Each problem consists of three statements. Based on the first two statements,…
2023
Each problem consists of three statements. Based on the first two statements, the third statement may be true, false, or uncertain.
Tanya is older than Eric.
Cliff is older than Tanya.
Eric is older than Cliff.
If the first two statements are true, the third statement is ________.
- A.
True
- B.
False
- C.
Uncertain
- D.
Insufficient Data
Show answer & explanation
Correct answer: B
Concept: When two statements establish a strict order between three entities using a transitive relation like "older than", the two orderings combine into one single fixed order via transitivity: if A is older than B, and B is older than C, then A is definitely older than C. Any third statement about the same three entities must then be checked directly against this single derived order — it is True if it matches, False if it contradicts it, and only Uncertain/Insufficient Data if the order is not fully pinned down.
Application:
Statement 1 gives Tanya older than Eric, i.e., Tanya > Eric.
Statement 2 gives Cliff older than Tanya, i.e., Cliff > Tanya.
Combining by transitivity: Cliff > Tanya > Eric.
This order places Eric as the youngest of the three and Cliff as the oldest.
Statement 3 claims Eric is older than Cliff, which directly contradicts Eric being the youngest.
Cross-check: Checking the reverse — if Eric were indeed older than Cliff, then together with Cliff being older than Tanya, Eric would have to be the oldest of the three, but statement 1 already fixes Tanya as older than Eric, so Eric cannot be the oldest. This confirms the derived order Cliff > Tanya > Eric is the only one consistent with both given statements, and therefore the third statement is false.
Answer: False.