Before we get stuck and give up, let’s make sure we remember the task. Just because we can’t measure the lengths of the arcs, doesn’t mean that we can’t find the difference in lengths between the two arcs. Let’s take a look at the real equation we need to solve.
First, let’s talk about our two radii. If we think about a radius extending from the center of the circle—wherever that may be—we know that it will reach the inner ring first. To get from the edge of the inner ring to the edge of the outer ring, that distance is simply the width of the lane, which we said before is 12 feet! So, we can substitute that back into our equation!
Before we do that however, let’s think about our other variable, theta. That variable measures the central angle that we need to measure. We know that both angles will end at the same place (where the traffic is allowed to merge on the freeway), but that the outer angle will be a bit smaller because of the one-car length difference in traffic. However, solving for the angular difference precisely seems extremely difficult. Perhaps we could estimate, but that’s about it. This poses yet another problem that we need to solve.
Here is where our equation sits now:
Can you figure out what the next step should be?
You solve it! Take a look at the following GRE Quant problem. Try it out:
Did you get this GRE question of the day right? Often the best way to answer a question correctly is using old-fashioned Math. Strategy and tactics are not likely to help you here. Hope these questions are helping you do regular GRE practice online.
Have you been following our Math Facts sections? Let me tell you, it contains an amazing summary of GRE Quant material that is very useful. Percentage changes is one of the concepts that is frequently tested on the Quant section of the GRE. Here is a percentage change question of the day:
How would you do it? Leave your comments if you think there are better ways to solve this problem quickly and more accurately.
Consider this quantity comparison question. Try it out!
Did you look at the solution? Did you assume that the two chords are diameters of the circle?