## Data Interpretation on the GRE Quant

On test day, when you sit down to take your GRE, you will have, among other things, two Quant sections. Each Quant section will have a Data Interpretation problem set towards the end of the section. This GRE Data Interpretation set will present data, information, in some graphical form, and it typically has three questions about the same data. So, you will see about 3 DI questions on each GRE Quant section, so about 6 DI questions on your test—or more if the experimental section is also a Quant section. As you can see, Data Interpretation practice is an important part of your GRE Quant prep.

## Why Data Interpretation?

Why is there Data Interpretation on the GRE? Why is this important? Well, do you know the old adage “*A picture is worth a thousand words*“? Well, a graph is worth even more. Geeky math & techie folks, such as I, absolutely love graphs and charts, because they present an efficient means to convey a truckload of information in way that is directly visually accessible. In our post-modern electronic world, the sheer amount of information available is simply mind-boggling. Graphs and charts are essential for keeping track of all this information.

Here’s one big suggestion for GRE Data Interpretation: if you are not a geeky math or techie person, start looking at graphs & charts. Look in the financial news, in scientific articles, and in international news in general. Most newspapers and news magazines are stuffed to the guppers with graphs & charts. Spend time studying them: each graph, each chart, has a “story” to tell. Spend enough time with each to understand its “story.”

Despite appearances, the GRE Data Interpretation questions are usually relatively easy compared to the rest of the questions on the Quant section. The whole point of graphs is to make information easy to see!

## What You Need to Know for GRE Data Interpretation

The GRE Data Interpretation will present information in any one of a number of visual formats. These include:

(a) pie charts

(b) bar charts

(c) line graphs

(d) scatterplots & best-fit lines

(e) boxplots

(f) histograms (*which are different from bar charts*!!)

(g) charts of numerical data

Of these, pie charts and line charts and charts of numerical data are probably self-explanatory, and there are examples below (pie chart & bar chart in Set #1, line chart in Set #2). Scatterplots and boxplots are somewhat less well-known, and each has its own blog giving more detail; there’s also an example of a scatterplot below, in Set #4.

I will say a few words here about bar charts vs. histograms. First of all, on a bar chart, there’s no particularly important difference whether the bars go horizontal or vertical (a.k.a. a “column” chart); this choice is more a matter of artistic preference in display, but it’s not meaningful for the data. In a bar chart, each bar represents a different item or group. The scale of some numerical variable is parallel to the bars, and the purpose of the graph is to compare the numerical values of the elements represented by different bars.

For example, in this bar chart, each bar is a particular continent, and the length of the bar, measured against the horizontal scale, indicates the area of the continents. For example, this bar chart indicates that Africa has considerably more area than North America, a conclusion not self-evident from a Mercator Projection map of the world.

If we want to show more complicated data, we might use segmented bars or side-by-side bars. You can read this GMAT post about this distinction. Set #3 below uses segmented bars.

A histogram is a chart that happens to use columns, but it is not a bar chart. On a true bar chart, each bar is a different element, and the scale is parallel to the bars. By contrast, on a histogram, the scale is perpendicular to the columns, and each column represents a particular range of the data. For an example, see the post on histograms. While the difference between a bar chart and a histogram is something that probably will be obvious from the problem set-up, this is an important distinction to understand for GRE Data Interpretation.

## GRE Data Interpretation Practice Sets

Try some GRE Data Interpretation practice to get an idea of what you can expect on test day.

### Set #1

The following pie chart shows the breakdown of revenues for a particular grocery store over the first quarter of last year. The bar chart shows the detail of breakdown for frozen foods.

1) What is the dollar amount of sales of canned goods in the first quarter of last year?

(A) $6,000

(B) $9,000

(C) $18,000

(D) $36,000

(E) $90,000

2) Frozen prepared meals constitute what percentage of the total sales for the first quarter last year?

(A) 2.4%

(B) 8.5%

(C) 20%

(D) 36%

(E) 54%

3) During the first quarter last year, this particular grocery store was finishing its construction of an expanded bakery facility, which, when opened at the beginning the second quarter, will offer dozens of new cakes and pies, a whole new line of pastries, and several flavors of gourmet coffee. Assume that in the second quarter, the bakery sales triple, and all other sale stay the same. Bakery would then account for what percentage of total sales in the second quarter?

(A) 12%

(B) 14.3%

(C) 16.1%

(D) 18%

(E) 25.3%

### Set 2

The following graph shows the total revenues and total costs of QN Corporation, a publicly traded company, over the span 2007-2015. Recall that, for any year, profit = (revenue) – (cost).

