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gMaT HANDBOOK INTEGRATED REASONING SECTION
July 2012
«To know and to will are two operations of the human mind. Discerning, judging, deliberating are acts of the human mind.» Leonardo da Vinci
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Contents Graph Interpretation.................................................................................................................... 3 Home assignment.................................................................................................................. 17 Answers and explanations..................................................................................................... 19 Table Analysis............................................................................................................................ 20 Home assignment.................................................................................................................. 27 Answers and explanations..................................................................................................... 29 Two-Part Analysis...................................................................................................................... 30 Home assignment.................................................................................................................. 36 Answers and explanations..................................................................................................... 37 Multi-Source Reasoning........................................................................................................... 39 Multi-Source Reasoning. Example 1...................................................................................... 41 Multi-Source Reasoning. Example 2...................................................................................... 44 Multi-Source Reasoning. Example 3...................................................................................... 48 Home assignment.................................................................................................................. 50 Answers and explanations..................................................................................................... 53 Vocabulary list for IR................................................................................................................. 55
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Graph Interpretation A graph is a visual representation of numeric values. People who create charts usually do so to make a point or to communicate a specific message. Often, the message is explicitly stated in the chart’s title or in a text box within the chart. In almost every case, the underlying message in a chart is some type of comparison. Examples of some general types of comparisons include •
Compare item to other items: for example, a chart may compare sales in each of a company’s sales regions.
•
Compare data over time: for example, a chart may display sales by month and indicate trends over time.
•
Make relative comparisons: an example is a common pie chart that depicts relative values in terms of pie “slices.”
•
Compare data relationships: For example, you might show the relationship between marketing expenditures and sales.
•
Frequency comparison: for example, to display the number (or percentage) of students who scored within a particular grade range.
•
Identify “outliers” or unusual situations: If you have thousands of data points, creating a chart may help identify data that is not representative.
TIME: you have an average of 2 minutes and 30 seconds for each IR question in the section, but some question types are more complicated than others. The recommendation is trying this one for 1.5 to 2 minutes initially, as it is shorter than some of the other question types.
Format Graph Interpretation has the widest variety of possible ways in which the information can be presented. All information will be presented visually, in a graph or a chart. Often there will be at least a small verbal prompt accompanying the graph or chart, and sometimes a detailed verbal explanation is given. One part of one chart may be detailed by another chart: for example, a single column in a column graph might be shown broken down into subdivisions in a pie chart. All GI questions involve drop-down menus. The question prompt will be a sentence, and at some point in the sentence there will be a gap; in the gap will be a drop down menu with 3-4 choices. Each GI question typically will have one or two sentence prompts, always with a total of two dropdown menus. You must get both correct to earn credit for the question, as there is no partial credit on the GMAT IR.
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Types of graphs To understand graphs more clearly you should be familiar with graph types. Let’s consider them in details.
Pie charts or circle graphs A pie chart (or a circle graph) is a circular chart divided into sectors, illustrating proportion. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. Together, the sectors create a full disk. A pie chart is useful when you want to show relative proportions or contributions to a whole. Example 1: Study the following pie chart and answer the questions given below (fractions of students who prefer each of the six beverages, expressed in degrees):
If there are 6800 students in total, then: • The difference between the total number of students who prefer Beverage A and C and the total number of students who prefer Beverage D and F is Answer choices: 3428 955 952 954 14 • The ratio between the number of students who prefer Beverage F and the number of those who prefer Beverage A is Answer choices: 3:11 3:13 6:11 5:11 30:11
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Explanation: Statement 1: Angle for Students who prefer beverages A and C is equal to 79.2°+14.4°=93.6°. Angle for Students who prefer beverages D and F is equal to 122.4°+21.6°=144°. Difference between the total number of students who prefer A and C and the total number of students who prefer D and F is 144°–93.6°=50.4°. Since the central angle for the whole circle is 360°, which corresponds to 6800 students, 50.4° will correspond to (50.4°)/(360°)x∙6800=(504∙68)/36=(56x68)/4=14x68=952. Statement 2: A lot of test takers will actually calculate the number of students who prefer beverage F and beverage A and then will find the actual ratio: The number of students who prefer beverage F is equal to 21.6/360 x6800=(216x68)/36=6x68=408. The number of students who prefer beverage A is equal to 79.2/360 x6800=(792x68)/36=22x68=1496. Ratio of these numbers is 408/1496=102/374=51/187=3/11. But if you notice, that in a pie chart the central angle of each sector proportional to the quantity it represents, so the ratio of the numbers of students is equal to the ratio of their corresponding degrees, you can solve the problem easier: 21.6/79.2=3/11.
