Reorient your View on Math Problems, Part 1
The Quant section of the GMAT is not a math test. Really, it isn’t! It just looks like one on the surface. In reality, they’re testing us on how we think.
As such, they write many math problems in a way that hides what’s really going on or even implies a solution method that is not the best solution method. Assume nothing and do not accept that what they give you is your best starting point!
In short, learn to reorient your view on math problems. When I look at a new problem, one of my first thoughts is, “What did they give me and how could it be made easier?” In particular, I look for things that I find annoying, as in, “Ugh, why did they give it to me in that form?” or “Ugh, I really don’t want to do that calculation.” My next question is how I can get rid of or get around that annoying part.
What do I mean? Here’s an example from the free set of questions that comes with the GMATPrep software. Try it!
* ” If ½ of the money in a certain trust fund was invested in stocks, ¼ in bonds, 1/5 in a mutual fund, and the remaining $10,000 in a government certificate, what was the total amount of the trust fund?
“(A) $100,000
“(B) $150,000
“(C) $200,000
“(D) $500,000
“(E) $2,000,000”
What did you get?
Here’s my thought process:
(1) Glance (before I start reading). It’s a PS word problem. The answers are round / whole numbers, and they’re mostly spread pretty far apart. I might be able to estimate to get the answer and I should at least be able to tell whether it’s closer to (A) or (E).
(2) Read and Jot. As I read, I jot down numbers (and label them!):
S = 1/2
B = 1/4
F = 1/5
C = 10,000
(3) Reflect and Organize. Let’s see. The four things should add up to the total amount. Three of those are fractions. Oh, I see—if I had four fractions, they should all add up to 1. So if I take those three and add them, and then subtract that from 1, that’ll give me the fractional amount for the C. Since I know the real value for C, I can then figure out the total.
But, ugh, adding fractions is annoying! You need common denominators. I’m capable of doing this, of course, but I really don’t want to! Isn’t there an easier way?
In this case, yes! Adding decimals or percents is really easy. Adding fractions is annoying. Plus, check it out, the fractions given are all common ones that we (should) have memorized. So change those fractions to percents (or decimals)!
(4) Work. Let’s do it!
S = 1/2 = 50%
B = 1/4 = 25%
F = 1/5 = 20%
C = 10,000
Wow, this is a lot easier. I know that 50 + 25 + 25 would equal 100, but I’ve only got 50 + 25 + 20, so the total is 5 short of 100. The final value, C, then must be 5% of the total.
So let’s see… if C = 10,000 = 5%, then 10% would be twice as much, or 20,000. And I just need to add a zero to get to 100%, or 200,000. Done!
The correct answer is (C).
What did we just learn?
There are two crucially important things to notice here.
First, I did NOT just start calculating immediately. I had 3 whole steps before I really starting doing any work! Don’t just dive in and start doing stuff. Figure out where you want to go first.
Second, don’t just accept what they give you. They gave the problem to us in fraction form precisely because fractions are so very annoying to add! They’re trying to see whether you notice that and can think flexibly enough to change your orientation on the problem and use percentages (or decimals) instead.
So, how are you going to remember that next time?
When I see: A problem with multiple fractions, decimals, or percents
Think: Is the form given really the easiest way to do the math? If not, and if the numbers given are easy to convert, then convert to one of the other forms!
And:
When I see: A problem requiring me to add fractions
Think: Can I convert easily to percentages or decimals? Would that make sense for this problem?
As you study, make sure that you are actually using all four of the broad steps that I outlined above:
(1) Glance
(2) Read and Jot
(3) Reflect and Organize
(4) Work
As you do the problem, keep an eye out for anything that you consider “annoying”—as in, they could have given this to me in an easier form, or I really wish I didn’t have to do this math that I’m doing right now! When this happens, take a step back to see whether you can spot a different, better approach.
While the clock is ticking, you might not figure it out. In the moment, either do the math the “annoying” way or just pick an answer and move on. Pretend it’s the test and make the call.
Afterwards, go back and figure it out. You can spend all the time you want playing with the problem, searching for alternative approaches. You can look up alternative solutions in our GMAT Navigator program or on the forums.
Your very last step is to ask yourself how you’re going to notice a similar situation the next time you see it. Here, your takeaway should be written in the “When I see ABC; Think XYZ” form I used above. For the first part, make sure that you write down what any problem would need to include in general. Do NOT write out the actual problem itself—you aren’t going to see that problem on the test!
Ready to test this out? This article is a 2-parter, so I’ll give you a homework assignment. (This problem is again from the free set that comes with GMATPrep.)
* ” If
, then
=
“(A) –1/2
“(B) –1/3
“(C) 1/3
“(D) 1/2
“(E) 5/2 ”
Click here for the second half of this article, where we discuss the solution to the above problem and also discuss a third problem. Further, make sure you practice using all 4 steps in the overall process so that you build the habit to reflect / organize your thinking before you dive into the work. This will help you learn to reorient your view and make GMAT math problems easier to tackle!
* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.