Consider the enrollments of three classes A, B and C. I. Class A has a higher enrollment than Class B. II. Class C has a lower enrollment than Class B. III. Class A has a lower enrollment than Class C. If the first two statements are true, then the third statement is:

Introduction / Context:
This is another logical comparison question, this time involving enrollments (number of students) in three different classes. You must decide whether the third statement can be true when the first two are accepted as facts. Such problems reinforce your understanding of ordering and transitive relationships between quantities.

Given Data / Assumptions:

• Let A, B and C represent the enrollments of classes A, B and C respectively.

• Statement I: Class A has higher enrollment than Class B, so A > B.

• Statement II: Class C has lower enrollment than Class B, so C < B.

• Statement III: Class A has lower enrollment than Class C, so A < C. We must test this against I and II.

Concept / Approach:
We convert the English sentences into numeric inequalities and then combine them to see the overall order of A, B and C. If the combined order directly contradicts Statement III, then III is always incorrect when I and II are true.

Step-by-Step Solution:
Step 1: From Statement I, A > B. Step 2: From Statement II, C < B. Step 3: If C < B and A > B, it follows that A is strictly greater than B, which is strictly greater than C. So we get A > B > C. Step 4: From this ordering, A is larger than C. In inequality form, A > C. Step 5: However, Statement III claims A < C, which is exactly the opposite inequality. Step 6: Therefore, Statement III directly contradicts the condition that A > B and B > C, and it cannot be true if the first two statements are true.

Verification / Alternative check:
Take a simple numerical example. Suppose B = 50 students. Let A = 60 (so that A > B) and C = 40 (so that C < B). Then we have A = 60, B = 50 and C = 40, which clearly gives A > C. It is impossible to find values that satisfy both A > B and C < B while also making A < C. Hence the third statement is always wrong once the first two are fixed.

Why Other Options Are Wrong:
Option A is wrong because the third statement does not follow; it contradicts the combined inequalities derived from the first two statements.
Option C is wrong because there is no uncertainty; A > B and B > C force A > C, so we can definitively say that A < C is impossible under these conditions.
Option D is wrong because the third statement talks about the same three classes and the same enrollments, so it is not independent or unrelated at all; it is just incorrect under the given premises.

Common Pitfalls:
A frequent error is to treat each statement in isolation and fail to combine them. Some students see A > B and C < B and conclude nothing about A and C, ignoring that if A is larger than B and C is smaller than B, then A must be larger than C. Always write out the inequalities explicitly and then order the values step by step.

Final Answer:
So, if Statements I and II are true, Statement III can never be true. The correct choice is Always incorrect; it contradicts the first two statements.