Bar graphs A bar chart (or bar graph) is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. Quantities can be compared by the height or length of a bar in a bar graph. You can compare different quantities or the same quantity at different times. Use your pencil or a piece of paper to compare bars that are not adjacent to each other. Example 2: The graph below shows the number of patients who visited three hospitals in a particular week:
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• What was the average (arithmetic mean) number of patients per hospital in the week? 250 265 275 300 • Which hospital records the maximum number of patients in the week? Hospital A Hospital B Hospital C None Explanation: Statement 1: We just need to find the total number of patients in all three hospitals and then divide by three. The total number of patients in Hospital A (blue bars) is 70+50+35+25+40+30+40=290. The total number of patients In Hospital B (red bars) is 60+45+25+30+30+35+30=255. The total number of patients In Hospital C (green bars) is 50+50+40+20+25+30+40=255. Hence, the average number of patients per hospital was (290+255+255)/3=800/3≈266,6. The answer is 265 patients. Hint (estimate): Actually, you can just summarize approximate average numbers of patients in each day: 60+50+30+25+30+30+35=260. Statement 2: This can be found by just adding up all the patients in the week for each hospital. From statement 1 we know that Hospital A recorded the maximum number of patients in the week. Alternatively, you can just see on the graph that almost every day of the week Hospital A was leading by the number of patients. The answer is Hospital A.
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Line graphs A line chart (or line graph) is a type of chart, which displays information as a series of data points connected by straight line segments. Line graphs are used to show how a quantity changes continuously. Very often the quantity is measured as time changes. If the line goes up, the quantity is increasing; if the line goes down, the quantity is decreasing; if the line is horizontal, the quantity is not changing. To measure the height of a point on the graph, use your pencil or a piece of paper (for example, the edge of the test booklet) as a straightedge. Example 3: This graph shows stock prices, in dollars, for two companies A and B.
• In May, the value of stock A was what percentage less than the value of stock B? 10% 15% 20% 25% • In which month did the sum of share prices of A and B increase by maximum value over its value in the previous month? March May June December
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Explanation: Statement 1: In May, the value of stock A was 12 dollars while the value of B was 16 dollars. In percentage, the value of stock A is less than that of stock B by (16-12)/16x100% =25%. The answer is 25%. Statement 2: Month January Feb March April May June July August September October November December
Share Price of A 14 14 14 14 12 13 14 12 15 13 12 12
Share Price of B 16 12 20 19 16 19 14 17 15 16 19 12
Sum 30 26 34 33 28 32 28 29 30 29 31 24
Difference -4 8 -1 -5 4 -4 1 1 -1 2 -7
From the table above, we can see that in March, the sum of the stocks increased by the maximum amount (8) over its value in the previous month. Hint (Estimate). Since there are only 4 possible answers, to answer the question we should consider only four month: March, May, June and December. In March the share price of A was unchanged over its value in the previous month, and the share price of B increased by 8$. So the sum of share prices of A and B increased by 8$. In May and December both share prices of A and B decreased. Hence, we don’t consider them at all. In June the share price of A increased by 1$, and the share price of B increased by 3$. So the sum of share prices of A and B increased by 4$. The correct answer is March.
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Scatterplot A scatter plot (or scatter graph) is a way of displaying bivariate data: that is, data in which we measure two different variables for each participant. For example, suppose we ask several people both their age and their weight, or both their annual income and the amount of debt they carry, or both their number of kids and number of credit cards; etc. In all of those cases, each individual would be a single dot on the graph, and the graph would have as many dots as individuals surveyed or measured. This type of chart is often helpful in suggesting whether it is likely to be possible to find any significant statistical relation between the two characteristics, and what type of function it is worth trying to fit. It also draws attention to any outlying observations which may merit special investigation. One reason we graph data in a scatter plot is because we are looking for patterns. The simplest of all possible patterns to find on a scatter plot is a straight line pattern. When the points on a scatter plot lie more or less in a straight line, it is called correlation. When it’s a straight line with a positive slope, going up to the right, that’s positive correlation, and when, it’s a line with a negative slope, that’s negative correlation. To say that A and B have a positive correlation is to say that when A goes up, B goes up.
