Question

A statement is given followed by two conclusions. Find which conclusion is TRUE based on the given statement.

Statement:
C = A ≤ T < D ≥ O; G ≥ D < S; T ≥ A
Conclusions:

1. A < O
2. C < G

• A. Only II
• B. Only I
• C. Either I or II
• D. Neither I nor II

Answer 1

Answer:

A. Only II

Analyzing the Logical Statement

• The given statement provides a series of inequalities: C = A ≤ T < D ≥ O and G ≥ D < S.
• From these, we can establish a clear chain of relationships between the variables.

Evaluating Conclusion I: A < O

• To determine the relationship between A and O, we must trace the path: A ≤ T < D ≥ O.
• Here, the relationship between T and D is T < D, and the relationship between D and O is D ≥ O.
• Because there are conflicting signs between T and O (specifically, the inequality directions point towards D from both sides), a definite relationship between A and O cannot be established.
• Therefore, A < O is not necessarily true.

Evaluating Conclusion II: C < G

• To determine the relationship between C and G, trace the path: C = A ≤ T < D ≤ G.
• Combining the components: C = A and A ≤ T means C ≤ T.
• Given T < D and D ≤ G (from G ≥ D), the combined inequality chain becomes C ≤ T < D ≤ G.
• Since T < D involves a strict inequality (<), this relationship forces C < G to be true.
• The presence of at least one strict inequality sign (<) in the path between C and G ensures that the relationship holds.

Key Takeaways for Exams

• Check for Conflicting Signs: Whenever a path between two variables contains both > and < symbols, no definite relationship can be concluded between those variables.
• Strict Inequality Rule: If there is at least one strict inequality sign (< or >) in the chain, the final relationship must be a strict inequality.
• Equality and Inequality: If C = A and A ≤ T, then C ≤ T. If the chain subsequently contains a strict inequality, the final result will be strict (e.g., C < T).