Consider the following statements : 1. A is older than B. 2. C and D are of the same age. 3. E is the youngest. 4. F is younger than D. 5. F is older than A. How many statements given above are required to determine the oldest person/persons ?

(a) Only two
(b) Only three
(c) Only four
(d) All five ✓ UPSC's answer

Why the answer is (d)

• Statement 3 establishes that E is the youngest, but this does not identify the oldest person among the others.

• Statement 2 states C and D are the same age, but without knowing their position relative to others, their age is undetermined.

• Statement 4 states F is younger than D, implying D is older than F, but this does not place D at the top of the hierarchy.

• Statement 5 states F is older than A, creating a chain D > F > A, but A's position relative to B and C is still unknown.

• Statement 1 states A is older than B, completing the chain D > F > A > B, yet C's age relative to D is still unknown.

• All five statements are required to establish the complete age hierarchy and confirm that D (and C, if C=D) is the oldest, as omitting any statement leaves the relative age of at least one person ambiguous regarding the maximum age.

Why the other options are wrong

(a) Only two: Only two statements are insufficient to establish a complete age hierarchy or identify the oldest person among five individuals.
(b) Only three: Only three statements do not provide enough relational links to determine the absolute oldest person among all five.
(c) Only four: Only four statements leave at least one person's age unconnected to the rest, making it impossible to definitively identify the oldest.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.