Question

Is person A older than person B? Statement (I): A is older than person C. Statement (II): C is older than person B.

• A. Statement I alone is sufficient, but Statement II alone is not sufficient.
• B. Statement II alone is sufficient, but Statement I alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Even both statements together are not sufficient.

Hint:

For comparison problems, combine inequalities carefully. If \(A>C\) and \(C>B\), then \(A>B\).

Answer 1

The Correct Option is C

Concept: Age comparison problems are based on transitive relations. If \[ A>C \] and \[ C>B, \] then automatically \[ A>B. \]

Step 1: Analyze Statement (I). Given: \[ A>C. \] No information about \(B\). Possible situations: \[ A>C>B \] or \[ B>A>C. \] Hence Statement (I) alone is insufficient.

Step 2: Analyze Statement (II). Given: \[ C>B. \] No information about A. Possible situations: \[ A>C>B \] or \[ C>B>A. \] Thus Statement (II) alone is insufficient.

Step 3: Combine both statements. From Statement (I): \[ A>C. \] From Statement (II): \[ C>B. \] Combining, \[ A>C>B. \] Therefore, \[ A>B. \] The answer to the question is definitely “Yes.” Hence both statements together are sufficient.