Bunuel wrote:
In order to cover less distance, a boy – rather than going along the longer and the shorter lengths of the rectangular path, goes by the diagonal. The boy finds that he saved a distance equal to half the longer side. What is the ratio of the longer to the shorter lengths of the rectangular path?
A. 15:7
B. 2:1
C. 3:2
D. 4:3
E. 5:4
This is an awesome example of a question where knowing how to take a standardized test can REALLY help. You are welcome to do the work to derive the answer and then find it among the answer choices, but if you remember that the answer choices are there for you to use and that the GMAT tests the same things over and over, you can get to the right answer much more quickly. No business school cares whether you can do the actual math; they care how you THINK, so learn to think like a test-taker instead of a mathematician.
Two things are in play here.
First, we are looking at the diagonal of a rectangle. That makes a right triangle. There are four types of right triangles that the GMAT tests over and over and over and over and over again. Two are defined by their angles: 45-45-90 and 30-60-90. And two are defined by their sides: 3-4-5 and 5-12-13. On all right triangle questions, be alert for these options.
Second, we can use PITA (Plug In The Answers). Test an answer choice. If it works, great. If not, try another one.
Okay, so on to getting the right answer.
Let's just test answer choices.
I notice that answer choices D and E have numbers that just might apply to a 3-4-5 triangle, so I'm instantly drawn to those. The numbers in the ratio are for the sides of the rectangle, so the legs of the triangle. The legs of a 3-4-5 triangle are the 3 and the 4. So, let's try answer choice D. The sides of the rectangle are 3 and 4. That makes the diagonal 5. If I were to walk the diagonal, I'd travel a distance of 5. If I were to walk the two legs, I'd travel a distance of 3+4=7. Did I save a distance equal to half the longer side? Yep, I saved a distance of 2 and the longer side is 4. Done.
Answer choice D.
ThatDudeKnowsPITA
ThatDudeKnowsRightTriangles