The figure above shows a path

Hi All,

We're told that the figure above shows a path around a triangular piece of land. Mary walked the distance of 8 miles from P to Q and then walked the distance of 6 miles from Q to R and Ted walked directly from P to R. We're asked by what PERCENT the distance that Mary walked exceeded the distance that Ted walked. This question is based around Geometry patterns and the Percent Change Formula.

To start, while you can certainly use the Pythagorean Theorem to figure out the distance from P to R (re: 6^2 + 8^2 = C^2), you would save time if you recognize that this is a 3/4/5 right triangle that's been "doubled" (so its sides are 6/8/10). Thus, Ted walked 10 miles to Mary's 14 total miles.

Next, the question asks by what percent MARY's distance was greater than Ted's.

Percent Change = (New - Old)/(Old) = (Difference)/(Original)

Mary's distance is the 'new' number and Ted's distance is the 'old/original' number... (14 - 10)/10 = 4/10 = 40%

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

boomgoesthegmat wrote:

The figure above shows a path around a triangular piece of land. Mary walked the distance of 8 miles from P to Q and then walked the distance of 6 miles from Q to R. If Ted walked directly from P to R, by what percent did the distance that Mary walked exceed the distance that Ted walked?

A) 30%
B) 40%
C) 50%
D) 60%
E) 80%

B

Since we have a right triangle, we see that we have a 6-8-10 right triangle.

Mary’s distance was 14, and Ted’s distance was 10, so Mary traveled 4 miles more than Ted.

4/10 = 40%

Answer: B