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.

ananya88888888888 · Answer

is this q relevant from gmat focus pespective  Bunuel ?

Bunuel · Answer

If the formula for the area of a circle is  not given , then this question is  not very likely  to appear on the current GMAT.

If the formula is provided in the question, however, then this type of probability question could still be relevant.

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

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

Prep Toolkit

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