Among schools A, B, C, and D, which school has the highest number of students? I. School A has fewer students than school D. II. School C has fewer students than school D.

Introduction / Context:
We need to identify the unique maximum among four schools given partial inequalities. DS focuses on whether D is necessarily the maximum or whether another school (e.g., B) could exceed D.

Given Data / Assumptions:

• I: A < D.
• II: C < D.

Concept / Approach:
Combine inequalities and check if D must be strictly the largest, or if another candidate (e.g., B) can surpass D under the constraints.

Step-by-Step Solution:

Verification / Alternative check:
Scenarios: (a) Let counts be A=100, B=400, C=90, D=300 ⇒ highest=B. (b) A=100, B=250, C=90, D=300 ⇒ highest=D. Both satisfy I and II.

Why Other Options Are Wrong:

• A/B/C/E: None force uniqueness; combined data still allow multiple maxima.

Common Pitfalls:
Assuming transitivity where none exists (no relation given for B).

Final Answer:
Both statements together are NOT sufficient.