Question

Four people P, Q, R, and S, of different ages, make the following observations.
P: I am younger than S.
Q: I am neither the youngest nor the oldest.
R: P is older than me.
Based on these observations, the youngest person is ______.

• A. P
• B. Q
• C. R
• D. S

Hint:

Turn each statement into an inequality between ages and compare all four.

Answer 1

The Correct Option is C

Step 1: Write each statement as an inequality.
P says "I am younger than S", so \( P < S \).
R says "P is older than me", so \( P > R \), which means \( R < P \).
Q says "I am neither the youngest nor the oldest", so Q is not the smallest and not the largest age among all four.

Step 2: Combine the P and R statements.
From \( R < P \) and \( P < S \) we get \( R < P < S \).
So among P, R, and S, R is already the smallest.

Step 3: Place Q using its own statement.
Q cannot be the youngest overall, so Q cannot sit below R, since that would make Q the youngest, which contradicts Q's own claim.
Q cannot be the oldest overall, so Q cannot sit above S.
So Q sits between R and S, which means \( R < Q \) as well.

Step 4: Check who is youngest.
We now have \( R < P \), \( R < Q \), and \( R < S \), so R is smaller than every other person.

Final Answer:
R has the smallest age among P, Q, R, and S, so R is the youngest. \[ \boxed{R} \]