Data Sufficiency — Salaries and Average (Five Persons) In a group of five employees A, B, C, D, and E, the average salary is ₹ 65,780 (so the total of all five salaries is fixed). What is the exact salary of A? I. The combined salary of B and C equals ₹ 88,545. II. The combined salary of D and E equals ₹ 59,020.

Introduction / Context:
This is a classic data sufficiency problem on averages and totals. We are not asked to compute a numerical salary for A directly unless forced; instead, we must judge whether the given statements provide enough information to determine A uniquely.

Given Data / Assumptions:

• Average salary of five people (A, B, C, D, E) is ₹ 65,780.
• Therefore, total T = 5 * 65,780.
• Statement I: (B + C) = ₹ 88,545.
• Statement II: (D + E) = ₹ 59,020.

Concept / Approach:
Averages convert to totals via T = average * count. If we know T and the sum of everyone except A, then A = T - (sum of others). We check whether each statement isolates (B + C + D + E).

Step-by-Step Solution:

Verification / Alternative check:
Once both partial sums are known, A is uniquely determined by subtraction from T. No other values can change A without changing I or II, so the solution is unique.

Why Other Options Are Wrong:

• Statement I alone sufficient: Wrong — lacks (D + E).
• Statement II alone sufficient: Wrong — lacks (B + C).
• Either one alone sufficient: Wrong — each alone is missing two salaries.
• Even both not sufficient: Wrong — together they fully determine A.

Common Pitfalls:
Confusing “average” with individual values; forgetting to multiply average by count; assuming extra information not given about individuals; or trying to compute everyone’s salary instead of only establishing sufficiency for A’s salary.

Final Answer:
Both statements together are sufficient; neither alone is sufficient.