Zoom In, Zoom Out
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.
Zooming Out
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?
- 140
- 145
- 150
- 190
- 200
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.
That plan should be particular to the question type. If the question type has patterns you recognize, you may find that zooming out really helps you save time and focus on the big concept being tested. Sometimes, you’ll have to zoom in instead because the question requires you to deal with some details. You may have to do both! But classifying the question type and trying to consciously choose which strategy will help you the most is a good thing to practice. Because once you make a plan, you can follow it. Making a plan won’t be time wasted – it’s the “measure twice, cut once” of test-taking. And if you can’t make a plan in a reasonable time? You can’t do the problem, and it’s time to guess and move on.
Zooming in
Take a look at the following problem.
An electronic train is moving along a track at a constant rate. How many feet does the train travel in one hour if it travels at five feet per second?
- 30
- 300
- 720
- 1800
- 18000
Now, your plan might be different from mine, but I read this and think, “Okay, I’m converting units. This is an easy thing for me to mess up in my head, but it’s also fast arithmetic. I’m going to zoom in.” I know that for me, this problem is best handled by writing out the math and canceling the units. You might be great at estimating here, since the answer choices vary so widely, but my practice tells me it’s worth the time for me to write this out. So I write
5 feet/1 second * 60 seconds/1 minute * 60 minutes/1 hour
Now I can see that minutes cancel and seconds cancel, and I’m left with feet per hour, which was my goal. I can also see that the denominator is 1. At this point, I’m going to zoom back out, because this is a multiple choice problem and only one of the answers is of a reasonable size to be 5 * 60 * 60. (But if I didn’t absolutely trust my skills here, I’d stay zoomed in and go right to the calculator.)
Thinking in terms of zooming in and zooming out has really helped me study for and understand the quantitative portion of the GRE. Sometimes, you can get through the problem with hardly any math at all, if you understand what concept is being tested. Other times, it’s best to get right into the arithmetic. Only you can know which method works best for you on which question types, but if you practice it, you’ll have a best plan of action for each question type as it appears on the exam.