175 INTRODUCTION TO GRAPHS AND CHARTS Graphs and charts appear in the quantitative section of the exam. Ability Tested You will need to understand and derive information from graphs, charts, and ta- bles. Many of the problems require brief calculations based on the data, so your mathematical ability is also tested. Basic Skills Necessary The mathematics associated with diagrammatic interpretation does not go beyond high-school level. Your familiarity with a wide range of chart and graph types will help you feel comfortable with these problems and read the data accurately. Directions You are given data represented in chart or graph form. Following each set of data are questions based on that data. Select the best answer to each question by refer- ring to the appropriate chart or graph and mark your choice on the screen. Use only the given or implied information to determine your answer. Analysis Remember that you are looking for the best answer, not necessarily the perfect an- swer. Often, graph questions ask you for an approximate answer; if this happens, don’t forget to round off numbers to make your work easier. Use only the information given; never “read into” the information on a graph. Suggested Approach with Samples Here are some helpful strategies for extracting accurate information, followed by some sample graph questions. Team-LRN 176 Part I: Analysis of Exam Areas Skim the question and quickly examine the whole graph before starting to work the problem; this type of prereading will tell you what to look for. Sometimes the answer to a question is available in supplementary informa- tion given with a graph (heading, scale factors, legends, and so on); be sure to read this information. Look for the obvious: dramatic trends, high points, low points, and so on. Obvious information often leads directly to an answer. You may need to scroll the graph to see all the information it contains. Charts and Tables Charts and tables are often used to give an organized picture of information, or data. Make sure that you understand the information that is given. Column head- ings and line items give you the important information. These titles give the num- bers meaning. First, pay special attention to what information is given in the chart. For example, the following chart shows the number of “Burger Sales for the Week of August 8−14.” The days of the week are given along the left side of the chart. The number of hamburgers for each day is given in one column and the number of cheeseburgers in the other column. Samples Questions 1–3 refer to the following chart. BURGER SALES FOR THE WEEK OF AUGUST 8−14 Day Hamburgers Cheeseburgers Sunday 120 92 Monday 85 80 Tuesday 77 70 Wednesday 74 71 Thursday 75 72 Friday 91 88 Saturday 111 112 Team-LRN 1. On which day were the most burgers sold (hamburgers and cheeseburgers)? A. Sunday B. Monday C. Friday D. Saturday E. Tuesday D. To answer this question, you must understand the chart and do some simple computation. Working from the answers is probably the easiest method. A. Sunday 120 + 92 = 212 B. Monday 85 + 80 = 165 C. Friday 91 + 88 = 179 D. Saturday 111 + 112 = 223 E. Tuesday 77 + 70 = 147 Another method is to approximate the answers. 2. On how many days were more hamburgers sold than cheeseburgers? A. 7 B. 6 C. 5 D. 4 E. 3 B. To answer this question, you must compare the sales for each day. Hamburgers outsold cheeseburgers every day except Saturday. 3. If the pattern of sales continues, A. the weekend days will have the fewest number of burger sales next week. B. the cheeseburgers will outsell hamburgers next week. C. generally, when hamburger sales go up, cheeseburger sales will go up. D. hamburgers will be less expensive than cheeseburgers. E. more customers will buy hamburgers than cheeseburgers next Saturday. C. To answer this question, you must notice one of the trends. Most days that hamburger sales go up, cheeseburger sales go up (with the exception of Saturday to Sunday). 