“8% of American adults have a master’s degree.” – US Census Bureau, 2012
What makes the GMAT frustrating? For many, it’s that you’ve studied and studied but on test day it seems like half the questions are things you’ve never seen before. Why do certain tricks and plug-and-chug processes only work on *some* rate problems, mixture problems, etc.? How can you do every problem in the Official Guide twice, take each GMAT Prep practice test multiple times, and still run into problems that you just don’t even know how to start?
The answer lies in large part in the statistics above. 80% of success in life probably is just showing up and following directions. High schools don’t want you to fail; in many cases if you’ve kept up with the attendance policy your teacher isn’t allowed to fail you. If you went to all the review sessions and office hours in college, listened when your TA mentioned that the professor “really thinks this is particularly important”, and raised your hand enough to earn participation points, graduating from college wasn’t nearly as hard as you might have thought it would be when you were a 12-year old struggling with algebra and long division. Which isn’t to say that those who have graduated from high school and college aren’t accomplished – showing up isn’t drop-dead easy and learning processes, following directions, doing homework and studying…a lot of people don’t do these things. But the point remains: when you’re taking the GMAT, you’re beyond that first 80% of success in which “just showing up” will suffice. Everyone taking the GMAT and considering graduate school has demonstrated to the world that they can do that. You want to get to that rarified air – you want that last 8% of success. And to get it you have to prove more than just showing up and following directions.
Because the GMAT exists as a separation mechanism – your percentile is every bit as important as your raw score, and probably more important – among those who have already proven that they’re capable of buckling down to study, learning the material, practicing and implementing processes. On some – many if you’re hoping to go into the high 600s or 700s – questions you won’t simply be able to throw the question into a formula and get the right answer. Most people taking the test are capable of doing that. To separate yourself you may have to do more. And the key to that may well just be learning to handle uncertainty.
Here’s we mean – if you’re faced with a new, challenging variation on a question you’ve seen, you won’t likely be able to design a process or system right away. You’ll probably have to think your way through it, and have a dialogue with yourself about how to process it. Consider the example:
A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree. How much of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?
This looks like a mixture problem and in many ways it is. But unlike many mixture / weighted-average problems, this one doesn’t come with a well-defined “plug the math into this equation and you’re done” way to do it. Instead, the math really comes secondary to your thought process. The challenge is in how you account for the changes from the original mixture to the new one. And that’s where “wait, wait…don’t tell me” comes in. You’ll probably have to jot down a few initial attempts at setting up the math, then challenge that thinking to make sure you’re doing it correctly. Here’s an example of how that would go:
- “I know that I have 15 cups total and that 40%, or 2/5, is chocolate and 60%, or 3/5, is raspberry. So that’s 6 cups of chocolate and 60% raspberry. But what I really want is equal amounts of each, so I guess 7.5 cups of each. And 1.5 is an answer. But wait, wait…I’m removing part of the mixture, not just the raspberry. So it’s not quite that easy.”
- “OK, so I need the 6 cups of chocolate, plus whatever I add, to equal the 9 cups of raspberry, plus whatever I take away. So I can at least set up the equation: 6 + _____ = 9 – ______ as a starting point. And I take away the same amount that I add, so I can call that amount x. So how about 6 + x = 9 – (the amount I take away)… But wait, wait – when I take away some of the current mixture, I’m also taking away some chocolate with that so I need to subtract something on the left, too…”