A trend line (regression line) is a line that is drawn over pivot highs or under pivot lows to show the prevailing direction of price. Trend lines are a visual representation of support and resistance in any time frame. A trend line points out general trends in the data. When you want to predict future data on your chart, you may want to use something called trend line. Trend lines help you see how your data may look like in the future.
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Example 4: A group of boys aged 7 to 10 had their heights measured and recorded. The results are below. The line drawn is the calculated trend line.
Age v Height
HEIGHT (in inches)
65 60 55 50 45 40 35 30 25 6.5
7
7.5
8
8.5
9
9.5
10
10.5
AGE (in years)
• The correlation between age and height for this group seems to be Positive Negative None Undefined • If a boy is between 8 and 8.5 years old with a height of 46 inches, he is above below at his age’s average height. • If a new boy was measured, and he was almost 10 and was 30 inches tall, he would be around 1.6 1.8 1.9 2.1 times shorter than average. Explanation: Statement 1: Since the data tends to rise from left to right, the correlation is POSITIVE. Statement 2: Looking on the AGE axis between 8 and 8.5 and going vertically up, the trend line (average) looks to be around 48 inches, so this child would be BELOW average. Statement 3: At a little under 10 years old, the average is around 58 inches. Since the new boy is 30 inches, he would be around 57/30=1.9 times shorter than average.
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Bubble Chart A bubble chart is a type of chart where each plotted entity is defined in terms of three distinct numeric parameters. On a bubble chart, the center of the “bubble” is exactly like a dot on a scatter plot — it shows you the value of a horizontal and vertical variable. The size of the bubble adds a third variable. In fact, the very point of bubble charts to display data points, each of which has a value in each of three different variables. Bubble charts provide a quick way to visually display what is going on with three different variables at once. Example 5:
The six regions in which Techtyx Appliance Company sells appliances are labeled A through F in the graph. The size of each circle and the corresponding number in the circle indicate the proportion of Techtyx customer transactions in that region. The position of each circle’s center relative to the vertical axis shows how many different product types are marketed in the region, and the position relative to the horizontal axis shows last year’s sales in thousands of euros for the region. For each of the following, use the drop-down menu to create the most accurate statement on the basis of the information provided. • Among the six regions, the one with the most Techtyx customer transactions ranks first second third fourth in the number of product types marketed there. • The region for which the value of the average transaction was the greatest is region A C E F
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Explanation: Statement 1: The graph indicates the relative number of customer transactions by the size of the circles and the number within – with larger circles and numbers indicating a greater proportion of Techtyx’s total transactions. The region with the most transactions, C, is lower on the vertical axis than D, E, and F, indicating that C has the fourth greatest number of product types marketed there. The correct answer is fourth. Statement 2: The value of the average transaction in a region can be derived by dividing the total sales in that region by the number of transactions in that region. Though we do not have sufficient information to determine the number of transactions in a given region, we do know the relative proportions of all of Techtyx’s transactions. Therefore, the region with the greatest average transaction value would be the one with the largest ratio of sales to proportion of total transactions. For A, that ratio is 500/0.29≈1,724; for C, 800/0.33≈2,424; for E, 700/0.05≈14,000; and for F, 900/0.15≈6,000. The correct answer is E.
