Question

If the average of four consecutive odd numbers is 16, find the smallest of these numbers?

• A. 5
• B. 7
• C. 13
• D. 11

Hint:

For any symmetric, evenly spaced set of numbers, the average lies exactly at the midpoint. For four consecutive odd numbers, the midpoint is 16.
This means the middle two numbers are 15 and 17.
Thus, the sequence is 13, 15, 17, 19. The smallest is 13.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Odd numbers increase sequentially by 2.
The average of a set of numbers is the sum of the numbers divided by the count of numbers.
Key Formula or Approach:
Let the four consecutive odd numbers be: \[ x, \quad x + 2, \quad x + 4, \quad x + 6 \] Where $x$ is the smallest odd number.

Step 2: Detailed Explanation:
Write the equation for their average: \[ \frac{x + (x + 2) + (x + 4) + (x + 6)}{4} = 16 \] Multiply by 4: \[ 4x + 12 = 64 \] Subtract 12: \[ 4x = 52 \] Divide by 4: \[ x = 13 \] The smallest of the consecutive odd numbers is 13.
The numbers are 13, 15, 17, and 19. Their average is indeed $\frac{13 + 19}{2} = 16$.

Step 3: Final Answer:
The smallest number is 13, which corresponds to Option (C).