SAT Math Multiple Choice Practice Question 192: Answer and Explanation

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Question: 192


The preceding diagram shows a target made up of two circles inscribed in a rectangle. Which answer is closest to the probability that an arrow that hits the target shown lands on the shaded part?

A. 10%
B. 20%
C. 30%
D. 40%
E. 50%

Correct Answer: B


B. For this problem you want to compare the area of the rectangle to the area of the circles. It would be easiest to assume that the radius of the circle is 1, so that the diameter of the circle is 2. That means the height of the rectangle is 2, and the width of the rectangle is 4. Now you know that the area of the rectangle is 2 × 4 = 8, and the area of each circle is πr2 = π(1)2 = π. Therefore, the area of the shaded part is the area of the rectangle minus twice the area of one circle, or 8 - 2π. You can plug that into your calculator to see that the area of the shaded part is approximately 1.72. The probability of hitting the shaded area will be , which is about 21%. Choice (B) is the closest to 21%.

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