GRE Charts and Graphs: A Guide to Interpreting Visual Data, Study Guides, Projects, Research of Mathematics

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Chapter 6

Charts and Graphs

THE JOY OF VISUAL DATA

GRE chart questions are pretty straightforward; you read a couple of charts and/or graphs and then you answer some questions about them.

Chart questions appear on a split screen; the chart(s) appear on the left, and the questions are on the right. When a chart question pops up, be sure to start by hitting the scroll bar to see just how much data you’re dealing with. There might be a second chart hidden below the first one, so don’t get thrown off if you see questions about a chart you don’t think exists.

Chart questions test four primary skills:

• how well you read charts
• how well you approximate percentage and percentage change
• how well you calculate exact percentage and percentage change
• how well you synthesize related data from two separate sources

When you have to answer chart questions, there are a couple things to remember.

1. Read all the charts. Before you answer any questions about a set of charts, look over the charts. Make sure you pay particular attention to the units involved. Is each axis in terms of a number of people, a percentage, a dollar amount? Look for a legend for the charts. Are we talking about 100 people, or 100 million people? Check to see if you need to scroll down for any additional charts. If there are multiple charts, spend a minute or so figuring out how the charts relate to each other. Do the charts show different aspects of the same information? For instance, does one chart show the jobs of a group of people, whereas the other chart shows the education level of those same people? Does one chart give more detail about a limited sliver of information from the previous chart? Spending time understanding the charts now will pay off later. 2. Find the information you need. Once you read a Charts question, figure out which chart and which data points you need to look at. 3. Use your scratch paper and label your information. Find the data points you need to answer the question, and write each one down on your scratch paper. Include units and a name for each data point. Don’t just write “23.” Write “2004 imports − 23 mil tons.” It adds only an extra couple of seconds of time, and makes it much less likely that you will make a mistake or get lost in the problem. 4. Estimate before you calculate. Look to eliminate answers before doing too many calculations. If 226 of

the 603 employees were fired, and the question wants to know what percentage were fired, then do a quick

estimation: ≈ 33%. Since we rounded 226 down to 200, our answer will probably be a

bit larger than 33%. Cross off any answers that are 33% or less, or much greater than 40%. If we can’t

choose an exact answer based on our estimation, then we can go back and calculate afterwards.

Percentage Change Quick Quiz

Remember all the reading you did about percentages and percent change in Chapter 3? Well, here are some questions. Let’s see how much skill you’ve retained:

change is or × 100 or 33 %. The correct answer is (B).

2. If a portfolio with $1,600 in it has 30% of the money withdrawn, then the amount of money withdrawn is

× 1,600, or $480. The portfolio has $1,600 - $480, or $1,120 remaining. This can be solved in one

fewer step by recognizing that withdrawing 30% is the same thing as leaving 70%. 70% of 1,600 is 1,120.

The correct answer is (E).

3. The stock portfolio is worth $1,120. Quantity A is the value of the portfolio. Quantity B states the portfolio

increased by 25% then decreased by 25%. If a stock portfolio worth $1,120 increase by 25%, then the

stock portfolio increases by × 1120, or $280, to $1,400. Then, if it lost 25% the value of the stock

portfolio drops from $1,400 to , or $1,050. Quantity A is greater than Quantity B, so the correct answer

is (A).

4. This problem states that a stock portfolio worth $1,600 increases by 200%. Because 200% of $1,050 is $2,100, the new value of the portfolio is $1,050 + $2,100, or $3,.
5. A portfolio that began with $1,200 and ended with $3,150 increased in value by $3,150 – $1,200 = $1,950. To determine the percent increase, divide $1,950 by $1,200 and multiply the result by 100. The portfolio grew 163%. The correct answer is (D).

FOCUS MINIMIZES CARELESSNESS

Reading charts is a lot like interpreting points that are graphed on the coordinate plane. It’s a process that anyone can learn with practice. The worst thing about GRE charts, however, is that they are often intentionally confusing and/or difficult to read, so it’s easy to make careless mistakes under stressful conditions. Above all else, resolve to be calm and systematic when you navigate the data that the GRE throws at you. If you can manage that, the rest should fall into place nicely.

The Formats

Most chart questions come in three formats: bar or line graphs, pie charts, and data tables. Additionally, the test often gives you two separate charts that are somehow related, however remotely.

Data tables are made up entirely of numbers, so all you need to do is crunch the numbers. Graphs and charts can be a little trickier because they require you to interpret them visually.

Bar Graphs

On bar graphs, data points are indicated with rectangular bars that can run either horizontally or vertically. Bar graphs get tricky when one bar contains two or more bits of data that are often colored or patterned differently, like this:

Line Graphs

Line graphs are very similar to bar graphs except they link data points with lines that can indicate overall trends.

Data Tables

Sometimes the GRE does away with graphics altogether and simply presents raw data in several rows and columns.

Ballparking, Redux

Many times, the numbers you’ll work with will be approximations rather than exact calculations. Working well with these approximations is an important skill.

Let’s look at an example: About how much bigger, in terms of a percentage, is the bar on the left than the bar on the right?

Pretty hard to tell, isn’t it? Now look at those same bars placed next to each other:

Now you have a very good (though not necessarily exact) idea of how large each bar is, and you can crunch some numbers to determine the percent decrease from Bar A to Bar B or the percent increase from Bar B to Bar A. Let’s work that into a sample question, shall we?

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Here’s How to Crack It For this question, you can estimate the value of each bar. Bar A is approximately 55; the value of Bar B is approximately 85. Now you can use the percent change formula (divide the change by the original value and then multiply by 100) to find your answer.

The change from A to B is 30, and the original value is 55, so the percent increase is × 100, or approximately

50%. Conversely, the percent decrease from B to A is × 100, or approximately 33%. The answer is (A).

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Here’s How to Crack It The favorable/unfavorable ratings are displayed in the line chart. Look at the line chart for the months in question and determine which month has a difference between favorable and unfavorable ratings greater than 10%. The only month of the answer choices for which is the difference is greater than 10% is March, so the correct answer is (A).

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Here’s How to Crack It Now look at the pie charts, because they’re the ones that reference the party affiliations of those polled. The November pie is on the far right, and 45% of the 1,340 people said they belonged to party Y. Because 1,340 × 0.45 = 603, the answer is (C).

And that’s the basic idea behind Charts questions. The wall of data is supposed to be intimidating, especially under test-taking pressure. But if you pay attention, keep your cool, and work methodically—and keep practicing—you’ll find they can be very approachable.

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Company X spent more on copper than it did on iron in 1975. The price per ton of copper was more than that of aluminum in 1990. Company X purchased fewer tons of iron in 1990 than it did “Other” metals in 1990.

Questions 6−10 refer to the following graphs.

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Questions 11−15 refer to the following graphs.