Flow chart A flowchart is a type of diagram that represents an algorithm or process, showing the steps as boxes of various kinds, and their order by connecting these with arrows. This diagrammatic representation can give a step-by-step solution to a given problem. Process operations are represented in these boxes, and arrows connecting them represent flow of control. Example 6:
The flowchart represents a mathematical algorithm that takes two positive integers as the input and returns a positive integer as the output. Processes are indicated in the rectangular symbols in the flowchart. Each process is symbolized by an equation, such as T=T+a. In this particular process, the current values of the variables T and are added together and the sum then becomes the value of T. For example, if the value of T is 3 and the value of is 7 before the process T=T+a is completed, then the value of is 10 and the value of T is 7 after the process is completed. Use the drop-down menus to fill in the blanks in the following statements based on the algorithm represented by the flowchart. • If 24 and 35 are entered as the values for a and b, respectively, then the first nonzero value of T is 24 48 96 192 384
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• If 35 and 27 are entered as the values for a and b, respectively, then after the process b=b/2 is completed for the second time, the value of b is 3 6 12 13 26 Explanation: To solve this problem, you should just go through diagram carefully, step by step: Statement 1. Step 1. T=0 Step 2. a=24 and b=35 Step 3. Is b odd? The answer is YES Step 4. T=T+a=0+24=24 And you should stop, because now you have positive value of T. T=24 Statement 2. Step 1. T=0 Step 2. a=35 and b=27 Step 3. Is b odd? The answer is YES Step 4. T=T+a=0+35=35. Step 5. b=b-1=27-1=26 Step 6. a=2a=2*35=70 Step 7. b=b/2=26/2=13 (first time!). Step 8. Is =1 ? The answer is NO. Step 9. Is b odd? The answer is YES. Step 10. T=T+a=35+70=105 Step 11. b=b-1=13-1=12. Step 12. a=2*a=70*2=140 Step 13. b=b/2=12/2=6 (second time!) So you should stop, because now you have completed b=b/2 for the second time. b=6.
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Radar chart A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point. The relative position and angle of the axes is typically uninformative. Example 7: The graph below shows the actual and expected revenues for the period January to June 2011. The green color shows the actual value while the violet color shows the expected revenue. All values are in ‘000 dollars.
• In which month, the difference between the actual and expected revenues is the highest? January February March June • What is the growth of the actual revenue (in percentage) from January to June? 60% 86% 100% 200% Explanation: Statement 1: From the graph, we can see the difference between the green point and the violet point is highest for June (approximately 260-170 =90) when compared to all the other months. Statement 2: The actual revenue in January was 140, while it was 260 in June. Hence, the % increase was ((260-140))/(140×100)=120/(140×100)=86%
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Graphics Interpretation strategies and tips 1. Estimate! Estimation is crucially important on GI. You need not read the precise value on the graph if the value is, for example, between ticks --- as a general rule, getting in the right ballpark will be enough to determine the correct answer. If you see the words “is nearest to”, “is closed to”, etc., that’s a clear invitation to estimate. 2. Get familiar with the graph types Practice reading the various graph types: get acquainted with what each graph does and doesn’t show. Practice reading graphs --- in the Economist magazine, in the Wall Street Journal, in the New York Times; any graph that appears in those news sources is an exemplar of what could appear on the GMAT. 3. Read all text carefully Any verbal information that comes with the graph should not be skimmed: read it word for word, as carefully as possible. Look very carefully at how the graph is labeled (title, axis labels, etc.) --- for example, it is in amounts or percents? If there are different marks or different colored dots on the graph, make sure you understand what each one means. Don’t be afraid of the simple answer. Don’t automatically assume you are doing something wrong just because it’s something a thirdgrader could do! That’s the nature of graphs! The math is there to see! 4. Invest some time up front analyzing the display Before you tackle the question(s), take at least 15 seconds to assimilate and make sense of the graphical display(s). Read all the information around each display. Get a sense for what the variables are and how they relate to one another. And in the case of two displays, ask yourself how they relate to each other. 5. Don’t confuse percentages with raw numbers. Always ask yourself which type of number the display is providing, and which type the question is asking for. 6. Don’t try to understand or learn everything about the graph. Know how it works and what kind of information it gives, but that’s it. You don’t need to take down a bunch of notes about the details of the graph, though there may be times that you’ll want to jot down a note about how the graph works. 7. Ask yourself: what data do I need to solve? Graphs and tables often give us extraneous information. You will not need everything to solve. Chances are the correct answer hinges on just 1 or 2 numbers from the data. Most people get Data Interpretation questions wrong because they do not know what data to use to solve, not because the Math involved is difficult. You will likely only be performing calculations as simple and easy as addition, subtraction, multiplication and division.
