## 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__

__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__

__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__

__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)__

__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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