Three Statements S1, S2 and S3 are given below followed by a Question: S1: C is younger than D, but older than A and B. S2: D is the oldest. S3: A is older than B. Question: Who among A, B, C and D is the youngest? Which one of the following is correct in respect of the above Statements and the Question?
- AS1 alone is sufficient to answer the Question
- BS1 and S2 together are sufficient to answer the Question
- CS2 and S3 together are sufficient to answer the Question
- DS1 and S3 together are sufficient to answer the Question.Correct
Explanation
Let's analyze the statements and the question:
S1: C is younger than D, but older than A and B. This can be written as: D > C > A and D > C > B. From S1 alone, we know D is the oldest (or among the oldest) and C is older than A and B. However, we don't know the relative age of A and B. So, the youngest could be A or B. S1 alone is not sufficient.
S2: D is the oldest. This means D > A, D > B, D > C. S2 alone doesn't give us any information about the relative ages of A, B, and C. So, S2 alone is not sufficient.
S3: A is older than B. This means A > B. S3 alone only tells us about A and B, not C or D. So, S3 alone is not sufficient.
Now let's evaluate the options:
A) S1 alone is sufficient to answer the Question As explained above, S1 (D > C > A and D > C > B) doesn't tell us whether A or B is younger. So, A is incorrect.
B) S1 and S2 together are sufficient to answer the Question S1: D > C > A and D > C > B S2: D is the oldest (confirms D is the oldest, but doesn't resolve A vs B) Combining S1 and S2 still leaves the ambiguity between A and B as the youngest. So, B is incorrect.
C) S2 and S3 together are sufficient to answer the Question S2: D is the oldest. S3: A > B. These statements tell us D is the oldest and A is older than B, but they don't provide any information about C's age relative to A or B. C could be older than A, younger than B, or in between. So, C is incorrect.
D) S1 and S3 together are sufficient to answer the Question. S1: D > C > A and D > C > B S3: A > B
Let's combine these: From S1, we know C is older than A (C > A). From S1, we know C is older than B (C > B). From S3, we know A is older than B (A > B).
Putting these together in order from oldest to youngest: We have D > C (from S1). We have C > A (from S1). We have A > B (from S3).
Therefore, the complete order is D > C > A > B. From this combined order, B is clearly the youngest. Thus, S1 and S3 together are sufficient to answer the question.
The final answer is D

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