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Passage: The ratio of the time taken by pipe B to fill the same tank is 3:4 respectively. Pipe A takes t hours to fill the tank and pipe C takes (t + 4) hours to completely empty the same tank. If all three pipes are opened together at 10 a.m., the tank gets filled at 5 p.m. For how many hours was pipe C opened during the process, if it is known that pipe C was closed in between the given duration? (I) Pipe A and pipe C together can fill \(\tfrac{7}{10}\) of the tank in 28 hours. (II) Pipe A and pipe B together can fill \(\tfrac{7}{8}\) of the tank in 3 hours. Question: Decide whether the data provided in the statements are sufficient to answer the question.

1. The data in statement I alone is sufficient to answer, while the data in statement II alone is not sufficient to answer the question.
2. The data in statement II alone is sufficient to answer, while the data in statement I alone is not sufficient to answer the question.
3. The data either in statement I alone or in statement II alone are sufficient to answer the question.
4. The data given in both statements I and II together are not sufficient to answer the question.

Correct answer: The data either in statement I alone or in statement II alone are sufficient to answer the question.

Solution

Statement I gives a direct relation between A and C, and with the given ratio information it is enough to determine the rates. Statement II also gives a direct relation between A and B, which again can be used with the given ratio to determine the needed values. Therefore, either statement alone is sufficient.

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