177 Introduction to Graphs and Charts Team-LRN Graphs Information may be displayed in many ways. The three basic types of graphs you should know are bar graphs, line graphs, and pie graphs (or pie charts). Bar Graphs Bar graphs convert the information in a chart into separate bars or columns. Some graphs list numbers along one edge and places, dates, people, or things (individual categories) along another edge. Always try to determine the relationship between the columns in a graph or chart. Question 4 refers to the following graph. 4. Candidate 1 has approximately how many more delegates committed than does Candidate 2? A. 150 B. 200 C. 250 D. 400 E. 450 C. To understand this question, you must be able to read the bar graph and make comparisons. Notice that the graph shows the “Number of Delegates Committed to Each Candidate,” with the numbers given along the bottom of the graph in 200 400 Delegates Number of Delegates Committed to Each Candidate Candidate 1 Candidate 2 Candidate 3 Candidate 4 600 800 0 178 Part I: Analysis of Exam Areas Team-LRN increases of 200. The names are listed along the left side. Candidate 1 has approx- imately 800 delegates (possibly a few more). The bar graph for Candidate 2 stops about three quarters of the way between 400 and 600. Now, consider that halfway between 400 and 600 would be 500. So Candidate 2 has about 550. 800 − 550 = 250 Samples Questions 5 – 7 refer to the following graph. 5. The 1994–96 gross receipts of Monster Burger exceeded those of Pizza in a Pot by approximately how much? A. 0.2 million B. 2 million C. 8.2 million D. 8.4 million E. 17 million B. In this graph, there are multiple bars representing each fast-food category; each single bar stands for the receipts from a single year. Gross Receipts of Several Fast-Food Restaurants 1994-1996 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 1994 1995 Monster Burger Gross Receipts Millions 1996 1994 1995 Cruncho Chicken 1996 Pizza in a Pot 1994 1995 1996 179 Introduction to Graph and Charts Team-LRN You may be tempted to write out the numbers as you do your arithmetic (3.5 mil- lion = 3,5000,000). This step is unnecessary, as it often is on graphs that use large numbers. Because all measurements are in millions, adding zeros doesn’t add pre- cision to the numbers. Referring to the Monster Burger bars, you see that gross receipts are as follows: 1994 = 2.5, 1995 = 2.5, 1996 = 3.4 (if you have trouble seeing how the bars line up with the numbers, you may want to use a piece of scratch paper against the screen as a straightedge to determine a number like this last one). Totaling the re- ceipts for all three years, you get 8.4. Referring to the Pizza In A Pot bars, you see that gross receipts are as follows: 1994 = 1, 1995 = 2.1, 1996 = 3 (don’t designate numbers beyond the nearest tenth, because the graph numbers and the answer choices prescribe no greater ac- curacy than this). Totaling the receipts for all three years, you get 6.1. So, Monster Burger exceeds Pizza In A Pot by 2.3 million. The answer that best approximates this figure is B. 6. From 1995 to 1996, the percent increases in receipts for Pizza In A Pot exceeded the percent increase for Monster Burger by approximately how much? A. 0% B. 2% C. 10% D. 15% E. 43% C. Graph questions on the GRE may ask you to calculate percent increase or per- cent decrease. The formula for figuring either of these is the same: ()startingamount follows the word amount of thechange from In this case, you may first calculate the percent increase for Monster Burger. Gross receipts in 1995 = 2.5 Gross receipts in 1996 = 3.4 Amount of the change = 0.9 180 Part I: Analysis of Exam Areas Team-LRN The 1995 amount is the “starting” or “from” amount. "" . . .% starting amount amount of change 25 09 036 36== = Percent increase for Pizza In A Pot: Gross receipts in 1995 = 2.1 Gross receipts in 1996 = 3 Amount of the change = 0.9 "" . . .