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.
Second-Tallest Person: Data Sufficiency Analysis
The problem requires determining the second-tallest person among five individuals (A, B, C, D, E) with different heights. We must evaluate the sufficiency of data provided in two statements.
Statement I Analysis: Partial Height Ordering
Statement I provides the following height relationships:
- E is shorter than A: $E < A$
- B is taller than D but shorter than E: $D < B < E$
Combining these inequalities yields a partial order: $D < B < E < A$. This establishes the relative heights of A, B, D, and E, indicating A is the tallest among this group. However, the position of person C is not specified in relation to A, B, D, or E. C could be taller than A, or shorter than A. Without definitive information on C's position relative to A, we cannot determine the overall second-tallest person.
Conclusion for Statement I: Insufficient.
Statement II Analysis: Determining Tallest and Second-Tallest
Statement II provides two pieces of information:
- "Only C is taller than A": This crucial phrase implies that the set of individuals taller than A consists solely of C. Given that all individuals have different heights, this means C is the tallest person overall, and A is the second-tallest person overall. The relationships derived are $C > A$, and $A$ is taller than all others ($B, D, E$).
- "D is shorter than E": This is stated as $D < E$. This fact helps to order the individuals shorter than A ($B, D, E$), but it does not alter the determination that C is the tallest and A is the second-tallest.
The ordering is established as C (tallest) > A (second-tallest) > {B, D, E in an order where $D < E$}.
Conclusion for Statement II: Sufficient.
Overall Conclusion on Data Sufficiency
Since Statement II alone provides enough information to identify the second-tallest person (A), while Statement I alone does not, the data in Statement II alone is sufficient.
Important Questions from Data Sufficiency
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Statement 2: Ena is 2 ranks above Seema and is 37" from the bottom.
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Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question:
Statement 1: Each of A and D is heavier than each of B, E and F, but none of them is the-heaviest.
Statement 2: A is heavier than D, but is lighter than C.
Question: Who is the heaviest among A,B,C, D and E?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question :
Statement-1 : The last day of the month is a Wednesday.
Statement-2 : The third Saturday of the month was the seventeenth day.
Question : What day is the fourteenth of the given month ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider the Question and two Statements given below :
Question : Is xan integer?
Statement-1 : x / 3 is not an integer.
Statement-2 : 3 xis an integer.
Which one of the following is correct in respect of the Question and the Statements?
Consider the Question and two Statements given below:
Question : What is the age of Manisha?
Statement-1: Manisha is 24 years younger than her mother.
Statement-2 : 5 years later, the ages of Manisha and her mother will be in the ratio 3 : 5.
Which one of the following is correct in respect of the Question and the Statements?
