Four friends P, Q, R and S are compared by height. P is shorter than Q but taller than R, and R is shorter than S. Based on this information, who is the shortest among all four friends?

Introduction / Context:
Height comparison questions ask you to use relative information to rank people from tallest to shortest or vice versa. They are common in analytical reasoning sections and test your ability to translate language into ordered relationships. Here we must determine who is the shortest among P, Q, R and S using a few simple statements about their heights.

Given Data / Assumptions:

• P is shorter than Q.
• P is taller than R.
• R is shorter than S.
• No two friends have exactly the same height.

Concept / Approach:
The idea is to express each sentence as an inequality. 'Shorter than' means less in height, and 'taller than' means greater. Once we convert each statement, we can chain them together to form a complete partial order and find the minimum element, which corresponds to the shortest person. This is a simple but important reasoning skill.

Step-by-Step Solution:
Step 1: From 'P is shorter than Q', write Q > P. Step 2: From 'P is taller than R', write P > R. Step 3: Combining these, we get Q > P > R. Step 4: From 'R is shorter than S', write S > R. Step 5: Now we know Q, P, and S are all taller than R, because Q > P > R and S > R. Step 6: We do not need the exact ordering of Q, P, and S among themselves, because the question only asks for the shortest person. Step 7: Since R is shorter than P, Q, and S, R must be the shortest among all four friends.

Verification / Alternative check:
Consider any numeric example that satisfies the inequalities. For instance, let Q have height 170 units, P have 165 units, R have 160 units, and S have 168 units. These values satisfy Q > P > R and S > R. In this example, R clearly has the smallest height, confirming that the reasoning is correct and that R is indeed the shortest.

Why Other Options Are Wrong:

• P: P is taller than R, so P cannot be the shortest.
• Q: Q is taller than P and therefore taller than R, so Q is not the shortest.
• S: S is taller than R by the given statement, so S is not the shortest.
• All four are of equal height: The statements clearly state some friends are taller or shorter than others, so equal height is impossible.

Common Pitfalls:
Sometimes students try to fully order every person even when it is not required, which can lead to confusion. Another mistake is misreading phrases like 'shorter than' and reversing the inequality. Drawing arrows or writing a chain like Q > P > R and S > R on paper is a quick and reliable way to avoid such errors and to see immediately who is at the bottom of the chain.

Final Answer:
The shortest among the four friends is R.