Multiple choice

The following questions are accompanied by three statements (A) or (I), (B) or (II), and (C) or (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. Q. What is the speed of a train? I. The train crosses a signal pole in 18 secs. II. The train crosses a platform of equal length in 36 secs. III. Length of the train is 330 metres.

  1. I and III only

  2. II and III only

  3. I and II only

  4. III and either I or II only

  5. Any two of the three
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed = Distance / Time. Statement III gives the length of the train (Distance). Either I or II provides the time required to cover a distance related to the train's length. With III and I, we get speed = 330m / 18s. With III and II, we get speed = (330m + 330m) / 36s. Thus, III and either I or II is sufficient.

AI explanation

To find the speed of the train, the formula is speed equals distance divided by time. If we use statement III, we have the train's length as 330 meters. Using statement I, the train crosses a pole in 18 seconds, meaning it covers its own length of 330 meters in 18 seconds, allowing us to calculate the exact speed. Alternatively, using statement II with statement III, the train crosses a platform of equal length, meaning it covers a total distance of 330 plus 330, or 660 meters, in 36 seconds, which also allows us to calculate the exact speed. However, statements I and II together without III only provide times without any actual length, making it impossible to find the speed. Therefore, statement III and either statement I or II are necessary and sufficient.

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