Among five friends - Jatin, Kalu, Lucky, Manish and Naresh each of a different…
2023
Among five friends - Jatin, Kalu, Lucky, Manish and Naresh each of a different height, who is the second tallest?
(I) Naresh is taller than Manish and Kalu. Kalu is shorter than Manish.
(II) Lucky is taller than Naresh. Jatin is not the tallest.
- A.
Statement I alone is sufficient to answer the question, while Statement II alone is not sufficient to answer the question
- B.
Statement II alone is sufficient to answer the question, while Statement I alone is not sufficient to answer the question
- C.
If the data either in Statement I alone or Statement II alone is sufficient to answer the question
- D.
Both Statement I and Statement II together are not sufficient to answer the question
Attempted by 2 students.
Show answer & explanation
Correct answer: D
In a Data Sufficiency question, a statement (or a combination of statements) is sufficient only when it fixes the quantity being asked - here, the identity of the second-tallest friend - to exactly one possible value. If more than one arrangement of heights remains consistent with the given facts, that statement (or combination) is not sufficient, even if it narrows things down considerably.
From Statement I alone: Naresh is taller than Manish, and Manish is taller than Kalu, giving Naresh > Manish > Kalu. Lucky's and Jatin's heights are not mentioned, so the second-tallest friend among all five cannot be fixed - Statement I alone is not sufficient.
From Statement II alone: Lucky is taller than Naresh, and Jatin is not the tallest. Manish's and Kalu's positions relative to Lucky, Naresh, and Jatin are not given, so the second-tallest friend cannot be fixed - Statement II alone is not sufficient.
Combining both statements: Statement I gives Naresh > Manish > Kalu, and Statement II adds Lucky > Naresh, so Lucky > Naresh > Manish > Kalu is fixed for four of the five friends. Since Jatin is not the tallest and Lucky already tops the other four, Lucky must be the overall tallest - but Statement II only rules Jatin out of the top rank; it does not fix which of the remaining four slots Jatin occupies.
Because Jatin could sit anywhere from just below Lucky down to the very bottom, the identity of the second-tallest friend changes across these valid arrangements, so even the two statements together are not sufficient.
Cross-check with two arrangements that both satisfy Statement I and Statement II: Lucky > Jatin > Naresh > Manish > Kalu makes Jatin the second tallest, while Lucky > Naresh > Jatin > Manish > Kalu makes Naresh the second tallest. Since both arrangements are equally valid under the combined data but give different second-tallest friends, the combined statements cannot uniquely answer the question.
Hence, both Statement I and Statement II together are not sufficient to answer the question.