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 ______.
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 ______.
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 ______.
Show Hint
Chain the two direct clues to get R < P < S, then use Q's statement to show Q cannot be below R or above S. R ends up below everyone.
Updated On: Jul 22, 2026
- P
- Q
- R
- S
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Translate each statement into an age order.
Use the symbol "<" to mean "younger than." P says "I am younger than S," which gives \(P < S\). R says "P is older than me," which means R is younger than P, giving \(R < P\). Q says "I am neither the youngest nor the oldest," which means Q's age sits strictly between the youngest and the oldest of the whole group, not at either extreme.
Step 2: Combine the two direct comparisons.
From \(R < P\) and \(P < S\), chain them together:
\[ R < P < S \]
So, considering only P, R, and S for a moment, R is the youngest of these three and S is the oldest of these three.
Step 3: Work out where Q must fit.
Q cannot be younger than R, because if Q were younger than R, Q would become the youngest person overall, which contradicts Q's own statement. Q also cannot be older than S, because that would make Q the oldest person overall, again contradicting the statement. So Q must fit strictly between R and S:
\[ R < Q < S \]
This holds whether Q sits below P, above P, or anywhere in between, since Q's exact position relative to P is never pinned down by the statements.
Step 4: Identify the overall youngest person.
Combining \(R < P < S\) and \(R < Q < S\), R is younger than both P and Q, and R is also younger than S from the first chain. So R is younger than everyone else in the group, which makes R the youngest person overall.
Step 5: Rule out the other options.
P cannot be the youngest because R is younger than P. Q cannot be the youngest, since Q's own statement rules that out directly. S cannot be the youngest because S is shown to be older than both P and R, and than Q as well, since Q is younger than S. Only R satisfies every condition.
Final Answer:
The youngest person is R. \[ \boxed{R} \]
Use the symbol "<" to mean "younger than." P says "I am younger than S," which gives \(P < S\). R says "P is older than me," which means R is younger than P, giving \(R < P\). Q says "I am neither the youngest nor the oldest," which means Q's age sits strictly between the youngest and the oldest of the whole group, not at either extreme.
Step 2: Combine the two direct comparisons.
From \(R < P\) and \(P < S\), chain them together:
\[ R < P < S \]
So, considering only P, R, and S for a moment, R is the youngest of these three and S is the oldest of these three.
Step 3: Work out where Q must fit.
Q cannot be younger than R, because if Q were younger than R, Q would become the youngest person overall, which contradicts Q's own statement. Q also cannot be older than S, because that would make Q the oldest person overall, again contradicting the statement. So Q must fit strictly between R and S:
\[ R < Q < S \]
This holds whether Q sits below P, above P, or anywhere in between, since Q's exact position relative to P is never pinned down by the statements.
Step 4: Identify the overall youngest person.
Combining \(R < P < S\) and \(R < Q < S\), R is younger than both P and Q, and R is also younger than S from the first chain. So R is younger than everyone else in the group, which makes R the youngest person overall.
Step 5: Rule out the other options.
P cannot be the youngest because R is younger than P. Q cannot be the youngest, since Q's own statement rules that out directly. S cannot be the youngest because S is shown to be older than both P and R, and than Q as well, since Q is younger than S. Only R satisfies every condition.
Final Answer:
The youngest person is R. \[ \boxed{R} \]
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