What is the number of 360-degree rotations that a bicycle wheel made w...
Statement (1):
The time taken for the bicycle wheel to travel the entire distance is 3 minutes.
We know that the bicycle wheel makes a complete rotation every time it covers a distance equal to its circumference.
Let's assume the circumference of the wheel is C.
Therefore, the distance covered by the wheel in 1 minute is C.
And the distance covered by the wheel in 3 minutes is 3C.
We are given that the wheel covers a distance of 150 meters in 3 minutes.
So, 3C = 150 meters.
From this equation, we can find the value of C (circumference).
Hence, statement (1) alone is sufficient to answer the question.
Statement (2):
The wheel makes twenty 360-degree rotations per minute.
Since the wheel makes 20 rotations per minute, it covers a distance equal to 20 times its circumference in 1 minute.
Therefore, the distance covered by the wheel in 1 minute is 20C.
But we don't know the actual value of C, so we cannot determine the distance covered in 3 minutes.
Hence, statement (2) alone is not sufficient to answer the question.
Statements (1) and (2) together:
From statement (1), we know that the wheel covers a distance of 150 meters in 3 minutes.
From statement (2), we know that the wheel makes twenty 360-degree rotations per minute.
Since the wheel makes 20 rotations per minute, it covers a distance equal to 20 times its circumference in 1 minute.
Therefore, the distance covered by the wheel in 3 minutes is 3 times the distance covered in 1 minute, which is 3 * 20C = 60C.
From statement (1), we know that 60C = 150 meters.
So, we can find the value of C (circumference) and determine the number of rotations.
Hence, both statements together are sufficient to answer the question.
Therefore, the correct answer is option (C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.