Data Sufficiency – Counting Employees Opting for VRS Question: How many employees of Bank Z opted for Voluntary Retirement Scheme (VRS)? Statements: I. 18% of the 950 officer-cadre employees and 6% of the 1,100 other-cadre employees opted for VRS. II. 28% of employees aged 51–56 and 17% of all other age groups opted for VRS.

Introduction / Context:
We must determine if the provided information is enough to compute the exact number of employees opting for VRS. One statement gives cadre-wise counts and percentages; the other gives age-wise percentages without population counts.

Given Data / Assumptions:

• I: Officers = 950 with 18% opting; Others = 1,100 with 6% opting.
• II: Percentages given by age bands (28% and 17%) but no headcounts per band.
• Populations are disjoint within each categorization (cadre or age) but totals are needed to compute a number.

Concept / Approach:
To compute a number from a percentage, you need both the rate and the base count. Statement I provides both rates and their corresponding base counts by cadre, which is sufficient. Statement II lacks the required base counts by age groups, which is insufficient.

Step-by-Step Solution:
Using I: Officers opting = 0.18 * 950 = 171. Using I: Others opting = 0.06 * 1,100 = 66. Total opting = 171 + 66 = 237. Thus I alone yields the exact figure.

Verification / Alternative check:
II alone: We do not know how many employees are in 51–56 vs. the rest. Without those base counts, no numeric total can be computed.

Why Other Options Are Wrong:
'II alone' or 'Either': Not valid because II lacks base counts. 'Both': Overstated; I already suffices. 'Neither': False; I works.

Common Pitfalls:
Attempting to use percentages without the relevant base population sizes.

Final Answer:
I alone is sufficient while II alone is not sufficient