4) In 2013, the dollar amount of the profit at QN Corporation was approximately which of the following?

(A) $80 million

(B) $160 million

(C) $190 million

(D) $240 million

(E) $350 million

5) From 2010 to 2015, revenue at QN Corporation increased by approximately what percent?

(A) 18%

(B) 47%

(C) 63%

(D) 84%

(E) 126%

6) From 2009 to 2010, profit at QN Corporation increased by approximately what percent?

(A) 81%

(B) 165%

(C) 300%

(D) 433%

(E) 533%

### Set 3

The following chart shows the employee breakdown, number of marketer vs. number of programmers, at six similarly sized companies in a particular internet market. All six have similar sized management teams that are not displayed: all the non-management employees are displayed.

7) At Pindar, there are approximately how many more programmers than marketers?

(A) 6

(B) 22

(C) 35

(D) 57

(E) 73

8) At Jericho, approximately what percent of the non-management employees are marketers?

(A) 28%

(B) 42%

(C) 51%

(D) 66%

(E) 72%

9) If were to take the average number of marketers at five of the companies, excluding Fermion, then this average would be approximately how many employees larger than if Fermion were included in the average?

(A) 6

(B) 13

(C) 20

(D) 26

(E) 33

### Set 4

Fifteen college seniors, none of whom took any math classes in college, were selected for a clinical trial. An online GRE Math Course was made available to them, and these students were allowed to study for however many hours they wanted. Then, each took the GRE for their first time. The graph below records how many hours each student studied, using the online material, and that student’s GRE Quant score. The best-fit line model shows the best prediction, given such a student’s hours of study, of what her GRE Q score might be.

10) Among the students in this trial who studied less than 25 hours, what is the highest GRE Quant score achieved?

(A) 146

(B) 149

(C) 154

(D) 157

(E) 165

11) For the students in this trial with the three highest scores, approximately what is the average number of hours they spend studying?

(A) 29

(B) 32

(C) 35

(D) 39

(E) 43

12) Among the students in this trial who studied for 20 hours or more, what fraction of them performed worse than expected, according to the best-fit line model? Express your answer as a fraction.

## Explanations for Practice Problems

1) This is a straightforward read-data-off-the-chart question. The pie chart tells us canned goods sales constitute 18% of $200,000. Don’t go to the calculator for such a straightforward percent question!

10% of $200,000 = $20,000

Double that.

20% of $200,000 = $40,000

We need an answer that is between those two, closer to $40,000. The only answer choice in that range at all is answer choice **(D)**, $18,000.

Another route to the answer. Obviously 18% of $100 is $18. Multiply both dollar amounts by 1000: then, 18% of $100,000 is $18,000. Now, double both dollar amounts: 18% of $200,000 is $36,000. There! An exact answer with no calculator, all mental math.

Answer = **(D)**

2) From the bar chart, prepared meals account for about $17,000 in sales. This $17,000 is what percent of $200,000? Again, please don’t jump to the calculator for this.

We know that $20,000 is 10% of $200,000. Take half of that: $10,000 is 5% of $200,000. So whatever percent $17,000, it must be between 5% and 10%. There’s only one answer choice in that range.

Answer = **(B)**

3) This is a tricky question, because there’s a tempting wrong answer. The bakery accounts for 6% of the total sales in first quarter, so if you triple that, it’s 18%, right? Wrong! The new amount would be 18% of the total sales in the first quarter, but we want to know what percent would it be of the total sales in the second quarter? That’s a new total because, even though everything else stayed the same, bakery sales increased.

We don’t need to consider the actual numbers: we can just work with the percents. Bakery sales triple from 6% to 18% — that’s the new “part.” Since the bakery goes up 12% from 6% to 18%, and all other sales stay the same, the new total is 112% — that’s the new “whole.”

Because the answers are relatively close, this is a rare problem on which it’s perfectly fine to use the calculator.

Answer = **(C)**

4) This is just a matter of reading numbers directly off the graph. In 2013, it appears that revenue = $350M and cost is about $160M. Subtract those and we get $190M.

Answer = **(C)**

5) In 2010, revenue was $250M, and in 2015, it was about $460M. The change is $460M – $250M = $210M, and we want this as a percent of the starting amount, $250. We don’t need a calculator. Notice that $210M is less than $250M, so the percent is less than 100% (choice (E) is wrong). Two thirds of $240M is $160M, so two-thirds of $10M more, $250, would be less than $170M; thus, $210 is much more than two-thirds of $250. We can eliminate (C) and anything less than that, which leaves only one answer.

