Question

The average of 25 results is 18. The average of the first twelve of them is 14 and that of the last twelve is 17. What is the thirteenth result?

• A. 75
• B. 78
• C. 80
• D. 82

Hint:

For average problems, use the formula for the sum of results (Sum = Average \(\times\) Number of terms) and break the problem into parts for easy calculation.

Answer 1

The Correct Option is B

Step 1: Total sum of all 25 results.
The average of all 25 results is 18, so the total sum of the 25 results is: \[ \text{Total sum} = 25 \times 18 = 450 \] Step 2: Total sum of the first twelve results.
The average of the first twelve results is 14, so the total sum of the first twelve results is: \[ \text{Sum of first 12 results} = 12 \times 14 = 168 \] Step 3: Total sum of the last twelve results.
The average of the last twelve results is 17, so the total sum of the last twelve results is: \[ \text{Sum of last 12 results} = 12 \times 17 = 204 \] Step 4: Using the sum of the first twelve and last twelve results.
The sum of the first twelve and last twelve results is: \[ \text{Sum of first 12 and last 12 results} = 168 + 204 = 372 \] Step 5: Finding the thirteenth result.
The sum of all 25 results is 450, and the sum of the first twelve and last twelve results is 372. So, the thirteenth result is: \[ \text{Thirteenth result} = 450 - 372 = 78 \] Thus, the thirteenth result is \( 78 \).