If A is taller than B, B is shorter than C and D is shorter than A, then which of the following statements is definitely true about their heights?

Introduction / Context:
This is a verbal reasoning problem based on comparison of heights. The question checks your ability to interpret inequality statements like A is taller than B and combine them logically to identify which conclusion must always hold, regardless of the exact heights. Such problems are extremely common in reasoning sections of competitive exams because they test pure logical consistency rather than calculation.

Given Data / Assumptions:

• A is taller than B.
• B is shorter than C, which also means C is taller than B.
• D is shorter than A.
• No information is given about the direct comparison of C with A or D, and no equal heights are explicitly mentioned.

Concept / Approach:
The approach is to rewrite each statement as a clear inequality and then see what relationships are guaranteed. We can write A taller than B as A greater than B. B shorter than C becomes B less than C. D shorter than A becomes D less than A. The task is to see which of the options is implied by these three inequalities in every possible arrangement that respects them. If an option could be false in some valid arrangement, it is not definitely true.

Step-by-Step Solution:
Step 1: Translate statements: A taller than B means A > B. B shorter than C means B < C. D shorter than A means D < A.Step 2: From A > B we know A is taller than B in every valid arrangement.Step 3: From D < A we know A is taller than D in every valid arrangement.Step 4: Therefore, A is taller than both B and D, so the statement A is taller than both B and D must always be true.Step 5: Examine A and C. Since we only know B < C and A > B, it is possible that C is taller than A or A is taller than C. Both scenarios can satisfy all the given inequalities, so no fixed relation between A and C is guaranteed.Step 6: There is no information linking D directly to C or B besides the relation through A, so conclusions involving D compared directly with B or C may not always hold.

Verification / Alternative check:
You can test with specific numerical heights. Take B = 150 cm, A = 160 cm, C = 170 cm, D = 155 cm. Here A is taller than B and D, and B is shorter than C. Now choose another valid arrangement: B = 150 cm, A = 160 cm, C = 155 cm, D = 140 cm. In both cases A is still taller than B and D, but in the first case C is taller than A, and in the second case A is taller than C. This confirms that A greater than B and D is fixed, while relations involving C can change.

Why Other Options Are Wrong:
D is taller than C is not guaranteed; we can pick C as very tall and D as quite short.A and C are of equal height is never stated and cannot be concluded.D is shorter than B is not forced, because D could be between A and B in height while still being shorter than A.C shorter than A is not guaranteed, because C can be chosen taller than A while still satisfying the conditions.

Common Pitfalls:
A typical mistake is to assume transitivity inappropriately, for example concluding that since B is between A and C in some imagined order, A and C must have a specific relation. Another error is to think that missing comparisons, such as between C and A, always follow a particular pattern, even when they are not constrained by the conditions. To avoid these issues, work with actual example values that satisfy the conditions and see which options always remain true.

Final Answer:
The statement that is definitely and always true is A is taller than both B and D.