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: Analyze rating distribution.
The mean of eight ratings is 30, yielding a total sum of \( 30 \times 8 = 240 \).

Step 2: Evaluate conditions for extreme ratings.
The top five ratings have a mean of 38, summing to \( 38 \times 5 = 190 \).
The bottom five ratings have a mean of 25, summing to \( 25 \times 5 = 125 \).

Step 3: Identify the incorrect assertion.
The combined sum of the highest and lowest groups is \( 190 + 125 = 315 \). This exceeds the total sum of 240, indicating a contradiction. Statement (C) is false because the third lowest rating cannot be 37.

Final Answer:
\[\boxed{\text{(C) The third lowest rating obtained is 37.}}\]