Directions: Read the information and answer the given questions. Eight…

Concept

In a rank-based age or year puzzle, first convert every birth year to an age using the reference year, then treat phrases such as “born between X and Y” or “immediately before” as statements about the RELATIVE ORDER (rank) of the birth years once they are sorted — not as literal calendar-year arithmetic. A given numeric property (here, a perfect cube) anchors one person to an exact rank; positional and range clues then propagate outward from that anchor until exactly one arrangement survives.

Application

1. Sort the eight birth years ascending and convert each to an age using 2025 minus the year: 1966→59, 1976→49, 1982→43, 1989→36, 1997→28, 1998→27, 2006→19, 2012→13; label these ranks 1 to 8 in that order.

2. Among these eight ages, only 27 is a perfect cube (3³ = 27), so the clue that Q's age is a perfect cube fixes Q at rank 6 (born 1998, age 27).

3. The clue that exactly one person is born between U and Q restricts U to a rank exactly two away from rank 6 — so U is at rank 4 (1989, age 36) or rank 8 (2012, age 13).

4. Testing U at rank 8: the clue that exactly two people are born between U and W then forces W to rank 5 (1997, age 28), the only rank within “older than 20 years” that sits three ranks from rank 8. But the three ages then left over (59, 49, 19) for the remaining people cannot satisfy both the R–S clue (gap at most 20 years) and the T–S clue (gap at most 10 years, S younger) together — whichever age is picked for S, no consistent pair remains for the other two. This branch fails.

5. So U is at rank 4 (1989, age 36). The “exactly two people between U and W” clue then places W at rank 1 (1966, age 59); the only alternative, rank 7 (2006, age 19), fails “older than 20 years.”

6. The clue that V was born immediately before P, together with both being younger than 45 years, restricts that pair to two adjacent ranks that are both under age 45. Among the ranks still open (2, 3, 7, 8), only ranks 7 and 8 (2006, age 19 and 2012, age 13) both qualify, so V takes rank 7 and P takes rank 8.

7. The three remaining ranks — 2, 3, and 5, holding ages 49, 43, and 28 — go to the last three people. Testing age 43 for S: age 28 is 15 years less, which fits the R–S clue (at most 20 years less), and age 49 is 6 years more, which fits the T–S clue (at most 10 years more, S younger). The other possible choice for S leaves no remaining age within the required 10-year gap above it, so this is the only consistent split.

Cross-check

The completed arrangement below satisfies every clue: exactly two people (ranks 2 and 3) sit between U (rank 4) and W (rank 1); W's age (59) exceeds 20; P's age (13) and V's age (19) are both under 45; Q (age 27) is not the youngest; R's age (28) is 15 years less than S's age (43), within the 20-year cap; exactly one person (rank 5) sits between U (rank 4) and Q (rank 6); V (rank 7) sits immediately before P (rank 8); Q's age (27) is a perfect cube; and T's age (49) exceeds S's age (43) by 6 years, within the 10-year cap.

Result

Only the combination “T-49 years” matches this completed assignment, so that is the correct combination.