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How to use Active Thinking in GMAT Problem Solving

Active Thinking for GMATQuick brainteaser for you: If 3 bunnies can eat 3 carrots in one hour, how many carrots can 1.5 bunnies eat in one hour?

Really take a moment to think about it.

Do you have an answer?

Ok. If you answered, or even were tempted to answer, “1.5 carrots,” then I’m glad that you’re reading this article! The thing is, while the bunnies are eating carrots at the rate of one per hour, it doesn’t follow that 1.5 bunnies will eat 1.5 carrots. 1.5 bunnies will only eat one carrot, because 1.5 bunnies is really just 1 bunny. (That half a bunny isn’t feeling very well and doesn’t want any carrots.)

I don’t mean to say that this is a GMAT-style problem, but if you found yourself answering “1.5 carrots,” then you are prone to operating on autopilot. Students who operate on autopilot will often fall into traps, and they may become overwhelmed by questions that don’t fall clearly into easily recognized patterns. And let me tell you – you will likely see many problems on the GMAT that don’t fall into common patterns!

Active Thinking

It’s imperative that you understand the role that active thinking plays in GMAT success. Sometimes I tell my students, “The GMAT is a math test the way that hockey is an ice skating contest.” They usually look at me like I’m crazy until I explain, so let me explain. Of course all hockey players can skate. They can skate backwards, forwards, sideways…. They can stop on a dime and accelerate just as easily. But they’re playing hockey while they’re doing all of that, right? They watch the puck, they shoot the puck, they defend their goal and attack the other goal. I’m not a hockey expert, but it seems to me that skating skills aren’t nearly enough. Hockey requires that you skate expertly, and yet it isn’t exactly an ice skating contest.

And that’s my entire point. The GMAT isn’t a math test, exactly. It assumes you can do math. It assumes you can solve for x in your sleep. It assumes that you can tick off the major exponent rules on your fingers and reverse-FOIL without taking a breath. But… then what? It’s not enough that you can do the math – you also have to do the thinking. A lot of students just work automatically through GMAT problems. But that’s not enough.

The GMAT often gives you questions that test your ability to think creatively. For example, consider this problem. (It’s based off of a real Official Guide question.)

A café sells cupcakes for $1.00 each and donuts for $1.30 each. If a customer buys some cupcakes and some donuts for a total of 13.10, how many cupcakes did the customer buy?

A)    4
B)    5
C)    6
D)    7
E)    8

Take a moment to see if you can solve the problem.

Really, try!

Did you give it a try? Ok.

A lot of students would begin working here on autopilot. Did you? The “automatic” response would be to write something like 1C + 1.1D = 13.10. Sure, there’s nothing particularly wrong with that. It’s a true representation of the mathematical relationship here. Unfortunately, it doesn’t help us solve the problem.

No one can actually use the equation C + 1.1D = 13.10 to solve for C or D. There are infinite solutions to that problem, if it’s looked at solely algebraically. You would need either another equation or the value of D in order to find C. Then how can this be solved?

The question makes it clear that there is only one solution, so there must be only one way that  $1 cupcakes and $1.30 donuts can add up to $13.10. The trick is to focus on the .10 part from the 13.10. How can we ensure that the sum ends in 10 cents?  

The cupcakes cost exactly $1 each, so it isn’t the cupcakes’ fault that the price includes ten cents. So, it must be that the price of the donuts ends in 10 cents. One donut would cost 1.30, two would cost 2.60, three would cost 3.90, four would cost 5.20, six would cost 6.50, seven would cost 7.80, and eight would cost 9.10. So it must be that the person bough eight donuts, so that the price would end in 10 cents. It’s the only way that it would end in 10 cents (knowing that the sum is only 13.10). Then we would just need enough cupcakes to bring the total to 13.10, so we’d need four cupcakes. The customer must have bought 4 cupcakes.

As you can see, this problem depended as much on your logic skills and focus as it did on your math skills. And that’s exactly my point. By all means, study your math skills. They’re foundational. But as you work through each problem, stay engaged and focused. Thinking – active, creative, and purposeful thinking – is just as necessary for success on the GMAT as strong math skills are. All the algebra drills in the world won’t tell you when not to use algebra, and no perfectly constructed proportion can explain why 1.5 bunnies can’t eat 1.5 carrots.

So, try this tonight. Try a practice set of quant questions, preferably from the Official Guide to GMAT review, with the goal of staying fully engaged. Begin each problem by keeping your hands behind your back for ten seconds while you think through the problem fully and make sure that you’re not operating on autopilot.

Expert Author

Laura has been working in the fast paced test prep industry in New York City for more than eight years. She has taught literally thousands of students and tutored thousands more. She has a Masters in Education and got a 780 on the GMAT – several times. She’s helped students improve more than 200 points, and has former students at Stern, Columbia, HBS, and Wharton. She believes that anything is possible!

twitter: @LauraGMATtutor
website: http://realusefulgmat.blogspot.com/
email: laura.tutoring@gmail.com

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