Difficulty: Medium
Correct Answer: can't be determined
Explanation:
Introduction / Context:
Weighted-average questions require either the subgroup averages or enough relations between them to solve for unknowns. Knowing only the overall mean and headcount ratio often isn’t sufficient.
Given Data / Assumptions:
Concept / Approach:
Let average salaries be E for executives and N for non-executives. Then overall average gives a single equation: (40*E + 20*N) / 60 = 12000. With two unknowns (E and N) and only one equation, infinitely many solutions exist unless another constraint is given.
Step-by-Step Solution:
Verification / Alternative check:
Pick E = 13000 ⇒ 40*13000 = 520000, then 20*N = 200000 ⇒ N = 10000. Pick E = 11000 ⇒ 40*11000 = 440000, then 20*N = 280000 ⇒ N = 14000. Multiple feasible values show non-uniqueness.
Why Other Options Are Wrong:
Common Pitfalls:
Assuming executives are always paid more and plugging a guess; the problem does not state subgroup averages or ordering constraints.
Final Answer:
can't be determined
Discussion & Comments