Introduction / Context:
This is a classic data sufficiency problem from verbal reasoning and aptitude. You are not asked to compute the numerical answer directly at first; instead, you must judge whether the given statements provide enough information to determine Gowtham's rank from the last. Understanding how to relate ranks from the top and from the bottom is the key idea here.
Given Data / Assumptions:
- Gowtham ranks 18th from the top in his class.
- Statement I: There are 47 students in the class.
- Statement II: Jagan ranks 10th from the top and 38th from the last in the same class.
- All ranks are unique and there are no ties.
Concept / Approach:
When a student is r-th from the top in a class of N students, the rank from the bottom is given by:
rank from last = N - r + 1
In data sufficiency questions, we check each statement alone and then together, deciding if they are individually or jointly sufficient to obtain Gowtham's rank from the last.
Step-by-Step Solution:
Step 1: Using Statement I alone: total students N = 47, Gowtham's rank from top r = 18.
Step 2: Apply the formula: rank from last = 47 - 18 + 1 = 30.
Step 3: Therefore, Statement I alone is sufficient to find Gowtham's rank from the bottom.
Step 4: Now test Statement II alone. Jagan is 10th from the top and 38th from the last.
Step 5: For Jagan, total students N = 10 + 38 - 1 = 47. This gives the total class strength again.
Step 6: We still have the information from the question stem that Gowtham is 18th from the top, and we now know N = 47 from Statement II.
Step 7: Using the same formula, rank from last for Gowtham = 47 - 18 + 1 = 30.
Step 8: Thus Statement II alone is also sufficient to give the required rank from the last.
Verification / Alternative check:
We can confirm that both statements independently fix the total number of students as 47. Once N is known, the conversion between top rank and bottom rank is straightforward and unique, so there is no ambiguity about Gowtham's rank from the last.
Why Other Options Are Wrong:
Statement I alone is sufficient: This is true, but the option ignores the fact that Statement II alone is also sufficient, so it is incomplete.
Both the statements together are needed: This is incorrect because each statement independently gives N = 47, so they are not required together.
Statement II alone is sufficient: This is again partially correct but fails to recognize that Statement I alone is also sufficient.
Neither I nor II is sufficient: Clearly wrong because each statement leads to a definite answer.
Common Pitfalls:
Students often think they must use both statements simply because both are provided. In data sufficiency questions, you must test each statement separately before considering them together. Another mistake is forgetting the formula linking top and bottom ranks, which can lead to arithmetic errors or the belief that the information is insufficient when it actually is enough.
Final Answer:
Therefore,
either Statement I or Statement II alone is sufficient to determine Gowtham's rank from the last.
Discussion & Comments