# Practice GMAT Problem Solving Question

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In May, the grounds keeper at Spring Lake Golf Club built a circular green with an area of 100π square feet. In August, he doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?

Correct Answer:

**B**- Since all we know about the relationship between the original and renovated greens is the doubling of the radius (i.e., distance from center to edge), we must find the radius of the new green based off the area of the original green.
- The formula for the area of a circle is A=πr
^{2}. The area A = 100π, so we must solve for r in the equation 100π=πr^{2}. - Divide both sides by pi to yield 100=r
^{2}. - Thus, the radius of the original is the square root of 100, which could be -10 or 10, but since we are dealing with distances, it must be positive. So the radius of the original green is 10 feet.
A = 100π = πr
^{2}

100 = r^{2}

r = 10 - Since the original radius is 10 ft, the renovated green has a radius double that: 20 ft.
- Now to calculate the total area of the renovated green:

A=πr^{2}

A=π20^{2}

A=400π

Thus, the correct answer is B.

Note: The question asked for the "total area" not the additional area.

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