# 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, 3√11)
- (0, –10)
- (–5, –7)
- (8, 6)
- (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 (*x*^{2} + *y*^{2} = *r*^{2}) 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, 3√11)

Theorem: (–1)^{2}+ (3√11)^{2}= 10^{2} - (0, –10)

Theorem: 0^{2}+ (–10)^{2}= 10^{2} - (–5, –7)

Theorem: (–5)^{2}+ (–7)^{2}≠ 10^{2} - (8, 6)

Theorem: 8^{2}+ 6^{2}= 10^{2} - (2, –4√6)

Theorem: 2^{2}+ (–4√6)^{2}= 10^{2}

The correct answer is (C).