GMAT question - The figure above shows a circular pond... - Review

Type: Problem Solving

Difficulty: 3 star rating

Circular pond with a 3 foot wide path around it.

The figure above shows a circular pond with it's center at O, surrounded by a circular path that is 3 feet wide. If the area of the path is mathematical expression square feet then what is the radius of the pond in feet?

  1. 8
  2. 9
  3. 10
  4. 11
  5. 12

Explanation

The area of the path is equal to the total area of the path and pond minus the area of the pond.

If the radius of the pond is r then the radius of the path and pond is r + 3.

Therefore we can calculate the area of the path in terms of the radius of the pond.

mathematical expression

Now we substitute in mathematical expression for the area of the path

mathematical expression

Divide both sides by mathematical expression

mathematical expression

Multiply out the brackets

mathematical expression

Simplify

mathematical expression

Subtract 9 from both sides

mathematical expression

And divide both sides by 6

mathematical expression

Therefore the radius of the pond is 9 feet and the correct answer is B.

Comments (1):

  1. gud enough

    cupidsnigdha on 18 Jul 2008 (permalink)

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