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Sample Problem: An optometrist compiled the following data about his patients.
◊◊◊◊ Wears Contacts
◊
◊
◊ ◊ ◊
◊ ◊
◊
Colorblind
◊ ◊
◊ = 5 patients
◊ ◊
◊ ◊
◊ ◊
Near-sighted -
• If a patient was randomly selected, the chance that he or she wears contacts, or is colorblind, or both is 1 in 4 3 in 4 1 in 7 7 in 10 • If a patient was randomly selected, the chance that he or she is both near-sighted and color blind is 1 in 20 3 out of 10 3 out of 20 11 out of 20
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Home assignment Problem 1
The graph represents the Wolf and Moose population on an Island from 1958 to 1996. 1. Increases in the moose population always correspond to Increases Decreases No change Intermediate in the wolf population. 2. In 1980, there were around half twice eight times sixteen times as many moose as wolves Problem 2 The following figure is showing the total Revenues and Expendictures of France in the year 1995 (in Billion).
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1. What percentage of the total Revenues was collected through Excise Tax? 12.54 % 14.54 % 15.54 % 13.54 % 2. What will be the percentage of expenditures on National Security of the total expenditures if the Government of France also tried to save money of $6 Billion in that year by keeping all the other expenditures and sources of revenues the same? 30.37 % 31.45 % 32.89 % 33.56 % Problem 3 The following figure shows the day by day earnings of two different organizations i.e. A and B in a week. The vertical line is showing the amount earned in dollars and the horizontal line is showing the days of the week. Analyzing the graph shown below answer the questions given
1. Throughout the week, Organization A Organization B earned more money. 2. Considering the trends in days Monday, Tuesday and Friday, Organization A Organization B was the lower earner
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Answers and explanations Sample problem Since there are 20 rhombuses, and each rhombus represents 5 patients, there are 100 total patients. Statement 1: Since “or” is used, we must count the total in either of the circles. There are 14 in total, this represents 70 patients. 70 out of 100 reduces to 7 in 10. Statement 2: Since “and” is used, we must only count those that are in both the near-sighted and the colorblind circles. Since there are 3 rhombuses, this represents 15 patients. 15 out of 100 reduces to 3 out of 20. Home assignment Problem 1 Statement 1: While one might expect the populations to be negatively correlated, and in general it is, there are certain points, like around year 1965, where the populations both increase. Yet around 1991, they are both decreasing. Around 1987, the moose is increasing while the wolf is decreasing. This all leads to not being able to make a correlation. Statement 2: Reading the graph, there are around 800 moose and 50 wolves. This means the moose to wolf ratio is around 800/50, or 16. Problem 2 Statement 1: Total Revenues = $ (70+32+20+6+92) Billion = $ 220 Billion Part of Revenue collected from Excise Tax = $32 Billion Percentage of Revenue collected from Excise Tax = 32/220×100 = 14.54% Statement 2: Total Expenditures as given in the figure = $(34+71+47+68) Billion = $220 Billion Savings = Revenues – Expenditures; 6 = 220 – Expenditures Expenditures = 220 – 6 = 214 Hence, the expenditures must be decreased by $6 Billion in the National Security because all the other Expenditures are the same. So, Reduced expenditures of National Security = 71-6 = $65 Billion Percentage of Reduced expenditures of National Security = 65/214×100 = 30.37 % Problem 3 Statement 1: Organization A The amounts of money earned by organization A on all the days, except Monday and Friday, are much higher than that of organization B by much larger values Statement 2: Organization B On Monday, organization A earned about $16,000 and organization B earned about $20,000. On Tuesday, Organization A earned about $26,000 and organization B earned about $10,000. On Friday, Organization A earned about $12,000 and organization B earned about $16,000. So the total amount of money earned by Organization A (i.e. $54000) is higher than that of organization B (i.e. $46000).
