Question

Eight employees of an organization have been rated on a scale of 1 to 50 for their performance. All ratings are integers. The overall average rating of the eight employees is 30. While the five employees with the highest ratings average 38, the five employees with the lowest ratings average 25. Which of the following, about the ratings obtained by the eight employees, is DEFINITELY FALSE?

• A. The second highest rating obtained is 38.
• B. The lowest rating obtained is 1.
• C. The third lowest rating obtained is 37.
• D. The median of the eight ratings is 37.5.
• E. The highest rating obtained is 40.

Hint:

When analyzing sets of numbers with specific conditions, break down the information into sums and averages to spot contradictions.

Answer 1

The Correct Option is C

Step 1: Understand the ratings distribution.
The average of the eight ratings is 30, so the total sum of all ratings is \( 30 \times 8 = 240 \).
Step 2: Apply the conditions for the highest and lowest ratings.
The highest five ratings average 38, so their total sum is \( 38 \times 5 = 190 \). The lowest five ratings average 25, so their total sum is \( 25 \times 5 = 125 \).
Step 3: Determine the false statement.
The sum of the ratings for the highest and lowest groups is \( 190 + 125 = 315 \), but the total sum is 240, so some conditions cannot hold true. Option (C) is the false statement because the third lowest rating cannot be 37.
Final Answer: \[ \boxed{\text{(C) The third lowest rating obtained is 37.}} \]