% starting amount amount of change 21 09 0 428 43ÜÜ= So, Pizza In A Pot exceeds Monster Burger by 7% (43% − 36%). The answer that best approximates this figure is C. 7. The 1996 decline in Cruncho Chicken’s receipts may be attributed to A. an increase in the popularity of burgers. B. an increase in the popularity of pizza. C. a decrease in the demand for chicken. D. predictable slump attributable to the increase in terrorist activity. E. It cannot be determined from the information given. E. Never use information that you know is not given. In this case, the multiple factors that could cause a decline in receipts are not represented by the graph. All choices except E require that you speculate beyond the information given. Line Graphs Line graphs convert data into points on a grid. These points are then connected to show a relationship between the items, dates, times, and so on. Notice the slopes of lines connecting the points. These lines will show increases and decreases. The sharper the slope upward, the greater the increase. The sharper the slope down- ward, the greater the decrease. Line graphs can show trends, or changes, in data over a period of time. Samples Questions 8–9 refer to the following graph. 181 Introduction to Graph and Charts Team-LRN 8. In which of the following years were there about 500,000 American Indians? A. 1940 B. 1950 C. 1960 D. 1970 E. 1975 C. To answer this question, you must be able to read the graph. The information along the left side of the graph shows the number of Indians in increases of 100,000. The bottom of the graph shows the years from 1910 to 1980. Notice that in 1960 there were about 500,000 American Indians in the United States. Using the edge of your answer sheet like a ruler helps you see that the dot in the 1960 column lines up with 500,000 on the left. 9. During which of the following time periods was there a decrease in the American Indian population? A. 1910 to 1920 B. 1920 to 1930 C. 1930 to 1940 D. 1960 to 1970 E. 1970 to 1980 American Indian Population in the United States from 1910 to 1980 700,000 800,000 600,000 500,000 400,000 300,000 200,000 100,000 0 1910 1920 1930 1940 1950 Years 1960 1970 1980 Population 182 Part I: Analysis of Exam Areas Team-LRN A. Because the slope of the line goes down from 1910 to 1920, there must have been a decrease. If you read the actual numbers, you notice a decrease from 300,000 to 250,000. Samples Questions 10–12 refer to the following graph. 10 . Between which two years was the greatest rise in average test scores? A. 1978 and 1979 B. 1979 and 1980 C. 1980 and 1981 D. 1981 and 1982 E. 1982 and 1983 E. The most efficient way to compute greatest rise is to locate the steepest upward slope on the chart. Note that the steepest climb is between 1982 and 1983. Therefore, choice E indicates the greatest rise in average test scores. Average Score (Statewide) on Student Aptitude Test 1978-1983 60% 50% 70% 80% 90% 100% 1978 1979 1980 1981 1982 Years 1983 Scores 183 Introduction to Graph and Charts Team-LRN 11. In which year was the average score approximately 85%? A. 1978 B. 1979 C. 1980 D. 1981 E. 1982 C. According to the graph, the average test score was approximately 85% in 1980 (C). In cases where you must read the graph for a precise measurement, using your answer sheet as a straightedge to more accurately compare points with the grid marks along the side may be helpful. 12 . Approximately what was the highest score achieved statewide on the test? A. 80% B. 85% C. 90% D. 97% E. cannot be determined E. The first thing you should do when confronted with a graph or chart is read its title to understand what the graph tells you. In this case, the graph is relating in- formation about average scores. It tells you nothing about the highest score achieved. Thus, E is the correct answer. Circle Graphs (Pie Charts) A circle graph, or pie chart, shows the relationship between the whole circle (100%) and the various slices that represent portions of that 100%. The larger the slice, the higher the percentage. 184 Part I: Analysis of Exam Areas Team-LRN [...]