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Table Analysis When you look at the Table Analysis question for the first time, you will probably think, that is looks very much like an Excel spreadsheet you deal with every day. The question then is “What functions does the table on the GMAT have?” And the answer is that the table can be sorted on any of its columns by selecting the column’s title from a drop-down menu – that’s it. What is really tested is the ability to sort data and interpret the results as well as the implications. You will be provided with a table and some additional information on the Table Analysis questions. Sort and analyze the data to answer a series of questions. Note, that some superfluous information may be given. The test takers must be able to efficiently assimilate and manipulate the data to determine the correct answers. That is how the GMAC explains the purpose of the table analysis questions: “An individual’s ability to handle Table Analysis questions will give you a clear sense of how well that potential student can use multiple sources of information to spot patterns and draw conclusions.” TIMEING: you will have 30 minutes to complete the Integrated Reasoning section, or an average of 2 minutes and 30 seconds to answer each question. Keep in mind, however, that each Table Analysis question has three parts that all need to be answered in the time allowed. The question presents three phrases, statements, numerical values, or algebraic expressions, and you must indicate for each one whether or not it meets a certain condition. For example, you may be asked whether • each statement is true (yes or no), according to the information in the table • each statement or numerical value is consistent or inconsistent with the information in the table • each statement or numerical value can or cannot be determined on the basis of the information in the table
Helpful tips for Table Analysis questions 1. Be sure to understand the nature of the numbers in each column and their interrelationship. Some column-heading will provide completely self-evident descriptions, but if accompanying text appears, you will need to read it carefully to determine the exact meaning of at least some of the columns. 2. Read the question carefully. The question presents the condition that each phrase, statement, numerical value, or algebraic expression does or does not meet (for example, is or is not consistent with the information provided, or can or cannot be inferred from the information provided). If you clearly understand the condition, you will find it easier to understand what choice you need to make. Some of the questions require your quantitative skills, others involve subsets, conditions or text analysis which are not necessarily mathematical.
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3. Read each phrase, statement, numerical value, or algebraic expression carefully to determine the data analysis required. Often sorting the table by one of the columns clarifies the relationship indicated in the phrase, statement, numerical value, or algebraic expression. Careful reading will help you to choose the most informative way of sorting the table. 4. Analyze each phrase, statement, numerical value, or algebraic expression carefully considering the condition specified. For each phrase, statement, numerical value, or algebraic expression, the two answer choices (such as yes or no, true or false, consistent or inconsistent) are mutually exclusive. Thus, you need to figure out whether or not the given condition has been met. Example 1: The table displays the composition of the team XYZ in the Champions League. There are players from 8 countries as shown below. Country England Brazil Germany France Italy Portugal Greece Argentina
Number of Football Players 4 5 4 6 6 8 5 6
Age greater than 30 2 2 1 5 2 6 1 2
Average Experience (in years) 3 4 5 5 3 4 3 3
For each of the following statements, select true, if the statement can be proved true with the above data. Otherwise, select False. Statement
True
False
No more than one fourth of the XYZ players come from the same country Portugal has the maximum ratio of players more than 30 years old to the players less than 30 years old. The total experience of all the players is highest for Portugal
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Let’s now solve the question above. 1. No more than one fourth of the XYZ players come from the same country (Infer) The total number of players in the team is 44. Hence, one fourth of the players is 11. Sorting the table by the column “Number of Football Players”, we get Country Germany England Greece Brazil Italy Argentina France Portugal
Number of Football Players 4 4 5 5 6 6 6 8
Age greater than 30 1 2 1 2 2 2 5 6
Average Experience (in years) 5 3 3 4 3 3 5 4
It’s clear, that the maximum number of players who come from one country is 8. Since no country is represented by more than 11 players in the team, the first statement is true. The table here is quite small, so it’s easy to find the maximum number of players without sorting, but in case of a bigger table sorting would be extremely helpful. 2. Portugal has the maximum ratio of players more than 30 years old to the players less than 30 years old. (Infer) Let’s sort the table by the column “Age greater than 30”. It will not give us the answer, but will help to quicker estimate the ratios. Country Germany Greece England Brazil Italy Argentina France Portugal
Number of Football Players 4 5 4 5 6 6 6 8
Age greater than 30 1 1 2 2 2 2 5 6
Average Experience (in years) 5 3 3 4 3 3 5 4
The maximum ratio of players more than thirty years old to players less than thirty years is for France as 5 of the 6 players have more than 30 years. The ratio 5/1 is higher than that of Portugal 6/2. Here the answer is FALSE.
