Hi GMATters,
This is a guest blog post from our friend Mark Skoskiewicz of Chicago-based Test Prep service MyGuru.
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GMAT Math and the Importance of Strategy
To excel on the GMAT, mastering core underlying mathematical concepts and skills is critical. The key to a 700+ score on the GMAT is certainly not “tips and tricks.”
At the same time, I can’t reinforce strongly enough that the GMAT is not a math test.
If you approach it that way, you will score below (likely far below) your potential score, whatever your level of underlying math knowledge happens to be.
Here are two key reasons why GMAT quant is best not thought of as a “math test:”
- You are often not asked to arrive at a 100% correct answer. Something that is about or approximately true is good enough.
- You get credit for choosing the right answer, not for demonstrating any given approach or method. You don’t get partial credit for showing your work and having been on the right track to the correct answer.
Keep in mind that the math covered does not typically go beyond grade 9 or 10 in the U.S. education system. So, you’re looking at algebra 2, geometry, and trigonometry. There are some topics, like probability or number theory, that violate this rule because many U.S. students learn these topics a little later (and sometimes not at all), but the basic idea is that the math itself is 9th or 10th grade in difficultly level.
That said, you are asked to apply your math knowledge creatively and use heavy doses of critical thinking. If you don’t internalize the two points above, you’ll find yourself trying to mathematically solve certain questions, spending a long time on what could be an easy question, and ultimately scoring well below your potential.
So, what is the right way to think about the GMAT section? If it’s not a math test, what is it?
It’s a test of logic, critical thinking, and strategy.
The tricky thing however is that the line between “tips and tricks” and “strategy” is sometimes not that thick. What may look like a “trick” to solving a problem is much better thought of as the application of a strategy that does rely on some core underling math knowledge, but which doesn’t treat the problem like a math test.
Let’s explore this idea with an example.
Thinking about GMAT Quant as a test of Logic and Strategy: An Example using Square Roots
Observe the question below:
A common, but far less than ideal, way to approach this question is to begin answering a math question that has to do with square roots. If you do this, you might start by recognizing that the sqrt (ab) = sqrt(a) * sqrt (b).
So, sqrt(80) = sqrt(20) * sqrt (4). That’s 2 * sqrt(20), which could then become 2 * sqrt(4) * sqrt (5). So, now you’re left with 2 *2 * sqrt (5), or [4 * sqrt (5)] + sqrt (125).
If you apply the same math to the sqrt (125), you end up with sqrt (25) * sqrt (5), or 5 * sqrt(5).
Now, you are left with [4 * sqrt (5)] + [5 * sqrt(5)].
First of all, by this point, you’ve spent a fair amount of time.
But let’s continue. A common step at this point is to say, ah! One of the answer choices is 20 * sqrt (5). That what my equation above seems to reduce to. So, to save time, since it seems pretty obvious what the answer is at this point, you choose B.
But are you correct?
Well, no, you aren’t. If you stop focusing on the mathematical rules for square roots and manipulation of the equation, you can see estimate that the square root of 5 is something close to 2.5. So, [4 * 2.5] + [5 * 2.5] is going to equal something close to 20. But, 20 * sqrt (5) will equal something close to 50. So, that can’t be right.
Now what do you do?
Here is another approach to this problem. Instead of starting with the math, apply the strategy of seeing if you can make a slight modification to the problem to work with whole numbers instead of fractions or decimals or square roots.
So, consider looking at the problem as something close to the square root of 81 plus the square root of 121, instead of 80 and 125. Now, you can quickly answer the question. That’s 9 + 11 = 20.
Now you can look at the problem this way –
Think about how long you’ve taken so far with this approach. We are talking seconds of your time so far. And you are extremely close to getting to the right answer, because take a look at the answer choices.
You can immediately see that choices B. and C. and E. are much too large, and clearly are wrong. Personally, D gave me a slight pause, but not too much trouble.
I know for sure and very quickly that 12 * 12 = 144. I was somewhat confident just by thinking about how the math would work as I started plugging in numbers above 12 that I would reach 200 well before 20. Indeed, 15 * 15 = 225, so D is too low.
So, the answer is A.
And, if after realizing you needed an answer choice that was close to 20, you had simply started estimating top to bottom, you would have landed on A. as the correct answer right away.
All in all, this second approach gets you to the correct answer with very limited math knowledge. Instead, you think critically, apply some simple strategies (i.e., the strategy of turning awkward numbers into whole numbers you can more easily work with, and then the strategy of the process of elimination) and do some simple calculation.
I always find this problem to be a great example of how critical thinking and problem solving is fundamental to GMAT success. Did you need to know a math concept to answer this correctly?
Kind of. You had to know what a square root was, but you didn’t really even have to know how to manipulate and break them down into components.
Were you well served by simply turning it into a math problem and working out the answer? No. Instead, you can modify the problem slightly, eliminate obviously incorrect answers, and quickly and with confidence arrive at the right answer.
Many GMAT problems can be approached “strategically” like this.
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