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Sub 505 Level|   Geometry|               
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Bunuel

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?

(1) The diameter of the circle is 1.5 meters.
(2) The particle P moves in a clockwise direction at 0.5 meter per second.



DS02602.01
Quantitative Review 2020 NEW QUESTION


Attachment:
2019-04-26_1826.png

distance travelled = 2*pi*r
#1
d=1.5
so
2*pi*1.5/2 ; 1.5*r
sufficient
#2 The particle P moves in a clockwise direction at 0.5 meter per second.


not sufficient we do not know radius
IMO A
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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.
      o 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 path travelled 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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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?

Rephrased: What is the circumference of the circle shown?

(1) The diameter of the circle is 1.5 meters.

Given the diameter, we can find the circumference. SUFFICIENT.

(2) The particle P moves in a clockwise direction at 0.5 meter per second.

Rate is irrelevant; INSUFFICIENT.

Answer is A.
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Bunuel

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?

(1) The diameter of the circle is 1.5 meters.
(2) The particle P moves in a clockwise direction at 0.5 meter per second.


The Particle will travel as long as the perimeter of the circle \(= 2\pi r\)

(1) We can calculate the \(= 2\pi r\) as diameter is given. Sufficient.

(2) If was given then we could calculate the distance. Insufficient.

The answer is A.
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