GMAT Math Word Problems: When in Doubt, Draw it Out

The GMAT is designed to be tricky, so it should come as no surprise that math questions do not always present information in the clearest, most straightforward manner.

Especially on word problems, the important numbers, figures or data can be spread throughout the question or hidden among the text. One moment a question may be talking about the ratio of water to sugar in lemonade and the next moment it’s asking you to calculate the total revenue of the lemonade stand.

How is the ratio related to price? And how do you find the answer given the limited information in the question? Often the hardest part of word problems isn’t the math, it’s figuring how to use what the question gives you to solve for the answer.

How drawing a table simplifies confusing problems

Diagrams, drawings, lists and tables help us organize information, and for confusing word problems, they free you from juggling all of a question’s information in your head. Even better, they help expose the latent mathematical relationships within the question, which helps you figure out how to solve for the correct answer.

Tables are perhaps the most useful. They’re easy to build and a convenient way to keep track of a question’s information. However, the most important factor in using any visual aid (apart from it representing information accurately) is that it works for you. So if you don’t like tables, use whatever drawings, lists or notations help you make sense of a question.

Let’s use a table to help solve a confusing word problem:

 

A popular soft drink is made by combining 3 parts coloring to 75 parts high-fructose corn syrup to 150 parts water. For a new version of the drink, the manufacturer decides to double the proportion of coloring to syrup and at the same time cut the coloring to water ratio in half. How many parts of water will the new formula have if it contains 150 parts of corn syrup?

(A) 400
(B) 600
(C) 875
(D) 900
(E) 1200
 
 

The density of this question can be overwhelming, especially if you haven’t practiced many solution questions. If you have no idea how to solve such a problem, start by simply organizing the question’s information into a table.

Here’s how you may start to build a table:

Coloring Syrup Water C:S C:W
Original formula 3 75 150 3/75 3/150

 

The question is about changing the formula of a soda, so we start by listing what we know about the original formula. Since we know the original proportions of ingredients, we can easily figure out the original ratios that change in the new formula: coloring to syrup and coloring to water.  Immediately we see that we can simplify each ratio; 3:75 is 1:25 and 3:150 is 1:50. This isn’t necessary but may make future calculations easier.

Next we want to list what we know about the new formula, so we add another row that looks like this.

 

Coloring Syrup Water C/S C/W
Original formula 3 75 150 1/25 1/50
New formula 150 X 2/25 1/100

 

The question tells use how the ratios of ingredients change in the new formula – C:S doubles, so we multiply the original ratio by 2, and C:W is halved, so we multiple the original ratio by ½. We know also from the question that the new formula contains 150 parts of syrup. Since we want to find out how many parts are water, we place an X in the appropriate table cell.

Now we have all the information from the question organized neatly, and it’s easier to see how to solve for X, the amount of water in the new formula. We can use the amount of syrup given in the question with the new ratio of coloring to syrup to find the amount of coloring in the new formula. Once we know the amount of coloring, we can use the second ratio to find the amount of water.

Now this question is a simple algebra problem.

[pmath size=16]2/25 = C/150[/pmath]

[pmath size=16]C = 12[/pmath]

Coloring Syrup Water C/S C/W
Original formula 3 75 150 1/25 1/50
New formula 12 150 X 2/25 1/100

 

[pmath size=16]1/100 = 12/x[/pmath]

[pmath size=16]x=1200[/pmath]

The beauty of a table like the one above is that it gives you abilities you may not have known you had. If you had never done a GMAT math solution problem like the one above, you may have figured you don’t know enough to answer it. But by building a table, the question can be broken down so that all you need to solve it is some common sense and multiplication and division skills.

So the next time your facing down a seemingly wicked word problem, don’t panic; draw it out. Use a simple table to help you understand what’s happening, and the problem suddenly won’t seem so difficult.