Data Sufficiency – Counting visitors (passes allow up to 3 guests) Question: How many visitors saw the exhibition yesterday in total? Statements: I. Each entry pass holder can take up to three persons with him/her. II. In all, 243 passes were sold yesterday.

Introduction / Context:
This DS problem involves maximum-capacity reasoning. A pass holder may bring guests, but the actual number of guests per pass can vary from 0 to the stated maximum. We must judge sufficiency to compute the total visitors.

Given Data / Assumptions:

• I: Each pass allows up to 3 accompanying persons.
• II: 243 passes were sold yesterday.
• Visitor count includes pass holders themselves plus any accompanying persons.

Concept / Approach:
To determine an exact total, we need both the number of passes and the actual number of companions used per pass. A bound such as 'up to 3' only provides a range, not a fixed value.

Step-by-Step Solution:

Verification / Alternative check:
Construct two valid scenarios with the same 243 passes: (a) Nobody brings a guest → 243 visitors; (b) Everyone brings 3 guests → 972 visitors. Both conform to the statements yet yield different totals, proving insufficiency.

Why Other Options Are Wrong:

• I alone or II alone: each clearly lacks essential information.
• Either I or II: false since neither alone suffices.
• Both I and II: still not enough because 'up to 3' does not fix a unique number.

Common Pitfalls:
Assuming 'up to 3' means 'exactly 3'; that would change the problem completely but is not stated. DS demands using only given facts.

Final Answer:
Neither I nor II is sufficient