Is Arun taller than Sachin? Statement I: Dinesh is of the same height as both Arun and Sachin. Statement II: Sachin is not shorter than Dinesh.

Introduction / Context:
This data sufficiency question asks a yes or no question: Is Arun taller than Sachin? Two statements give information about heights involving a third person, Dinesh. The goal is to see whether either statement alone, or both together, allow us to answer definitively whether Arun is taller than Sachin, shorter than Sachin, or equal in height, and thus to answer the yes or no question.

Given Data / Assumptions:
- Question: Is Arun taller than Sachin?
- Statement I: Dinesh is of the same height as Arun and Sachin.
- Statement II: Sachin is not shorter than Dinesh.
- All height comparisons are exact; there are no rounding issues.

Concept / Approach:
In data sufficiency, for a yes or no question, information is sufficient if it allows us to answer definitively yes or definitely no. If Arun and Sachin are found to be of equal height, the answer to "Is Arun taller than Sachin?" is a definite "no", which counts as sufficient. We must analyze each statement separately, then consider them together if needed, while resisting the temptation to combine them prematurely.

Step-by-Step Solution:
Step 1: Interpret statement I. It says that Dinesh is of the same height as Arun and Sachin. This implies Arun, Sachin and Dinesh are all of equal height. Step 2: If Arun and Sachin are of equal height, then Arun is not taller than Sachin. The answer to the question "Is Arun taller than Sachin?" is a definite "no". Step 3: Because statement I alone leads to a clear and unique answer, it is sufficient to answer the question. Step 4: Now analyze statement II alone. It says Sachin is not shorter than Dinesh, which means Sachin is either taller than or equal in height to Dinesh. Step 5: Statement II alone does not provide any comparison between Arun and Dinesh, and therefore no direct comparison between Arun and Sachin. Arun could be taller than Dinesh, equal to Dinesh, or shorter than Dinesh. Accordingly, Sachin could still be taller than, equal to, or shorter than Arun. Therefore, statement II alone is not sufficient to answer the question. Step 6: Since statement I alone is sufficient and statement II alone is not, there is no need to consider both together for sufficiency.

Verification / Alternative check:
To double check, imagine the height values. From statement I, let Dinesh, Arun, and Sachin each have height h. Then Arun is clearly not taller than Sachin; they are equal. Any value of h works, and the equality remains. Statement II alone allows multiple possibilities, such as Dinesh having height h, Sachin having height h, but Arun having any height greater or smaller than h, so we cannot resolve the question from II alone.

Why Other Options Are Wrong:
- Option b is wrong because statement II alone does not identify whether Arun is taller than Sachin or not.
- Option c is incorrect because only statement I alone is sufficient; statement II alone is not.
- Option d is wrong because both statements together are not needed; I alone suffices.
- Option e is wrong because the data are not insufficient; the first statement clearly answers the question.

Common Pitfalls:
Students sometimes forget that equality provides a definitive "no" answer to a "taller than" question. Another pitfall is misreading "not shorter" as "strictly taller", while it actually means "greater than or equal to". Also, some may try to combine both statements automatically without first checking sufficiency of each statement on its own, which is contrary to the standard data sufficiency procedure.

Final Answer:
Statement I alone is sufficient to answer the question with a definite "no", while statement II alone is not sufficient. Therefore, the correct data sufficiency choice is option A.