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 spoken clue into an inequality first (P < S, R < P), then use Q's clue only to rule out placements at the two extreme ends.

Answer 1

The Correct Option is C

Step 1: Convert each statement into an inequality.
P says 'I am younger than S', so \(P < S\) (using '<' to mean 'younger than').
R says 'P is older than me', so R is younger than P, giving \(R < P\).
Combining these two facts gives the chain \(R < P < S\), so among these three people R is the youngest and S is the oldest so far.

Step 2: Bring in Q's statement.
Q says 'I am neither the youngest nor the oldest' of the whole group of four. This tells us Q cannot occupy either extreme position once all four ages are ranked.

Step 3: Check whether Q could be younger than R.
If Q were placed below R, the order would become \(Q < R < P < S\). Here Q would be the overall youngest, which directly contradicts Q's own statement. So this placement is impossible.

Step 4: Check whether Q could be older than S.
If Q were placed above S, the order would become \(R < P < S < Q\). Here Q would be the overall oldest, again contradicting Q's statement. So this placement is also impossible.

Step 5: The only consistent placement is between R and S.
Since Q cannot go below R or above S, Q must sit somewhere strictly between R and S, for example \(R < Q < P < S\) or \(R < P < Q < S\). In every such arrangement, R stays below everyone else in the group.

Step 6: Conclude the youngest person.
No matter where exactly Q is inserted between R and S, R remains at the bottom of the ranking. Therefore the youngest person is R, which is option (C).