Pankaj is taller than Vinod, and Vinod is shorter than Pramod. Usha is taller than Priyanka but shorter than Vinod. Pramod is shorter than Pankaj. Based on these comparisons of height among the five friends, who is the tallest?

Introduction / Context:
Ranking people by height based on a series of pairwise comparisons is a very common type of analytical reasoning question. The aim is to translate verbal statements into an ordered list and then answer a question such as who is tallest or who is shortest. Here we need to find the tallest person among five friends: Pankaj, Vinod, Pramod, Usha and Priyanka.

Given Data / Assumptions:

• Pankaj is taller than Vinod.
• Vinod is shorter than Pramod.
• Usha is taller than Priyanka but shorter than Vinod.
• Pramod is shorter than Pankaj.
• No two people are of exactly the same height.

Concept / Approach:
We need to convert the relational statements into inequalities and then chain them together to form a complete ordering. Using symbols like greater than for taller and less than for shorter, we can represent the relations numerically and then find the maximum element in that order. This is essentially a problem of arranging items based on comparative information.

Step-by-Step Solution:
Step 1: From 'Pankaj is taller than Vinod', we write Pankaj > Vinod. Step 2: From 'Vinod is shorter than Pramod', we write Pramod > Vinod. Step 3: From 'Pramod is shorter than Pankaj', we write Pankaj > Pramod. Step 4: Combine these to get Pankaj > Pramod > Vinod. Step 5: From 'Usha is taller than Priyanka but shorter than Vinod', we get Vinod > Usha > Priyanka. Step 6: Combine everything to get a complete order from tallest to shortest: Pankaj > Pramod > Vinod > Usha > Priyanka. Step 7: The tallest person is therefore the first in this chain, Pankaj.

Verification / Alternative check:
We can check the order against each sentence. Pankaj > Vinod is satisfied. Pramod is between Pankaj and Vinod, so Pramod > Vinod holds and Pankaj > Pramod also holds. Vinod > Usha > Priyanka follows the last information. All original statements fit the order Pankaj, Pramod, Vinod, Usha, Priyanka without contradiction, confirming that Pankaj is indeed tallest.

Why Other Options Are Wrong:

• Pramod: Pramod is shorter than Pankaj, so he cannot be the tallest.
• Vinod: Both Pankaj and Pramod are taller than Vinod, so this is not correct.
• Usha: Usha is shorter than Vinod and therefore also shorter than Pankaj and Pramod.
• Priyanka: She is the shortest, since Usha is taller than Priyanka and all others are taller than Usha.

Common Pitfalls:
A common mistake is to miss one of the comparisons or to fail to combine them correctly, which can lead to an incorrect ranking. Another pitfall is to assume transitive relations without writing them out clearly. Drawing a simple vertical list or using inequality symbols to show taller and shorter relationships is a reliable method to avoid confusion.

Final Answer:
The tallest among the five friends is Pankaj.