OGQR 2020: Question No. 212
P is a particle on the circle shown above. What is the length of the path traveled by P in one complete revolution around the circle?
- The diameter of the circle is 1.5 meters.
- The particle P moves in a clockwise direction at 0.5 meter per second.
| Source | OGQR 2020 |
| Type | Data Sufficiency |
| Topic | Geometry/Word Problems |
| Sub-Topic | Circle/Distance |
| Difficulty | Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
We are given:
- P is a particle on the circle, as shown in the given diagram.
We need to find the length of the path travelled by P in one complete revolution around the circle.
- In one complete revolution, P will cover the entire length of the circle.
- For any circle, its entire length is equal to the perimeter of the circle which is equal to 2πr.
- Thus, we need to find r to find the length of the path travelled by P in one complete revolution around the circle.
With this understanding, let us analyse the statements.
Step 3: Analyse Statement 1
“The diameter of the circle is 1.5 meters.”
- Diameter = 2 × radius
Hence, we can find the radius from this statement.
Thus, statement 1 is sufficient to answer the question.
Step 4: Analyse Statement 2
“The particle P moves in a clockwise direction at 0.5 meter per second.”
We know that Distance covered = time × speed
- Here, Speed = 0.5 m/s.
- However, we do not know in how much time P can complete one revolution of the circle.
Hence, we cannot find the length of the path traveled by P in one complete revolution around the circle.
Thus, statement 2 is not sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we could determine the answer from statement 1 individually, this step is not required.
Hence, the correct answer is option A.
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