... answers to each other and approximate Practice Graphs and Chart Problems Set 1 Questions 1–5 refer to the following graphs AVERAGE FAMILY'S EXPENSES 18% Food and Drink 10% Medical 7% nt e inm r ta te En s 5% Saving Other 12% Medical 7%nt e inm r ta te En s 4% Saving Other 25% Housing 1970 Average Income $12,000 188 22% Food and Drink Team-LRN 32% Housing 1975 Average Income $16,000 Introduction to Graph and. .. available? A 16% B 27% C 33% D 48% E 66% 15 If 100 total coins are available for sale, how much more would a collector pay for all the average circulation coins of fine condition than for all the small circulation coins of average condition? A $15 B $25 C $35 D $63 E $88 194 Team-LRN Introduction to Graph and Charts Answers and Explanations for Graphs and Charts Sample Problems Set 1 1 C In 1970, housing... Introduction to Graph and Charts 1 For the year in which the average family’s housing expenses were $3000, what were the average family’s medical expenses? A $600 B $1000 C $1200 D $1920 E $2400 2 What was the approximate ratio of income spent on housing in 1970 to income spent on housing in 1975? A 4 to 7 B 3 to 5 C 25 to 32 D 1 to 1 E 3 to 2 3 What was the percent increase from 1970 to 1975 in the percentage...Introduction to Graph and Charts Samples Questions 13–15 refer to the follow graph 20% in the bank 20% car and bike repair 25% entertainment 15% his hobby 10% 10% misc school items supplies How John Spends His Monthly Paycheck 13 John spends one fourth of his monthly paycheck on A his hobby B car and bike repair C entertainment D school supplies E in the bank C To answer this question, you must be able to read... $100 to $200 B $100 to $150 C $50 to $100 D $30 to $100 E $0 to $30 7 The price range realized in September for a near-mint–condition Mickey Mantle card was A $150 to $400 B $400 to $600 C $440 to $660 D $480 to $720 E $600 to $800 8 At the start of the season, which of the following cards had the greatest ratio of near-mint–condition range to excellent-condition range? A Willie Mays B Whitey Ford C... II only C III only D I and II only E II and III only 192 Team-LRN Introduction to Graph and Charts Set 3 Questions 11–15 refer to the graph below 3% U.S Indian Head Nickels Average Retail Cost 6% 5% 16.60 12.20 8% 10.20 10 % 8.80 10 % 8.80 % Uncirculated 23 3.20 on % 4.30 18 4.90 17 % 6.30 Average nd Co Average Small iti Fine Large Circulation Percentages indicate percent of total coins available for... Introduction to Graph and Charts PERCENT OF REALIZED PRICE PRICE FLUCTUATION DURING SEASON OF 5 SELECTED 1956 CARDS 130% MANTLE 120% YS MA 110% AARON KOUFAX 100% FORD 90% 80% 70% APR MAY JUNE JULY AUG SEPT OCT (start of season) (end of season) 6 At the start of the 1991 season, the price range realized for a 1956 Bob Feller card in excellent condition was A $100 to $200 B $100 to $150 C $50 to $100 D $30 to. .. of coins is irrelevant Since 3%, 5%, and 8% add up to 16%, we have the following: 16.60 × 3% plus 10.20 × 5% plus 8.80 × 8% = 1.712, and 1.712/.16 = 10.70, which is the average price 13 14 D The coin collector previously collected only fine condition coins, or a total of 17% + 10% + 6% = 33% of the coins available for sale Now the collector collecting both fine and uncirculated coins adds another 16%... receipts earned by other restaurants in 1996 amount to precisely how much? A $1,810,650 B $810,000 C $547,500 D $453,150 E $405,000 B In 1996, other restaurants earned precisely 10% 10% of $8,100,000 = $810,000, (B) A PATTERNED PLAN OF ATTACK Graphs and Charts Skim the first question Examine the entire graph Notice headings, scale factors, legends, and dramatic trends Focus on what you are looking for... PP–Pizza In A Pot Introduction to Graph and Charts 16 The gross receipts for 1994 are approximately what percentage of the gross receipts for all three years? A 30% B 46.3% C 46.7% D 50% E It cannot be determined from the information given A You can solve this problem without referring to the graphs; the necessary information is available in the list of gross receipts below the graphs Don’t write out all . 175 INTRODUCTION TO GRAPHS AND CHARTS Graphs and charts appear in the quantitative section of the exam. Ability Tested You will need to understand and. bar graphs, line graphs, and pie graphs (or pie charts) . Bar Graphs Bar graphs convert the information in a chart into separate bars or columns. Some graphs