Two people stand around a circular duck pond which has radius R meters

Question

Two people stand around a circular duck pond which has radius R meters. They are placed randomly (uniformly along the circumference of the duck pond) and independently.
What is the probability that they are more than R meters apart from each other?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

chetan2u · Answer

So, 2 people on the circumference of a circle...
Let the first person be at A, so the second will be within R meters if he is between B and C.
So the probability is the fraction of bigger arc BC to total circumference..

Take  	riangle {OAB} ... All sides are R, so  \angle{AOB}=60 
Now, take  	riangle {OAC} ... All sides are R, so  \angle{AOC}=60 
So,  \angle{BOC}=120 , and the major arc BC =  \frac{360-120}{360}=\frac{240}{360}=\frac{2}{3}

D

SaquibHGMATWhiz · Answer

Solution: radius.png According to the above diagram, the required probability =\frac{ ext{length of arc AC + length of arc BD}}{ ext{full circumference of the circle}} =\frac{\frac{120}{360} imes 2\pi R+\frac{120}{360} imes 2\pi R}{2\pi R}=\frac{2}{3} Hence the right answer is Option D

popgraham · Answer

Would this appear on GMAT FE?

Bunuel · Answer

____________________________________
No.

Bhargavikomara · Answer

How to differentiate the gmat questions to non gmat questions ?

Bunuel · Answer

For the  Quantitative section (Problem Solving) , the only difference is that the new GMAT no longer includes hardcore geometry questions, meaning anything that depends on specific geometry knowledge.

Check these two topics:

GMAT Syllabus for Focus Edition  
  Geometry Tested on GMAT Focus?

While specific geometry knowledge is not tested on GMAT Focus, not everything involving shapes, volumes, or areas requires specialized geometry knowledge. The area of a square or rectangle, the volume of a cube or rectangular solid, and the Pythagorean theorem are not considered specific geometry knowledge by the GMAT and can still be tested. Moreover, a question can involve shapes but test another area, such as combinations or other topics. There are several  questions involving these concepts in the GMAT Prep Focus mocks .

The chapter on coordinate geometry, including planes and slopes, is still present in the recent Official Guides. That said, it is tested to a much smaller extent. For example, you might see some questions involving graphs, either in Problem Solving or in Data Insights graph-based questions. However, those usually fall under the functions category rather than pure coordinate geometry, so they typically won’t involve distance calculations, angles, or similar topics.

For  Data Insights (DS, MSR, Tables, Graphs, and TPA) , the new GMAT also removes geometry in the same way as PS, plus pure algebraic questions are no longer part of the  DS syllabus .

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

Hope it helps.

Kinshook · Answer

Two people stand around a circular duck pond which has radius R meters. They are placed randomly (uniformly along the circumference of the duck pond) and independently.

What is the probability that they are more than R meters apart from each other?

Angle formed at the center formed by any random point and point at left and right side at distance R from the random point =  2\pi/3

Angle formed by rest of the circumference at the center =  2\pi - 2\pi/3 = 4\pi/3

The probability that they are more than R meters apart from each other =  \frac{4\pi}{3 / 2\pi} =  2/3

IMO D

Two people stand around a circular duck pond which has radius R meters

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Two people stand around a circular duck pond which has radius R meters

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

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Perfect 805 Score Debrief by Julia

My Rewards