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Data Sufficiency in Percentages — Workforce Composition “In this company: 60% employees are male, 40% are female; 80% of all employees are sincere; 40% of all employees are from Rawalpura.” What can be concluded with certainty?

Difficulty: Medium

Correct Answer: None of these

Explanation:


Introduction / Context:
This problem tests understanding of aggregate percentages and the danger of inferring intersections without sufficient data. We are given overall percentage splits by gender, sincerity, and location, but no cross-tabulation.



Given Data / Assumptions:

  • Males = 60% of total; females = 40% of total.
  • Sincere employees = 80% of total.
  • From Rawalpura = 40% of total.
  • No information about overlaps between these categories.


Concept / Approach:
Percentages of whole categories do not determine how they overlap unless additional constraints are given. Many different cross-distributions can fit the same margins, making strong statements about subgroups unjustified.



Step-by-Step Solution:

Test option (a): “All male employees are from out station.” Margins do not force this; up to 40% of all employees are from Rawalpura, and some could be male.Test option (b): “All male employees are sincere.” With 80% sincere overall, it is possible but not necessary that all males are sincere; some sincerity could be among females.Test option (c): “20% of female employees are not sincere.” Non-sincere overall is 20% of total, but we do not know the split across genders; it could be any mix consistent with margins.Test option (d): “All female employees are from Rawalpura.” Rawalpura accounts for 40% of all employees, which equals the female percentage, but that does not prove identity; the entire 40% Rawalpura group could be a mix or even all male.


Verification / Alternative check:
Construct examples: one distribution could place all 40% Rawalpura as males; another could place them all as females. Both satisfy the given margins but contradict (a) and (d) respectively.



Why Other Options Are Wrong:
Each asserts an intersection fact that the marginal totals do not uniquely determine.



Common Pitfalls:
Equating equal percentages (40% females and 40% Rawalpura) with the same set of people, or assuming uniform distribution of sincerity across genders.



Final Answer:
None of these

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