Average salary of 15 employees — which statements suffice? I. Average salary of 7 clerical employees is $8,500. II. Average salary of 5 officer employees is $10,000. III. Average salary of 3 sub-staff employees is $2,500.

Introduction / Context:The task is to decide which statements are sufficient to compute the overall average salary of 15 employees, given subgroup averages and subgroup sizes.

Given Data / Assumptions:

• Total headcount = 15 (7 clerical, 5 officers, 3 sub-staff).
• I: Average of 7 clerical = $8,500.
• II: Average of 5 officers = $10,000.
• III: Average of 3 sub-staff = $2,500.

Concept / Approach:The combined average is a weighted mean: (Σ subgroup_total) / 15, where each subgroup_total = (subgroup_avg * subgroup_count). To compute the overall average uniquely, we need all subgroup totals (or an equivalent).

Step-by-Step Solution:

Verification / Alternative check:Missing any one subgroup leaves an unknown portion of the total, preventing a unique overall average.

Why Other Options Are Wrong:

• Only I / Only II / Only III: Insufficient; partial data.
• Any two: Still leaves the third subgroup unknown.

Common Pitfalls:Assuming the remaining subgroup can be deduced; it cannot without additional constraints.

Final Answer:All I, II and III together