The average of four consecutive even numbers is 15. The 2nd highest number Is:

Options

A. 12
B. 18
C. 14
D. 16

Answer

To find the second highest number among four consecutive even numbers whose average is 15, we can follow these steps:

### Step 1: Understand the concept of average
The average of a set of numbers is calculated by summing all the numbers and dividing by the total count of numbers.

### Step 2: Set up the equation
Let the four consecutive even numbers be:
- \( x \) (the smallest)
- \( x + 2 \) (the second smallest)
- \( x + 4 \) (the second highest)
- \( x + 6 \) (the highest)

### Step 3: Write the equation for the average
The average of these four numbers is given as 15. Therefore, we can write the equation:
\[ \frac{x + (x + 2) + (x + 4) + (x + 6)}{4} = 15 \]

### Step 4: Simplify the equation
Combine the terms in the numerator:
\[ \frac{4x + 12}{4} = 15 \]

### Step 5: Multiply both sides by 4 to eliminate the fraction
\[ 4x + 12 = 60 \]

### Step 6: Solve for \( x \)
Subtract 12 from both sides:
\[ 4x = 48 \]
Now, divide by 4:
\[ x = 12 \]

### Step 7: Identify the four consecutive even numbers
Now that we have \( x = 12 \), the four consecutive even numbers are:
- \( 12 \) (smallest)
- \( 14 \) (second smallest)
- \( 16 \) (second highest)
- \( 18 \) (highest)

### Step 8: Find the second highest number
The second highest number is \( 16 \).

### Final Answer
The second highest number is **16**.

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