A square dart board has four dark circular regions of radius 3 inches

Question

https://gmatclub.com/forum/download/file.php?id=59750 A square dart board has four dark circular regions of radius 3 inches as shown in the design above. Each point on the dart board is equally likely to be hit by a dart that hits the board. What is the probability that a dart that hits the board will his one of the circular regions? A. \frac{\pi}{16} B. \frac{\pi}{48} C. \frac{\pi}{64} D. \frac{1}{3} E. \frac{1}{4} 1.jpg Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

CrackverbalGMAT · Answer

Probability = Favorable Outcomes / Total Outcomes

Favorable Outcomes = Dart hits the shaded area = 4 * π *  r^2  = 36π

Total Outcome = Area of the square region = 24 * 24 = 576

The Required Probability = 36π / 576 = π/16

Option A

Arun Kumar

TarunKumar1234 · Answer

P (E) = Area of 4 circles /Area of dart board = π*3^2 *4 /(24*24) = π/16 So, I think A.

AndrewN · Answer

Hello, everyone. For those who may want to get to the answer a little quicker, you can reduce the fraction without multiplying everything out first. That is, you can think of the probability in the following way:

P=\frac{(4*π*3^2)}{(24*24)}

P=\frac{36π}{(24*24)}

P=\frac{(12*3)π}{((12*2)*(8*3))}

P=\frac{π}{(2*8)}

P=\frac{π}{16}

The answer must be (A).   You can practice such a question mentally, without writing down any numbers, although I would not advise doing so on the test. With a little knowledge of factoring, the question should take about a minute, and you could spend that extra time on a tougher question that may warrant it.

Good luck with your studies.

- Andrew

ScottTargetTestPrep · Answer

Solution:
 
The probability that a dart that hits the dart board will hit one of the circular regions is the combined area of the 4 circular regions divided by the area of the dart board.

The combined area of the 4 circular regions is 4 x (π x 3^2) = 36π square inches.

The area of the dart board is 24^2 = 576 square inches.

Therefore, the desired probability is 36π/576 = π/16.

Answer: A

A square dart board has four dark circular regions of radius 3 inches

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A square dart board has four dark circular regions of radius 3 inches

Prep Toolkit

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