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 carefully and decide the appropriate answer.
Among 5 people, A, B, C, D and E, each of a different height, who is the second-tallest?
I: E is shorter than A. B is taller than D but shorter than E.
II: Only C is taller than A. D is shorter than E.
Correct Answer :
The data in statement II alone is sufficient to answer the question while data in statement I is not
Solution :
The correct answer is: The data in statement II alone is sufficient to answer the question while data in statement I is not.
Goal: We need to determine who is the second-tallest person among 5 people: A, B, C, D, and E, each having a distinct height.
Let us order the positions from 1st (tallest) to 5th (shortest):
1st (Tallest) > 2nd > 3rd > 4th > 5th (Shortest)
Evaluating Statement I:
Statement I tells us:
1. E is shorter than A (A > E).
2. B is taller than D but shorter than E (E > B > D).
Combining these conditions, we get the partial height order:
A > E > B > D
However, Statement I gives no information about the position of C. C could be taller than A, between A and E, or anywhere else. Therefore, we cannot uniquely identify who the second-tallest person is.
Thus, Statement I alone is NOT sufficient.
Evaluating Statement II:
Statement II tells us:
1. "Only C is taller than A."
This statement explicitly implies that C is the tallest person of all 5 people (1st position), and A is shorter than C but taller than everyone else. This means A MUST be in the 2nd position (the second-tallest).
2. "D is shorter than E" gives extra height information about D and E, but it is not needed to answer the question since the 2nd position is already uniquely determined.
From Statement II, the ordering starts as:
C (1st) > A (2nd) > ...
Since A is definitely the second-tallest person, Statement II alone IS sufficient to answer the question.
Conclusion:
The data in statement II alone is sufficient to answer the question, while the data in statement I is not.
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