You can attend the first session of any of our online or in-person GRE courses absolutely free. Crazy, right? Check out our upcoming courses here.
If you’ve ever taken a GRE, you’ve encountered something like this:
This is a good ole GRE Quantitative Comparison question—a “QC” for short. They’re always the first questions you see on the test. And they always have the same answer choices. Read more
Recently, we discussed various strategies for translating word problems into math. Let’s put that knowledge to the test on a challenging problem from a category that everybody hates: Rates.
Set your timer for 2 minutes and GO! (© ManhattanPrep)
* A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 300 miles apart, at what time will the trains pass each other?
One of the strategies we discussed in the translation article was make the situation real. Put yourself into the situation and imagine you’re the one doing whatever the problem is describing. That will help you to set things up cleanly and correctly.
So what’s going on in this particular situation? First, you’re the conductor on the Kyoto train. At noon, you pull out of the station (instantly and magically traveling 240 miles per hour from the very start!). The track is 300 miles long; after one hour, where are you?
After one hour, it’s 1pm and you’ve gone 240 miles, so you’re just 300 “ 240 = 60 miles from Tokyo.
Okay, now switch jobs. You’re the Tokyo train conductor and you leave Tokyo at 12:10pm. After one hour, where are you? You’re going 160 miles an hour, so after 1 hour, it’s 1:10pm and you’re 300 “ 160 = 140 miles from Tokyo.
By 1:10p, have the two trains passed each other? Definitely, because train K (for Kyoto) is even further towards Tokyo at that point. Now, make a guess: do you think that the trains had already passed each other by 1p? Think about it before you read the next paragraph.