Answer = **(D)**

6) We have a few different calculations to do here, but fortunately, the answers are spread out, so we can estimate. In 2009, revenue was about $110M and cost was about $80M, so profit was about $30M. In 2010, revenue was $250M and cost was about $90M, so profit was about $160M. That’s more than 5 times.

This is tricky. If something doubles, that’s a 100% increase. If it triples, that’s a 200% increase. Following this pattern, if something is multiplied by five, that’s a 400% increase, because four identical parts were added to the original part.

In this problem, $160M is more than five times, but less than six times, $30M. Thus, the percent increase has to be between 400% and 500%. The only possibility is **433%**.

Answer = **(D)**

7) At Pindar, the separation of marketers and programmers appears to be at 35, so there are 35 marketers. The top line appears to be at 92, so that’s 92 employees in total. If 35 are marketers, then 92 – 35 = 57 are programmers. How many more programmers than marketers? That’s 57 – 35 = **22**.

Answer = **(B)**

8) At Jericho, the green bar is what percent of the total green/purple bar? Well, if the green part were exactly 2/3, then two of the purple lengths would exactly equal the green length. Clearly, two of the purple lengths are shorter than the full green length, so the green is more than 2/3 of the whole bar, more than 66%. The only option this leaves is 72%.

Answer = **(E)**

9) First, take the average of the five excluding Fermion. Terrene has about 57 marketers; Pindar, about 35; Jericho, about 66; Endor, about 45; and Diomedes, about 52. The average is

average = (57 + 35 + 66 + 45 + 52)/ 5 = 255/5 = 51

Fermion has only 18 marketers. That’s a gap of 33 below the average of the other five. If we included Fermion, this gap of 33 would be divided six ways among the companies, so the new average would be 33/6 less than the original average. That’s a drop of 33/6 = 5.5, which is close to **6**.

Answer = **(A)**

__Trivia about the names of the companies in this set__ (you don’t need to know this for the GRE!) **Terrene** is an archaic English word, long out of use, meaning “*of the earth, worldly*.” Yes, Chris Lele would know this word! **Endor** & **Jericho** are from the Bible. In the first book of Samuel, Saul visits the witch of Endor and it doesn’t turn out well for him; this name, “Endor,” was borrowed by George Lucas for the forest moon in *Return of the Jedi*. Jericho, one of the oldest cities in the worlds, was a mentioned in the both the Hebrew Bible and the New Testament: the walls of Jericho fell to Joshua, and much later, a man traveling to Jericho was beset by thieves and then cared for by the Good Samaritan. **Pindar** (522 – 433 BCE) was a real person, an Ancient Greek poet. **Diomedes** was a hero in Greek mythology who was said to have fought in the Trojan War. A **fermion**, named for physicist Enrico Fermi (1901 – 1954) is a subatomic particle with half-integer spin: the three constituents of the atom (protons, neutrons, electrons) are all fermions; quarks are fermions as well.

10) For this problem, we just have to look in the correct region of the graph.

We ignore all the points that are at 25 hours studied and more: that’s the point on the vertical 25-hour line and all the points to the right—all of those are ignored. The only ones we care about are the ones less than 25-hours. Of these, the highest is the one furthest to the right, at a height of 154. This person studied less than 25 hours and got a GRE Q score of **154**.

Answer = **(C)**

11) The three highest scores, the three highest dots on the graph, are

- a) person with Q = 165 who studied 45 hours
- b) person with Q = 170 who studied 29 hours
- c) person with Q = 169 who studied 44 hours

We don’t need a calculator. Subtract 30 from each hour amount for simplicity. Then we have hours of {15, –1, 14}. The sum of those is 28, and 28/3 = 9.33. Add back 30 now: that’s an average of 39.33. The closest answer choice is **39**.

Answer = **(D)**

12) Again, we have to look in the right part of the graph. We have to look at all the dots to the right of the 20-hour line: these are the only dots that count. Dots above the line are students who exceeded the prediction. Dots below the line are students who fell short of the prediction.

The gray dots on the left are out, because those are times less than 20 hours. Of the remaining dots, the 7 green dots are above the line and 3 red dots are below the line. Ten dots altogether are above the 20-hour line, and 3/10 performed worse than expected.

*Editor’s Note: This post was originally published in April, 2012, and has been updated for freshness, accuracy, and comprehensiveness.*