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GMAT Quantitative Practice, Problem Solving

Question 5

All of the following xy-coordinate points lie on the circumference of a circle whose radius is 10 and whose center is the (x,y) point (0,0) EXCEPT:

  1. (–1, 3√11)
  2. (0, –10)
  3. (–5, –7)
  4. (8, 6)
  5. (2, –4√6)

Explanatory Answer

Each point along a circle's circumference is one endpoint of a line segment whose other endpoint is the circle's origin (0,0). Each such line segment is one leg of a right triangle whose hypotenuse is 10, the circle's radius (r). Apply the Pythagorean Theorem (x2 + y2 = r2) to each answer choice in turn. The xy-pair that fails to conform to the Theorem is the one associated with the correct answer choice:

  1. (–1, 3√11)
    Theorem: (–1)2 + (3√11)2 = 102
  2. (0, –10)
    Theorem: 02 + (–10)2 = 102
  3. (–5, –7)
    Theorem: (–5)2 + (–7)2 ≠ 102
  4. (8, 6)
    Theorem: 82 + 62 = 102
  5. (2, –4√6)
    Theorem: 22 + (–4√6)2 = 102

The correct answer is (C).