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 a "younger than" relation first, then check which single person is younger than all three of the others without breaking any statement.

Answer 1

The Correct Option is C

Step 1: Write each statement as an age comparison.
P says "I am younger than S", so P is younger than S.
R says "P is older than me", so P is older than R, which is the same as saying R is younger than P.
Putting these two together gives one chain: R is younger than P, and P is younger than S.

Step 2: Use Q's statement to place Q in the chain.
Q says Q is neither the youngest nor the oldest of all four. If Q were younger than R, Q would become the youngest of all four, which breaks Q's own statement, so Q must be older than R. If Q were older than S, Q would become the oldest of all four, again breaking Q's statement, so Q must be younger than S. This gives R is younger than Q, and Q is younger than S.

Step 3: Combine both chains.
From Step 1: R is younger than P, and P is younger than S. From Step 2: R is younger than Q, and Q is younger than S. In both chains, R sits below both P and Q, and S sits above both of them. So no matter whether P is younger than Q or Q is younger than P, R stays younger than both, and S stays older than both.

Step 4: Identify the youngest and rule out the rest.
P cannot be the youngest, since R's own statement makes R younger than P. Q cannot be the youngest, since Q's statement rules that out directly. S cannot be the youngest, since P's statement makes P younger than S, and R is younger still. R is younger than P (Step 1), younger than Q (Step 2), and therefore younger than S too, so R is younger than all three others, which makes R the youngest.

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