Today’s post comes from Rowan Hand, a tutor available through Prep4GMAT‘s Tutor Marketplace. Rowan is the head coach at Your GMAT Coach, a London based consultancy, and has over 9 years of experience helping his clients get into excellent business programs, including LBS, Harvard, INSEAD, Wharton, and others. Check him out on Prep4GMAT or on his website www.yourgmatcoach.com
The GMAT doesn’t like people who apply formulas blindly.
So how is it possible to apply a formula and not “apply it blindly?”
Applying formulas blindly is something like throwing some apples, flour, butter, and sugar in a microwave and expecting the machine to spit out an apple pie. After all, we know that the microwave will heat it up a bit, right? And if we cross our fingers, maybe everything will just sort itself out inside the machine.
Then, at some point after cleaning a lot of hot, soggy, apple-y bits out of the inside of the microwave, we just say, “Well, I’m no good at making apple pies so I’ll just stop forever.”
This is how a lot of GMAT topics are tossed on the “I’m no good at this” pile.
A formula is like the microwave. We don’t really understand it fully, even though we have a vague understanding of its function. Its major advantage is that it’s “set it and forget it.” Push a button, and hopefully something works. If it doesn’t, too bad!
What the GMAT Wants to See: Intelligent Application of Process
Now imagine that you had a full kitchen, a stocked pantry, and a fairly solid grasp of the language of cooking. If someone asked you to make an apple pie, it wouldn’t be hard to:
Recipe? That’s pretty much all the precision my Great Aunt ever used, and her pies were AWESOME.
What’s the difference here?
In the case of the “Process Pie,” you take a few basic ingredients (think: “core truths” like multiplication tables) and combine them with a few basic principles (think: processes to solve problems).
Even if the outcome is not 100% perfect, at least it will look like what it’s supposed to look like. That’s all you need. GMAT reasoning is not about dotting i’s and crossing t’s. It is about getting close enough to the correct answer to make a solid guess.
In a process, we can lay out the facts on the table. We can see how these facts apply to one another. We can explain what is happening every step of the way.
Sometimes, we even manage to build formulas—ones tailored to our specific circumstances.
Wait – I thought formulas were all bad!
In some sense, formulas are just neatly packaged processes. However, they are often bulky and geared toward very particular circumstances. This is where the GMAT expects the sub-650 test-taker to trip.
Let’s take an example:
For any positive integer n, the sum of the first n integers will be equal to . What is the sum of every odd integer between 50 and 100 ?
First, I would be immediately skeptical because the question itself proposes an equation.
Red Flag: An invitation to apply a particular formula here suggests that it won’t easily fit the particular criteria of the problem.
Let’s try process instead.
First, we need to find the sum of a group of consecutive integers. The definition of average for any set of integers is equal to the sum of the set divided by the number of numbers in the set.
average = sum of numbers/number of numbers
We can simply move the bottom right to the top left:
average(number of numbers) = sum of numbers
Now, it is clear that the sum of a set of integers must be the average times the number of numbers. The average of the odds, then, is actually the average of 51 to 99.
By definition, the number of numbers in any set is the last number minus the first number, plus 1.
Pro tip: Always count ALL the numbers, then determine whether you have more odds or evens. That is, you can’t have evens.
Notice that the first number is odd (51) and the last number is odd (99). Therefore, you have more odd numbers than even numbers: that is, 25 odds and 24 evens.
Number of odd numbers: 25.
The sum of these numbers is therefore
Process. Notice that we completely ignored the equation.
Refer to a similar OG problem* if you insist upon using the formula provided. Notice that using the formula requires significantly more time and effort than simply recognizing the process and applying it piece-by-piece.
So What Is the Point of Formulas, Anyway?
Formulas are useful tools if you have a decided outcome and fixed circumstances. If you can assume that the circumstances will always be the same, rather than altered slightly, then using formulas is fine.
Once you learn how many minutes a particular brand of popcorn takes in a particular microwave, you’re set. However, once you get a new microwave or a friend brings over a different style of popcorn, it will take a little tweaking to arrive at a good bag of popcorn.
Similarly, you can’t just plug numbers into for every rate problem and expect the correct result. Each problem requires “tweaks.”
You don’t give up eating microwave popcorn because it didn’t work once (although it’s a good idea — that stuff is bad for you!), so don’t give up on a problem because your formula doesn’t work.
Learn HOW and WHY equations work. Build the equation you need based on the particular circumstances of the problem using principles you already know.
*Problem Solving 172 in the Official Guide to the GMAT 2015 Edition / 13th Edition