A is taller than B. B is shorter than C but taller than D. Based on these comparisons of heights, who is the shortest among A, B, C and D?

Introduction / Context:
This question is a straightforward height comparison puzzle. You are given relative height information for four people A, B, C and D, and must determine who is the shortest. These types of questions test your ability to interpret inequalities and arrange individuals in increasing or decreasing order based on given statements, without needing any actual numerical heights.

Given Data / Assumptions:
- A is taller than B. - B is shorter than C. - B is taller than D. - All four individuals have distinct heights. - We are asked to identify the shortest person among A, B, C and D.

Concept / Approach:
The statements can be translated into inequalities that express a strict order. A taller than B means A is above B in height. B shorter than C means C is above B. B taller than D means B is above D. Combining these relations allows us to rank all four people. The shortest person is the one who does not have anyone below them in this ordering. It is helpful to visualise this by placing the names on a vertical line in order of increasing or decreasing height.

Step-by-Step Solution:
Step 1: From A is taller than B, write A > B in terms of height. Step 2: From B is shorter than C, write C > B. Step 3: From B is taller than D, write B > D. Step 4: Combine the inequalities to form a consistent order. We know both A and C are taller than B, and B is taller than D. Therefore, at least we have A > B > D and C > B > D. Step 5: Although we do not know whether A or C is taller than the other, this uncertainty only affects the top of the order, not the bottom. Step 6: D is below B, and B is below both A and C. Hence D has no one shorter than them, making D the shortest person.

Verification / Alternative check:
To verify, assign sample heights that satisfy the inequalities. For example, let D be 150 cm, B be 160 cm, A be 170 cm and C be 175 cm. Then A is indeed taller than B, B is shorter than C, and B is taller than D. In this example, D is clearly the shortest. Even if we swap the heights of A and C while keeping both above B, D will always remain the smallest because D is still below B, and B is below both A and C. This consistency shows that the conclusion about D is reliable.

Why Other Options Are Wrong:
- B is taller than D, so B cannot be the shortest. - C is taller than B, which is itself taller than D, so C is certainly not the shortest. - A is taller than B and thus taller than D as well, so A also cannot be the shortest. - The relationships are sufficient to determine the ordering, so claiming that it cannot be determined is incorrect.

Common Pitfalls:
Learners sometimes attempt to create a full tallest to shortest order before answering, and may get confused by the unknown order between A and C. However, the question only asks for the shortest, so the unresolved comparison between A and C does not matter. Another pitfall is misreading taller and shorter and accidentally reversing the inequalities, which leads to wrong conclusions. Carefully writing each relation in inequality form greatly reduces these errors.

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