How many students are in the class? I. The number is more than 20 but less than 27. II. The number is more than 24 but less than 31, and the class can be partitioned into equal groups of 5.

Introduction / Context:
We must determine a unique class size using two overlapping ranges and a divisibility condition.

Given Data / Assumptions:

• I: 20 < n < 27 ⇒ n ∈ {21, 22, 23, 24, 25, 26}.
• II: 24 < n < 31 and n is a multiple of 5 ⇒ n ∈ {25, 30}.

Concept / Approach:
Intersect the candidate sets from I and II.

Step-by-Step Solution:
From I: {21,22,23,24,25,26}.From II: {25,30}.Intersection ⇒ {25} only. Thus n = 25.

Why Other Options Are Wrong:
Neither statement alone yields a unique value; together they do.

Final Answer:
Both statements together are necessary.