If a point is arbitrarily selected inside a circle of radius R, what i

Question

If a point is arbitrarily selected inside a circle of radius R, what is the probability that the distance from this point to the center of the circle will be greater than R/2 ?

A. 1/2
B. 3/4
C. 7/8
D. 1/4*R^2
E. 3/4*R^2

firas92 · Accepted Answer

Any point within the yellow region shown below will be at a distance greater than R/2 from the centre.

Therefore the question basically asks, what is the probability that the selected point lies within the yellow region.

Probability = \frac{Required Area}{Total Area}

Probability = π(R^2-(R/2)^2)/π*R^2 = 1-(1/4)/1 = 3/4

Answer is  (B)

Archit3110 · Answer

let radius of R = 2 so R/2 = 1 area outside R/2 would be = 4pi-pi= 3pi 
and total area = 4pi
so point from center of circle P = 3pi/4pi = 3/4
IMO B

ScottTargetTestPrep · Answer

/(πR^2)

3/4

Alternate Solution:

Let’s assume that the radius of the circle is 2. This problem can be approached by considering the entire circle (with area of 4π) and then drawing a concentric circle whose radius is half that of the bigger circle (so radius = 1). The area of this smaller circle is π. Any point inside this smaller circle will be less than 1 unit from the center of the circle, and the probability of a point being in this smaller circle will be π/4π = 1/4. Thus, any point outside the smaller circle (but inside the larger circle) will satisfy the requirement of being more than 1 unit from the center of the circle, and its probability will be 1 - ¼ = ¾.

Answer: B

Sujithz001 · Answer

Hey  Bunuel   firas92   chetan2u   KarishmaB   gmatophobia ,

My doubt might seem basic,

My thought process was the same at arriving soln. but I got 1/4 as the answer, can you help identify my flaw?

= pi.r^2 - pi.(r/2)^2
= pi (r - (r/2))^2
= pi (r/2)^2

Hence,1/4 was my answer.

AbhinayaGMAT30 · Answer

a^2 - b^2 = (a-b)(a+b)
(a-b)^2 = (a-b)(a-b)

It is clear that both the expressions on the left mentioned above are not equal.

Hence, r^2 - (r/2)^2 is not same as (r-r/2)^2.

If a point is arbitrarily selected inside a circle of radius R, what i

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a point is arbitrarily selected inside a circle of radius R, what i

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards