Among P, Q, R, S and T, each one is having a different height. Q is shorter than only T and S is shorter than P and Q. S is not the shortest. Who among them is the shortest?
R
Determining the Shortest Person
The problem asks us to identify the shortest person among P, Q, R, S, and T, given specific comparative statements about their heights. All individuals have distinct heights.
Analyzing the Clues Provided
Let's break down the information given:
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Clue 1: "Q is shorter than only T."
- This implies that T is the only person taller than Q.
- Therefore, T > Q.
- It also means that Q is taller than everyone else in the group besides T. So, Q > P, Q > R, and Q > S.
- From this clue, we can establish a partial order: T > Q > {P, R, S}. This tells us that Q is the second tallest person, and P, R, and S are all shorter than Q.
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Clue 2: "S is shorter than P and Q."
- This means P > S and Q > S.
- This clue is consistent with the deduction from Clue 1 (Q > S).
- It provides a direct comparison: P > S.
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Clue 3: "S is not the shortest."
- This means there must be at least one person who is shorter than S.
- So, S > X, where X represents someone shorter than S.
Combining Clues to Establish Order
Now, let's synthesize the information:
- From Clue 1, we know the order involves T > Q > {P, R, S}. The set {P, R, S} contains the three shortest people.
- From Clue 2, we know P > S. This gives us the relative order between P and S.
- From Clue 3, we know S is not the shortest. This means someone must be shorter than S.
- Consider the set {P, R, S}. We know P > S. The people taller than S are P, Q, and T.
- Since S is not the shortest, the person shorter than S must be someone from the set {P, R}.
- It cannot be P, because we know P > S.
- Therefore, the person shorter than S must be R. This gives us the relationship S > R.
- Combining the relationships P > S and S > R, we get the order: P > S > R.
- Integrating this with the order from Clue 1 (T > Q > {P, R, S}), the complete height order from tallest to shortest is: T > Q > P > S > R.
Identifying the Shortest Person
Based on the established height order (T > Q > P > S > R):
- T is the tallest.
- Q is the second tallest.
- P is the third tallest.
- S is the fourth tallest.
- R is the shortest.
Therefore, R is the shortest person among the group.
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