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Difficulty: EasyData Sufficiency with Visual and Tabular Contexts

The table below displays the number of employees and the average salary per employee across three departments at Company Z:

DepartmentNumber of EmployeesAverage Salary ($)
Marketing2060,000
EngineeringEE80,000
Sales3050,000

What was the overall average salary per employee across all three departments combined?

(1) The total number of employees across all three departments combined is 100.
(2) The total annual payroll for the Engineering department is $4,000,000.

  1. A
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. B
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. C
    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.Answer
  5. E
    Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

EACH statement ALONE is sufficient.
The question target requires finding the weighted average salary across all departments, which reduces to finding the value of the unknown employee count EE. Statement (1) yields 20+E+30=10020 + E + 30 = 100, so E=50E = 50. Statement (2) yields E×80,000=4,000,000E \times 80,000 = 4,000,000, so E=50E = 50. Since each statement independently determines EE, each statement alone is sufficient.

Step-by-Step Solution

1
Rephrase the question stem target
Overall average salary = 20(60,000)+E(80,000)+30(50,000)20+E+30=2,700,000+80,000E50+E\frac{20(60,000) + E(80,000) + 30(50,000)}{20 + E + 30} = \frac{2,700,000 + 80,000E}{50 + E}. Finding the value of EE is sufficient to answer the question.
The overall average salary is a weighted average that depends solely on the single unknown parameter EE.
2
Evaluate Statement (1) independently
Total employees = 20+E+30=100  ⟹  E=5020 + E + 30 = 100 \implies E = 50. Since EE is uniquely determined, the overall average salary can be calculated.
Statement (1) provides a direct linear equation in EE.
3
Evaluate Statement (2) independently
Engineering total payroll = E×80,000=4,000,000  ⟹  E=50E \times 80,000 = 4,000,000 \implies E = 50. Since EE is uniquely determined, the overall average salary can be calculated.
Statement (2) gives the total department cost, which divided by the known average salary gives EE directly.
4
Conclude sufficiency classification
Each statement alone gives E=50E = 50, making each statement individually sufficient.
Both Statement (1) and Statement (2) yield a unique value for EE independently.

Key Concept

Weighted average determination from tabular data using Data Sufficiency logic
Estimated Time:1m 0s
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Topics

Data Sufficiency with Visual and Tabular Contexts

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