Data Sufficiency — Ranks in a Class (Total = 25 students) Question: What is Sachin's rank from the top in a class of 25 students? Statements: I. Sachin ranks three positions above Amit, who ranks 18th from the bottom. II. Sachin's rank from the top is two positions below Deepti, who ranks 23rd from the bottom.

Difficulty: Medium

Correct Answer: Either I or II is sufficient

Explanation:


Introduction / Context:
This is a classic Data Sufficiency problem on ranking. We must determine whether the information in the statements is enough to find Sachin's exact rank from the top out of 25 students. We do not need to compute the rank twice if either statement independently gives a unique answer.


Given Data / Assumptions:

  • Total students = 25.
  • From bottom to top conversion: top_rank = total - bottom_rank + 1.
  • “Above” from the top means a smaller (better) top rank number.


Concept / Approach:
Convert any rank given from the bottom into rank from the top, then apply the stated positional gaps. If one statement yields a unique rank for Sachin without using the other, that statement alone is sufficient.


Step-by-Step Solution:

From I: Amit = 18th from bottom → Amit from top = 25 - 18 + 1 = 8. Sachin is three positions above Amit (from top), so Sachin from top = 8 - 3 = 5. Statement I alone gives a unique rank (5th), so I is sufficient. From II: Deepti = 23rd from bottom → Deepti from top = 25 - 23 + 1 = 3. Sachin is two positions below Deepti (from top), so Sachin from top = 3 + 2 = 5. Statement II alone also gives a unique rank (5th), so II is sufficient.


Verification / Alternative check:
Both statements independently produce rank 5 from the top, confirming internal consistency and uniqueness.


Why Other Options Are Wrong:

  • I alone not sufficient / II alone not sufficient: False, each alone gives the exact rank 5.
  • Neither sufficient: False.
  • Both required: Overkill; either one suffices.


Common Pitfalls:
Mixing up “from bottom” conversions or misinterpreting “above/below” in rank order leads to incorrect arithmetic. Always convert bottom ranks to top ranks before applying relative positions.


Final Answer:
Either I or II is sufficient.

More Questions from Data Sufficiency

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion