GMAT Studying: Correct Answers Can Be a Bridge to Success.
For about a year, I always used the same method to solve the following GMAT problem:
How many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 5 percent sugar solution?
“This is simple percentages,” I would say. “Just start by taking 3% of 50 liters, which is 3 over 100 times 50, which comes out to 1.5 liters sugar…”
But one day, teaching this same quantitative problem, a student’s hand shot straight up. “Yes, James?” I said. (That wasn’t his real name, by the way, but it will do.)
“Eli, who cares about the sugar?”
I paused. “Well, the sugar will help us figure out the solution.”
“But you don’t need it!” James explained. “I’ve been a chemical engineer for years, so I do this problem all the time. The sugar is a constant. The amount of sugar doesn’t change, and that amount is always equal to the concentration times the volume. So just do CV = CV; 50 times 3 is equal to the final volume times 5!”
I paused, impressed, and amazed—and have taught his timesaving shortcut ever since.
However, there is a bigger lesson here than simple mixture problems. I had approached that problem uncritically. I “knew” how to find the right answer, so I never gave it a second thought. I spent far more time prepping the combination and probability problems given their complexities and hidden challenges. As a result of my complacency, I made extra work for myself.
In other words, the takeaway is this: don’t focus exclusively on your mistakes. Review your correct answers as carefully as your errors. There might be a time-saving shortcut that you missed the first time through. Or better yet, you might have used such a technique that you can notice, reconstruct, and repeat! It’s very tempting to spend all of your time studying those red X’s on your quizzes and CATs. But avoid that trap; looking at your right answers as well as your errors will help you stay positive, and more importantly, will give you many opportunities to raise your score.