What is Reena's rank in the class? Statement I: There are 26 students in the class. Statement II: There are 9 students who have scored less than Reena.

Difficulty: Medium

Correct Answer: If the data in both statements I and II together are needed to answer the question.

Explanation:


Introduction / Context:
This is a ranking based data sufficiency question. You are asked to determine Reena's rank in a class, which means identifying her exact position among all students, usually counted from the top. Two statements provide partial information about the total number of students and the number of students who scored less than Reena. Your goal is to decide which combination of these statements, if any, is enough to determine Reena's exact rank.


Given Data / Assumptions:
- The question: What is Reena's rank in the class?
- Statement I: There are 26 students in the class.
- Statement II: There are 9 students who have scored less than Reena.
- All students are assumed to have distinct scores for a unique ranking unless otherwise mentioned.
- Rank is interpreted in the usual way as the position counted from the top (best performer has rank 1).


Concept / Approach:
For ranking problems, the position of a student from the top can be derived if we know both the total number of students and the number of students below that student. Specifically, if there are N students in total and k students with lower scores, then the rank from the top is N - k. In data sufficiency, we first determine what can be derived using statement I alone, then statement II alone, and finally both together.


Step-by-Step Solution:
Step 1: Use statement I alone. It tells us there are 26 students in the class. However, this gives no information about where Reena stands among them. Her rank could be anywhere from 1 to 26. Therefore, statement I alone is not sufficient. Step 2: Use statement II alone. It states that 9 students scored less than Reena. While this tells us her position from the bottom (10th from the bottom), we do not know how many students are in the class, so we cannot convert this into a rank from the top. Therefore, statement II alone is also not sufficient. Step 3: Now combine statements I and II. From statement I, total students N = 26. From statement II, the number of students scoring less than Reena is 9. Step 4: Reena is therefore ahead of those 9 students. The number of students who scored greater than or equal to Reena is 26 - 9 = 17. Since all ranks are distinct, Reena must be 17th from the top. Step 5: Thus, with both statements together, we can uniquely determine Reena's rank as 17.


Verification / Alternative check:
We can verify by imagining the class list. If there are 26 students and exactly 9 of them scored less than Reena, there are 16 students with scores greater than or equal to hers, including Reena herself. That places her at position 17 from the top. There is no other possible rank consistent with both a fixed total and a fixed number below her. Therefore the combination of I and II is sufficient, and neither statement alone is enough.


Why Other Options Are Wrong:
- Option a is wrong because statement I alone leaves Reena's position completely undetermined.
- Option b is wrong because statement II alone only provides a partial rank from the bottom and cannot be translated into a top rank without knowing the total class size.
- Option c is incorrect, as neither statement alone can answer the question; both are needed together.
- Option e is wrong because we have seen that the two statements together are indeed sufficient to find Reena's rank.


Common Pitfalls:
Students often misinterpret rank information, confusing rank from the top with rank from the bottom. Another common mistake is to assume a total class size based on typical examples instead of using the value given in the statement. In data sufficiency problems, it is crucial to separate the analysis of each statement and not assume extra data that has not been explicitly provided.


Final Answer:
Both statements I and II together are needed to determine that Reena is 17th in the class. Therefore, the correct data sufficiency choice is option D.

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