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
  1. Begin with the two important circle formulas.
    Area = πr2
    Circumference = 2πr, where r is the radius.
  2. Since circles x and y have the same area, the length of their respective radii must be the same.
    Areax = πrx2 = Areay = πry2
    π(rx)2 = π(ry)2
    rx2 = ry2 divide by π
    rx = ry
  3. With the information given in the question, you can write the following equation:
    Circumferencex = 2πrx = 16π
    2rx = 16 divide by π rx = 8
  4. Remembering that rx = ry, you know that ry = 8. Consequently, "half of the radius of circle y" is (1/2)(8) = 4. Answer C is correct.

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