As you are probably well aware, success on the quantitative section of the GMAT requires not only computational ability, but also test taking acumen. For example, the fact that you are capable of determining a particular quantity from the information given in a problem does not mean that it is necessarily in your best interest to do so. At this point, you may assume that what follows is a discussion of data sufficiency (DS) strategy.
Of course, the DS construct is one in which a determination of sufficiency can frequently be made without a full “solution” to the problem in question. However, even problem solving questions can bait test takers into performing far more work than is required for a definitive answer. So, how do you avoid this pitfall? In short, look before you leap (or, in this case, solve).
At Veritas Prep, our guiding principles for solving word problems require that test takers digest all given information and decide on the best approach before diving into calculations. Unfortunately, this step is frequently overlooked by students, especially those with strong algebraic skills who are typically able to muscle their way through equations quickly and believe that they can easily make up for any time lost on the occasional unnecessary computation. But, beware! Even the best test takers ignore this guideline at their own peril.
To illustrate, I use the following problem (#182) from the Official Guide for GMAT Review, 13th Edition:
A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer’s initial cost. What was the dealer’s approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?
- 7% loss
- 13% loss
- 7% profit
- 13% profit
- 15% profit
Most people read this problem and immediately launch into a myriad of calculations. Not only have they taken the time to learn all of those equations for cost, percent change, profit and loss, they’ve also learned how to use them, and they conclude that this is the perfect opportunity to capitalize on their hard work. The only problem is that none of these equations provides the most efficient means to answering the question asked.
Can you reach a solution via the route of initial cost and percent change? Yes, you can (as evidenced by the published solution). But, can you complete those calculations in less than two minutes? It’s not likely. So, let’s go back to the beginning and look before we leap.
As is often the case with word problems, a fair amount of the difficulty here lies simply in understanding what we’ve been given. So, to summarize, we are dealing with a total of 60 cameras, divided into two groups: sold (54 cameras) and unsold (6 cameras).
The 54 cameras which were sold each yielded a 20% profit on initial cost, while the 6 that were unsold each resulted in a 50% loss (also on initial cost). Both the 20% profit and the 50% loss are based on the same initial cost (they represent percentages of the same quantity), so we can compare those percentages directly. Given two groups, each with its own respective average for a given quantity (gain/loss), how do we find the overall average for the combined set?
If you’re thinking weighted average, you’re right! The vast majority of the cameras were sold at a 20% profit, so that figure will be weighted much more heavily than the 50% loss and your overall answer should be significantly closer to +20% than -50%. Specifically, the result should be nine times closer to +20% than it is to -50%, since 54 (cameras) is nine times as many as six, but let’s do the math and verify:
[(+20%)(54 cameras) + (-50%)(6 cameras)]/(60 cameras) = +13% (or, 13% profit)
The correct answer is (D), and the calculation probably took less than a minute to perform – a much better option than slogging through all of those numbers for initial cost, sale price, and refund on return. So, we don’t need the $250 sale price? That’s right. Don’t assume that you’ll always need to use every number you’re given on a problem solving question.
Although the $250 can be used to calculate the aforementioned quantities, and thus ultimately to solve the problem, it is not required and you can save yourself a significant amount of time and mental energy by solving via weighted average. Recognize that the mindset of “do I really need this information to solve?” is not just for data sufficiency!
The ability to view problems from various different perspectives is invaluable on the GMAT, and represents one of the essential skills which separates strong performers (those scoring 700+) from elite test takers (those scoring above 760). Cultivating the habit of looking (and evaluating) before you leap has the potential not only to save critical minutes of test taking time, but also to elevate your GMAT performance to the highest level.
Jennifer Rich is a Veritas Prep GMAT instructor based in San Antonio. She received a BS in Chemical Engineering from Virginia Tech and was commissioned as a US Naval Officer upon graduation. She went on to Oklahoma State for an MS in Management Information Systems and graduated with a 4.0 GPA.