Question

Jerry and Silvia wanted to go from the southwest corner of a square field to the northeast corner. Jerry walked due east and then due north to reach the goal, but Silvia headed northeast and reached the goal walking in a straight line. Which of the following is closest to how much shorter Silvia's trip was, compared to Jerry's trip?

$30\%$

$40\%$

$50\%$

$60\%$

$70\%$

Answer: A

Concepts:Pythagorean Theorem percentage

Difficulty rating: 1200

Solution:

If the square has side $x,$ Jerry walks $x+x=2x,$ while Silvia walks the diagonal $\sqrt{x^2+x^2}=x\sqrt2.$

The fraction by which Silvia's trip is shorter is $\begin{aligned} &\dfrac{2x-x\sqrt2}{2x}=1-\dfrac{\sqrt2}{2} \\ &\approx 1-0.707=0.293. \end{aligned}$

This is closest to $30\%.$

Thus, the correct answer is A.

2017 AMC 12A Problem 4

Answer: A

Difficulty rating: 1200

Solution:

Problem 4 in Other Years