UPSC CSE Prelims 2021

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?

EXPLANATION

Correct Option (3)

Both Statement-1 and Statement-2 are required to answer the Question.

To determine the heaviest person among A, B, C, D, and E, both statements must be considered:

From Statement-1: A is heavier than B, E, and F (A > (B, E, F)). Similarly, D is heavier than B, E, and F (D > (B, E, F)). The statement also specifies that neither A nor D is the heaviest among all individuals mentioned (A, B, C, D, E, F). This implies that another individual, specifically C within the context of the question, must be heavier than A and D. However, Statement-1 alone does not explicitly define the weight relationship between C and A or D.
From Statement-2: C is heavier than A, and A is heavier than D (C > A > D). This establishes a clear hierarchical order for C, A, and D.

Combining both statements:

Statement-2 provides the order C > A > D.
Statement-1 indicates that A and D are heavier than B, E, and F.

By integrating these facts, the complete weight hierarchy can be deduced as C > A > D > (B, E, F). When considering only the individuals A, B, C, D, and E as specified in the question, C is definitively established as the heaviest. Therefore, both statements together are necessary and sufficient to answer the question.

Incorrect Options:

Statement-1 alone is insufficient because:

It establishes that A and D are heavier than B, E, and F, and that A and D are not the heaviest. While this suggests C might be the heaviest among the given options (A, B, C, D, E), it does not provide a direct comparison or confirm C's weight relative to A or D. Without this explicit relationship, C's position as the absolute heaviest cannot be confirmed solely from Statement-1.

Statement-2 alone is insufficient because:

It establishes the order C > A > D.
However, Statement-2 provides no information regarding the weights of B or E. Consequently, it is impossible to determine the heaviest person among A, B, C, D, and E using only Statement-2.

Neither Statement-1 alone nor Statement-2 alone is sufficient, as individually they lack the complete information required to establish the definitive heaviest individual among A, B, C, D, and E.