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.

Eli Meyer has been a Kaplan teacher since 2003. He has spent the past four years focused almost exclusively on the GMAT, and also has prior experience helping students ranging from middle-schoolers taking the ISEE to professors retaking the GRE for their second PhD. During his Kaplan career, Elis has also written and revised Kaplan course materials and acted as a community liaison on several popular GMAT message boards, all the while helping his students succeed both in and out of the classroom.

Thanks Eli, but can you set up the equation? I don’t seem to understand where the shortcut is

Thanks Eli, but can you set up the equation? I don’t seem to understand where the shortcut is. By the way, I did this problem in class with my kaplan teacher! (we seemed to have done it the first way though, so a shortcut would be appreciated!)

Hi Char- the equation would be Concentration1 * Vol1 = Concentration2 * Vol2 i.e. 50 * 3 = Vol2 * 5, therefore Vol2 = 150/5 = 30 which is same as the answer found from regular technique. 3% of 50 = 1.5 lit. For new solution 1.5 lit is 5% of the solution therefore total volume of new solution = 20 * 1.5 = 30. So volume of water to be evaporated is 50 – 30 = 20 lit.

C1 * V1 = C2 * V2 works because the amount of sugar in solution is same in both the solutions.

Shikhar, thanks for saving me the trouble; your explanation is spot-on and wonderful!

could you please complete the article with the answer ?

Hi SP, check the other comments! Your fellow students have already provided an excellent explanation. Let me know if you have specific questions about it!