Difficulty: Hard
Correct Answer: The data in both statements I and II together are sufficient to answer the question, but the data in either statement alone are not sufficient.
Explanation:
Introduction / Context:
This problem is a data sufficiency question involving relative heights of six people: Akhilesh, Bhavesh, Cindy, Divakar, Erika, and Farheen. You must decide which statements give enough information to uniquely identify the tallest person. Importantly, the task is not to find the exact order in every case but to judge whether the information guarantees a single tallest person. This type of question evaluates your skill in combining rank information from different clues.
Given Data / Assumptions:
Concept / Approach:
In data sufficiency, we consider each statement alone and then both together. A statement is sufficient if it leads to a unique answer in every possible arrangement satisfying that statement. When combining statements, we merge all the given constraints and see whether the added information removes any ambiguity that existed when using each statement individually. Ranking style clues often translate into fixed positions like “third tallest” or “second shortest”, which help pin down individuals in the order.
Step-by-Step Solution:
Step 1: Analyze Statement I alone. If only two persons are taller than Bhavesh among six people, Bhavesh must be the third tallest. If only one person is shorter than Erika, Erika must be the second shortest, that is, fifth in height order.
Step 2: From Statement I, we also know Akhilesh is taller than Cindy but not the tallest. However, Divakar and Farheen are not linked to these fixed positions. Therefore, with Statement I alone, we know:
There are still multiple possibilities for who is tallest (it could be Divakar or Farheen, or possibly someone else depending on arrangements), so Statement I alone is not sufficient.
Step 3: Consider Statement II alone. From it we have:
This gives a chain: Farheen > Divakar > Akhilesh > Cindy, and Bhavesh is above Akhilesh but below some unknown. Erika is not mentioned at all. There is still uncertainty about who is tallest because it could be Farheen or possibly another person depending on Erika's position. Hence Statement II alone is also not sufficient.
Step 4: Now combine Statements I and II. From Statement I we know Bhavesh is third tallest and Erika is fifth tallest. From Statement II we have the chain Farheen > Divakar > Akhilesh > Cindy and Bhavesh > Akhilesh.
Step 5: Use the fixed ranks to place everyone. Since Bhavesh is third tallest, there must be exactly two people taller than him and three shorter. Erika, being fifth tallest, is the second shortest, meaning only one person is shorter than her. Let us number positions from 1 (tallest) to 6 (shortest):
Step 6: Since Erika is fifth, only one person can be below her, so Cindy must be sixth (shortest). From Statement II, Akhilesh is taller than Cindy and shorter than Bhavesh. With Bhavesh fixed at 3, Akhilesh cannot be 1 or 2 (that would make him taller than Bhavesh) and cannot be 5 or 6 (because he is taller than Cindy and Erika is already at 5). Thus Akhilesh must be at position 4.
Step 7: So far we have:
The remaining positions 1 and 2 must be occupied by Divakar and Farheen.
Step 8: From Statement II, Farheen is taller than Divakar. Therefore Farheen must be in position 1 and Divakar in position 2. Thus, the tallest person is uniquely determined to be Farheen when both statements are used together.
Verification / Alternative check:
You can try to rearrange the six people while keeping all statements true and the rank positions fixed. You will see that the only way to satisfy all conditions is with Farheen as the tallest. Any attempt to place someone else at the top will violate at least one part of the combined clues. However, each statement taken individually leaves room for multiple tallest candidates, confirming that only the combination is sufficient.
Why Other Options Are Wrong:
Option a: Statement I alone is not sufficient, as it leaves the top two positions ambiguous.
Option b: Statement II alone is not sufficient, as Erika's height is unknown and the tallest could be Farheen or someone else.
Option d: Saying that both together are not sufficient is incorrect because together they uniquely identify Farheen as tallest.
Option e: Either statement alone being sufficient is clearly false based on the analysis above.
Common Pitfalls:
A common mistake is to misinterpret “only two persons are taller than Bhavesh” or “only one person is shorter than Erika” and not convert them into exact rank positions. Another frequent error is failing to merge the two statements properly, for example by not noticing that who is third tallest in one statement must still align with the chain of comparisons in the other. Always write down approximate rankings and adjust step by step until the order is consistent.
Final Answer:
The data in both statements I and II together are sufficient to answer the question, but the data in either statement alone are not sufficient.
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