I’m a terrible photographer because I don’t zoom in a reasonable manner. I try to zoom in on things that really can’t be appreciated without context. I try to zoom out and capture a whole panorama when the scene is too busy for any viewer to appreciate it. I suppose I could practice, but instead I’ve just stopped taking pictures and let other people do it for me.
But when it comes to the quantitative section of the GRE, I know exactly how to zoom, and I try to make sure my students know how to do the same. If you took all your photos with the camera on its factory setting, they would all be okay, but none of them would be really great. You want to get closer and more into the minutiae sometimes, and take a broader view other times, skipping all the details. The same is true when studying for (and taking) the GRE.
Consider the following problem:
If x is the median of all the even multiples of 7 from 15 to 100, and y is the mean of all the even multiples of 7 from 16 to 104, what is the value of x - y?
With your mental math camera on the regular setting, your approach might sound something like, “Okay, I know how to find the median. I’ll list out all the terms, and choose the middle one. After I’ve done that, I can find the mean by average out the first and last terms, because this is an evenly spaced set. Once I find both those numbers, I’ll subtract to find the difference.”
This approach is okay, and it will get you to the right answer. But zooming out a little allows you to look at the problem collectively, as a whole, and think something like, “Hey, both these sets of numbers are the same, since they both start at 21 and end at 98. And in an evenly spaced set, the mean and median are the same. So their difference is zero.”
Zooming out lets you pick up patterns in the exam and take advantage of the fact that you’ve studied them and notice them. It allows you to notice trends in the exam, which helps you know quickly what issues to consider and can also help you make an educated guess. Let’s take a look at another sample problem.
What is the average (arithmetic mean) of all the multiples of ten from 10 to 290 inclusive?
On a regular setting, I’m looking at this and thinking, “Great, I know how to find the mean. I’ll list all the multiples of ten, add them up, and divide by the number of terms.” By zooming out, I can realize, “Hey, I know the GRE doesn’t want me to do that. This test rewards me for reasoning; is there a faster way? Yeah, this is an evenly spaced set of terms, so the middle one is the mean. And I can find that by just taking the mean of 10 and 290.
Making a Plan
The purpose of zooming out (or zooming in, as we’ll see in a second) is to make a plan. Each question should cause you to clarify what information you’re being given (“What are they telling me?”) and what you’re being asked to find from it (“What are they asking me?). Then, make a plan. Continue Reading…