Name and Conquer

I was reading through a math textbook the other day and came across a great catchphrase: "Name and Conquer." In short, the idea is that as you try to solve a problem, name the variables to gain a better understanding of what you're up against. Simply naming the variables won't give you much, but as you do so, it's tough not to think about what they represent, how they relate to other variables, and what you can do with them.

In fact, the idea of "Name and Conquer" is the combination of two guidelines that I've been teaching to GMAT students for years:

• Write everything down. As you read through a math problem (especially if it's a word problem), get it down on your scratch paper. This usually involves translating words to variables.
• Look for what you know. Once you've read through the question and got something on paper, figure out what tools you have that apply to the situation.

Part of what makes word problems so difficult is that every one seems like a unique challenge. If you do a series of symbolic algebra problems, eventually you'll see patterns. But when you face a new real-life scenario with every question, it's tough to make those connections.

That's the benefit of naming. If you can reduce a word problem to algebra (or arithmetic, or whatever), you can see the patterns more readily. If you're afraid of the algebra...well, that's a dilemma you'll need to solve. Unless you're comfortable solving equations and manipulating symbols, you're going to have a really hard time doing well on the GMAT quant section.

An Example

Here's question #149 from the 12th edition of The Official Guide:

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?

There's a lot going on here. We have an average speed, as well as two speeds for parts of the trip. Since rate is the ratio between distance and time, if there are three different speeds, there are three different distances and times, as well!

To simplify matters, let's say that the entire trip is 100 miles and start naming:

• First part of the trip: d = x miles (x percent of 100 miles), r = 40mph, t = ?
• Second part of the trip: d = 100 - x miles, r = 60mph, t = ?
• Entire trip: d = 100 miles, r = ?, t = ?

That's a lot of variables, but if you know how to deal with simple rate questions, you can start to make progress on this one. t = d/r, so for the first part of the trip, t = x/40. For the second part, t = (100 - x)/60.

From there, we can add the two times for the time of the entire trip. Since we have the distance for the entire trip and we can find the time for the entire trip, we can solve for the average speed. The algebra gets fairly involved, but that's a mechanical issue. Once we write down all the details and name them in a familiar way (d, r, t), the fact that it's a cumbersome word problem ceases to be an issue.

Don't be afraid to name plenty of variables. The more objects to deal with in the question, the more important it is to get away from the language of the word problem and move into the realm of algebra. Do that, and some of the most difficult word problems will start looking a whole lot more like the easy ones.

About the author: Jeff Sackmann has written many GMAT preparation books, including the popular Total GMAT Math, Total GMAT Verbal, and GMAT 111. He has also created explanations for problems in The Official Guide, as well as 1,800 practice GMAT math questions.

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