# Practice GMAT Problem Solving Question

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If circles x and y have the same area and circle x has a circumference of 16π, half of the radius of circle y is:

Correct Answer:

**C**- Begin with the two important circle formulas.

Area = πr^{2}

Circumference = 2πr, where r is the radius. - Since circles x and y have the same area, the length of their respective radii must be the same.

Area_{x}= πr_{x}^{2}= Area_{y}= πr_{y}^{2}

π(r_{x})^{2}= π(r_{y})^{2}

r_{x}^{2}= r_{y}^{2}divide by π

r_{x}= r_{y} - With the information given in the question, you can write the following equation:

Circumference_{x}= 2πr_{x}= 16π

2r_{x}= 16 divide by π r_{x}= 8 - Remembering that r
_{x}= r_{y}, you know that r_{y}= 8. Consequently, "half of the radius of circle y" is (1/2)(8) = 4. Answer C is correct.

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