Reorient Your View on Math Problems - Part 1

by , Oct 18, 2013

The Quant section of the GMAT is not a math test. Really, it isnt! It just looks like one on the surface. In reality, theyre testing us on how we think.

As such, they write many math problems in a way that hides whats 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? Heres an example from the free set of questions that comes with the GMATPrep software. Try it!

* If 1/2of the money in a certain trust fund was invested in stocks, 1/4in bonds, 1/5in 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?

Heres my thought process:

(1) Glance (before I start reading). Its a PS word problem. The answers are round / whole numbers, and theyre 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 its 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. Lets see. The four things should add up to the total amount. Three of those are fractions. Oh, I seeif 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, thatll 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. Im capable of doing this, of course, but I really dont want to! Isnt 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. Lets 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 Ive 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 lets 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! Dont just dive in and start doing stuff. Figure out where you want to go first.

Second, dont just accept what they give you. They gave the problem to us in fraction form precisely because fractions are so very annoying to add! Theyre 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 annoyingas in, they could have given this to me in an easier form, or I really wish I didnt have to do this math that Im 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 its 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 alternate approaches. You can look up alternate solutions in our OG Archer program or on the forums.

Your very last step is to ask yourself how youre 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 itselfyou arent going to see that problem on the test!

Ready to test this out? This article is a 2-parter, so Ill give you a homework assignment. (This problem is again from the free set that comes with GMATPrep.)

* If [pmath]{x/y}={2/3}[/pmath], then[pmath]{x -y}/x =[/pmath]

(A) -1/2

(B) -1/3

(C) 1/3

(D) 1/2

(E) 5/2

Click herefor 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!