Question

Among five persons \( D, E, F, G, H \), each having different heights, who is the second tallest? Statements:
I. \( D \) is taller than only \( G \) and \( E \). \( F \) is not the tallest.
II. \( H \) is taller than \( F \). \( G \) is taller than \( E \) but shorter than \( D \).

• A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient.
• B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient.
• C. If the data in Statement I alone or in Statement II alone are sufficient to answer the question.
• D. If the data in both the Statements I and II together are not sufficient.

Hint:

To determine ranking problems, arrange elements in ascending or descending order based on given conditions.

Answer 1

The Correct Option is A

Step 1: Analyzing Statement I.
- \( D \) is taller than only \( G \) and \( E \), meaning \( G \) and \( E \) are the shortest.
- So, the height order of these three is: \[ E<G<D \] - Since there are five persons, the remaining two must be \( F \) and \( H \).
- \( F \) is not the tallest, which means \( H \) must be the tallest.
- Therefore, the order from shortest to tallest is: \[ E<G<D<F<H \] - The second tallest person is \( F \).
- Thus, Statement I alone is sufficient to determine the second tallest person.
Step 2: Analyzing Statement II.
- \( H \) is taller than \( F \), so \( H \) is not the second tallest.
- \( G \) is taller than \( E \) but shorter than \( D \), so \( G \) is not the second tallest either.
- Since no information is given about whether \( F \) is taller than \( D \), we cannot determine the second tallest person.
- Statement II alone is insufficient to answer the question.
Step 3: Conclusion.
- Statement I alone is sufficient, but Statement II alone is not sufficient.
- Thus, the correct answer is (A).