Enrollment comparison puzzle: Class A has a higher enrollment than Class B, and Class C has a lower enrollment than Class B; assess whether the statement "Class A has a lower enrollment than Class C" must be true given only these two premises.

Given data

• Premise 1: A > B (Class A has higher enrollment than Class B).
• Premise 2: C < B (Class C has lower enrollment than Class B).
• Claim to test: A < C.

Concept / ApproachChain inequalities around B and derive the relative order between A and C.

Step-by-step reasoningStep 1: From A > B and C < B, we have A on the right of B and C on the left of B on the number line.Step 2: Therefore A > B > C, which implies A > C.Step 3: The claim A < C contradicts A > C derived above, so it cannot be true under any values consistent with the premises.

Verification / Alternative viewExample: Let B=30, A=35 (A>B), C=20 (CC. No choice of numbers that respects the premises will make A

Common pitfalls

• Thinking "both are different from B" leaves A and C incomparable. Here, the directions relative to B determine a strict order.

Final AnswerDefinitely false.