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    Question

    In each of the following questions, two statements or three statements are given. You are expected to solve them and determine which statement or combination of statements is sufficient to answer the question.

    A cyclist travels between two cities, A and B and returns back, following a specific path. What is the total time taken by the cyclist to complete the journey?

    Statements:

    I: The cyclist travels from City A to City B at a constant speed of 15 km/h, and the journey covers a distance of 90 km.

    II: After reaching City B, the cyclist takes a 30-minute rest and then returns to City A at 75% of the original speed.

    III: The cyclist faces a wind resistance that reduces the speed by 10% during the last 30 km of the journey to City B.

    A Only Statement I alone is sufficient. Correct Answer Incorrect Answer
    B Only Statement II alone is sufficient. Correct Answer Incorrect Answer
    C Statements I and III together are sufficient. Correct Answer Incorrect Answer
    D Statements I and II together are sufficient. Correct Answer Incorrect Answer
    E None of the statements alone is sufficient. Correct Answer Incorrect Answer

    Solution

    Statement I: This gives us the distance and speed for the journey from A to B, allowing us to calculate the time taken to travel one way. However, we don’t have the total time including the return trip or rest period, so this statement alone is insufficient. Not sufficient. Statement II: This tells us about the return trip and the rest period, but without knowing the speed of the cyclist on the return trip or the distance, this statement alone is insufficient. Not sufficient. Statement III: This modifies the speed during part of the trip but doesn’t provide enough detail about the cyclist’s entire journey. On its own, it’s not sufficient to determine the total time. Not sufficient. Combining Statements I and III: Using the speed and distance from Statement I and adjusting for the wind resistance in Statement III, we can calculate the total time for the journey from A to B. However, we still lack information about the return trip unless we use information from Statement II. Not sufficient. Combining Statements I and II: Using the distance and speed from Statement I and the modified speed and rest period from Statement II, we can calculate the total time for the entire journey. Sufficient. The answer is D .

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