A question is given, followed by two statements labelled I and II. Decide which of the statements is/are sufficient/necessary to answer the question and select the correct answer. Question: Who is the shortest among Shamita, Tanya and Rekha? Statements: I. Shamita is taller than Rekha. Rekha is shorter than Tanya. II. Rekha is shorter than Surbhi. Surbhi is taller than Shamita. Tanya is shorter than Surbhi. (A) Statement I alone is sufficient to answer the question, whereas Statement II alone is not sufficient to answer the question. (B) Statement II alone is sufficient to answer the question, whereas statement I alone is not sufficient to answer the question. (C) Both statements I and II together are not sufficient to answer the question. (D) Both statements I and II together are necessary to answer the question.
A
To determine who is the shortest among Shamita, Tanya, and Rekha, we need to analyze the information given in the statements.
Statement I:
- Shamita is taller than Rekha.
- Rekha is shorter than Tanya.
From Statement I, we can deduce the following order based on height: \(Tanya > Rekha\) and \(Shamita > Rekha\). This means Rekha is shorter than both Shamita and Tanya. Therefore, Rekha is the shortest among the three.
Statement II:
- Rekha is shorter than Surbhi.
- Surbhi is taller than Shamita.
- Tanya is shorter than Surbhi.
From Statement II, we can establish: \(Surbhi > Shamita\), \(Surbhi > Tanya\), and \(Surbhi > Rekha\). However, Statement II does not provide any direct information about how Shamita, Tanya, and Rekha relate to each other in terms of height, except their individual relations with Surbhi.
Conclusion:
Statement I alone is sufficient to determine that Rekha is the shortest among Shamita, Tanya, and Rekha. Statement II, however, does not give enough information to determine the shortest individual among the three.
Thus, the correct answer is (A) Statement I alone is sufficient to answer the question, whereas Statement II alone is not sufficient to answer the question.
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