac{\text{Sum of the numbers}}{5} \]
Given that the average is 42, we can set up the equation:
\[ 42 = \frac{\text{Sum of the numbers}}{5} \]

3. **Finding the Sum**:
To find the sum of the 5 numbers, we can rearrange the equation:
\[ \text{Sum of the numbers} = 42 \times 5 = 210 \]

4. **Identifying the Numbers**:
Since we are looking for 5 consecutive even numbers, we can denote them as:
\[ x, x+2, x+4, x+6, x+8 \]
where \(x\) is the smallest even number in the sequence.

5. **Setting Up the Equation**:
The sum of these numbers can be expressed as:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 5x + 20 \]
We know this sum equals 210, so we can set up the equation:
\[ 5x + 20 = 210 \]

6. **Solving for x**:
Now, we can solve for \(x\):
\[ 5x = 210 - 20 \]
\[ 5x = 190 \]
\[ x = \frac{190}{5} = 38 \]

7. **Finding the Largest Number**:
The 5 consecutive even numbers are:
\[ 38, 40, 42, 44, 46 \]
The largest number in this sequence is:
\[ 46 \]

### Final Answer:
The largest of the 5 consecutive even numbers is **46**.