Eight people — P, Q, R, S, T, U, V, and W — are seated in a straight line facing north. Each has a distinct age from the set \{8, 11, 15, 17, 21, 25, 27, 30\}, but not necessarily in that order. The following conditions apply:

- P sits at one extreme end. There are exactly three people between P and the person who is 11 years old.
- R sits third to the left of the person who is 17 years old.
- The 17-year-old is not an immediate neighbor of the 11-year-old.
- R is not 11 years old. P is not 17 years old.
- Q is 15 years old. S is not the youngest.
- R is older than P, but R's age is not a perfect square.
- The number of people between P and R equals the number of people between W and the 30-year-old.
- T sits immediately to the left of the 8-year-old.
- Q sits third to the left of S.
- The youngest person sits at the extreme right end.
- Everyone to the left of W is younger than W.
- U is older than V.
- Q does not sit at the extreme left end.

**Question:** Which of the following statements is true based on the above conditions?

Question

Eight people — P, Q, R, S, T, U, V, and W — are seated in a straight line facing north. Each has a distinct age from the set \{8, 11, 15, 17, 21, 25, 27, 30\}, but not necessarily in that order. The following conditions apply:

- P sits at one extreme end. There are exactly three people between P and the person who is 11 years old.
- R sits third to the left of the person who is 17 years old.
- The 17-year-old is not an immediate neighbor of the 11-year-old.
- R is not 11 years old. P is not 17 years old.
- Q is 15 years old. S is not the youngest.
- R is older than P, but R's age is not a perfect square.
- The number of people between P and R equals the number of people between W and the 30-year-old.
- T sits immediately to the left of the 8-year-old.
- Q sits third to the left of S.
- The youngest person sits at the extreme right end.
- Everyone to the left of W is younger than W.
- U is older than V.
- Q does not sit at the extreme left end.

**Question:** Which of the following statements is true based on the above conditions?

Accepted Answer

**Solution:**

1. Since P sits at one extreme end and there are three people between P and the 11-year-old, the 11-year-old must be fourth from P.

2. The youngest person (8 years old) sits at the extreme right end.

3. T sits immediately to the left of the 8-year-old, so T is second from the right.

4. Q is 15 years old and does not sit at the extreme left end.

5. Q sits third to the left of S, so S must be to the right of Q by three seats.

6. R sits third to the left of the 17-year-old, and R is not 11 years old.

7. R is older than P, but R's age is not a perfect square (so R cannot be 25, since 25 is a perfect square).

8. The number of people between P and R equals the number of people between W and the 30-year-old.

9. Everyone to the left of W is younger than W.

10. U is older than V.

By carefully placing the individuals according to these conditions, the arrangement that satisfies all conditions shows that W sits immediately to the right of Q (who is 15 years old).

Hence, the correct statement is:

**(e) W sits immediately to the right of the person who is 15 years old.**

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