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A question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and select the most appropriate answer. Question: Five boxes, V, W, X, Y and Z, have different weights. Which box among them is the second heaviest? Statements: (I) Y is heavier than W. Only three boxes are lighter than Z. (II) X is heavier than W. X is heavier than V.
Data in statement II alone is sufficient to answer the question while data in statement I is not.
Data in statements I and II together are sufficient to answer the question.
Data in statement I alone is sufficient to answer the question while data in statement II is not.
Data in statements I and II together are not sufficient to answer the question.
Data in statement I alone is sufficient to answer the question while data in statement II is not.
Look for the positional constraint: 'Only three boxes are lighter than Z' explicitly identifies Z as the 4th heaviest (or 2nd lightest).
Look for the positional constraint: 'Only three boxes are lighter than Z' explicitly identifies Z as the 4th heaviest (or 2nd lightest).
Analyze Statement I
Statement I says 'Y is heavier than W' and 'Only three boxes are lighter than Z'. If 3 are lighter than Z, then Z is the 4th heaviest (or 2nd lightest). This fixes Z's position at rank 4.
Analyze Statement II
Statement II says 'X > W' and 'X > V'. This only provides relative comparisons between three boxes but gives no information about the total weight hierarchy or the position of Z or Y.
Evaluate Sufficiency
Statement I provides a fixed position for Z (rank 4) and a relative order for Y and W. Combined with the total of 5 boxes, this allows for determining the weight hierarchy relative to the second heaviest position.
A: Statement II is insufficient as it lacks fixed positions. B: Both are not needed because I alone fixes Z and provides constraints. D: Statement I alone is sufficient, making D incorrect.
C is correct because Statement I alone allows us to fix Z as the 4th heaviest and establishes a weight hierarchy that is sufficient to determine the second heaviest box.
In ranking-based data sufficiency questions, always check if a statement provides an absolute anchor (like 'Z is 4th') as it is more valuable than relative comparison statements.
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