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, chain them together, then use Q's statement to rule out who can be at either extreme.

Answer 1

The Correct Option is C

Step 1: Turn each statement into an inequality.
P says I am younger than S, so \( P < S \) in age.
R says P is older than me, so \( R < P \).
Putting these two together gives a chain, \( R < P < S \).

Step 2: Use Q's statement to place Q.
Q says I am neither the youngest nor the oldest, so Q cannot be the smallest age of all four people, and Q cannot be the largest age of all four people.

Step 3: Check whether Q could be younger than R.
Suppose Q were younger than R. Since the chain already says \( R < P < S \), that would put Q below R, below P and below S all at once, making Q the youngest person overall.
That contradicts Q's own statement, so Q cannot be younger than R. This forces \( R < Q \).

Step 4: Combine everything into one order.
We now know \( R < P < S \) and \( R < Q \).
R is smaller than P, smaller than S, and smaller than Q, so R sits below all three of the others no matter where exactly Q falls between R and S.

Step 5: Confirm R is the unique youngest.
Since every one of P, Q and S is shown to be older than R, R must be the youngest of the four, and this fits Q's statement too, because Q ends up somewhere in the middle, neither the smallest (that is R) nor necessarily the largest.

Step 6: Why the other options fail.
P cannot be youngest because R < P is given directly.
Q cannot be youngest because Q's own statement rules it out.
S cannot be youngest because both P and R are shown to be younger than S.

Final Answer:
The youngest person is R.
\[ \boxed{R} \]