A is taller than B. C is taller than A. D is taller than E but shorter than B. Who is the tallest among A, B, C, D and E?

Introduction / Context:
This height comparison problem is a direct application of inequality reasoning. You are given several relative height statements and are asked to identify the tallest person among five individuals. It teaches you how to combine several pieces of comparative information into a single consistent ordering.

Given Data / Assumptions:

• A is taller than B.
• C is taller than A.
• D is taller than E but shorter than B.
• We have five people in total: A, B, C, D and E.
• No two people are stated to have equal heights.

Concept / Approach:
We translate the verbal comparison statements into inequalities and then build a height order. When we see phrases like C is taller than A and A is taller than B, we can chain them to deduce C is taller than both A and B. With D and E, we only know their positions relative to B and to each other, which lets us place them lower in the overall ordering. The tallest person will be the one who is not shorter than any other individual based on these comparisons.

Step-by-Step Solution:
Step 1: From A is taller than B, we write A > B.Step 2: From C is taller than A, we have C > A.Step 3: Combining these two, C > A > B. Therefore, C is taller than both A and B.Step 4: From D is taller than E but shorter than B, we get D > E and D < B.Step 5: Since B is shorter than A and C, and D is shorter than B, D and E must both be shorter than A and C.Step 6: Overall ordering from tallest to shortest is C, then A, then B, then D, then E.

Verification / Alternative check:
You can test this with sample numerical heights. Let C be 180 cm, A be 175 cm, B be 170 cm, D be 165 cm and E be 160 cm. All conditions are satisfied: C is taller than A, A is taller than B, B is taller than D, and D is taller than E. Among these values, C is clearly the tallest. Any other set of numbers that respects the same relative inequalities will also make C the tallest, which proves that the identity of the tallest person is fixed by the information given.

Why Other Options Are Wrong:
A cannot be tallest because C is explicitly given as taller than A.B cannot be tallest because A is taller than B and C is taller than A.D cannot be tallest because D is shorter than B, who is already shorter than A and C.E cannot be tallest because E is shorter than D, who is in turn shorter than B, A and C.

Common Pitfalls:
A frequent mistake is to focus only on one or two comparisons instead of chaining all of them together. Some students may forget the relationship between D and B and wrongly consider D as a candidate for tallest. Others may misread C is taller than A as A is taller than C. Carefully rewriting each statement as a symbolic inequality and then ordering them from greatest to smallest is the safest method.

Final Answer:
The tallest person among A, B, C, D and E is C.