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3. The total experience of all the players is highest for Portugal. (Infer) The total experience of all the players can be obtained by multiplying the number of players by the average experience. Here we can sort the table by the column “Number of Football Players” or by “Average Experience (in years)”. But as the number of players range is greater, than that of the years of experience, the sorting by the column “Number of Football Players” will be more informative for us:
Country Germany England Greece Brazil Italy Argentina France Portugal
Number of Football Players 4 4 5 5 6 6 6 8
Age greater than 30 1 2 1 2 2 2 5 6
Average Experience (in years) 5 3 3 4 3 3 5 4
Portugal has the highest experience with 8 × 4 = 32 years. All other countries have less than that, so the answer is TRUE. Below are examples of the quantitative skills you may need to analyze the table: • determine statistics such as mean, median, mode, or range • determine ratios, proportions, or probabilities • identify correlations between two sets of data • compare an entry’s rank in two or more of the table’s categories All these skills have been covered in your preparation for the quantitative section, except for the identifying the correlation.
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Example 2: Study the following table that shows the distribution of shares of a certain company. Consider the cost of each share to be $10. For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table, otherwise select No. No. Of shares per person 100-500 600-1000 1001-2000 2001-3000 3001-4000 4001-5000 5001-10000 10001-20000
No. of shareholders 800 55 22 17 9 4 2 2
Total number of shares 399745 44000 28000 45000 35000 18000 13000 25000
Yes No There are exactly 55 persons each of whom holds exactly 800 shares. Any shareholder chosen at random from all these people will hold at least minimum 200 shares.
There is a positive correlation between the total number of shares and the number shareholders.
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Explanation: 1. (Infer) Clearly we are referring to the second category here. This data should be read carefully. This means that there are 55 people of whom each holds a minimum of 600 shares and a maximum of 1000 shares, but we are not given any data about individual shareholding, so this cannot be inferred. The answer is No. 2. (Infer) We have to refer to the first line here because the remaining lines are about shareholders who have more than 200 shares each. If the shares of 1 person from the first line have to be minimized then we have to maximize the shares of all the remaining people in that group i.e. out of 800 people, if we increase the share of 799 people to 500 shares each, then the last person will have minimum share left. So minimum shares possible = 399745 - 799500 = 245. The answer is Yes. 3. (Recognize) Let’s sort the table by the “Total number of shares” No. Of shares per person
No. of shareholders
Total number of shares
5001-10000
2
13000
4001-5000
4
18000
10001-20000
2
25000
1001-2000
22
28000
3001-4000
9
35000
600-1000
55
44000
2001-3000
17
45000
100-500
800
399745
A positive correlation between the 2nd and the 3rd column now means, that as the Total number of shares increases, the No. of shareholders increases as well. Obviously, it is not true. In fact, there is no correlation between the number of persons and the total number of shares.
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Sample Problem: There are four movie stores in town. The table below shows the in town movie rentals and sales breakdown by genre at Mark’s Movie Emporium. Genre Action Animation Comedy Documentary Drama Family Romance Sci-Fi ‘;[‘Suspense
Rentals % 30 10 43 50 23 13 56 32 5
Rentals Rank 3 4 2 1 2 3 1 2 4
Sales % 32 15 29 38 25 12 60 40 8
Sales Rank 2 3 3 2 1 4 1 1 4
For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table. Otherwise select No. Yes No For all genres that Mark’s leads in rentals, it does not always lead in sales. All the other stores combined rent more Documentaries than Mark’s. No single store rents more than 25% of the town’s Drama movies.
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Home assignment Problem 1 Refer to the table given below to answer these questions. For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table, otherwise select No. Country
China Australia America Germany Kenya India Yes
Production and consumption of Stone Production(million Per Capita tonnes) Consumption(in Kg) 1988 1989 1988 1989 84.89 87.80 689 631 38.32 39.72 656 582 129.28 123.01 483 388 33.50 35.47 520 482 29.06 28.89 506 447 19.56 18.26 32 25
No In 1989, the maximum reduction in per capita consumption of stone took place in India. Since the production of stone increased in China from 1988 to 1989 but the per capita consumption reduced, so this implies that population of China has increased from 1988 to 1989. There are 3 countries whose production in the year 1988 is more than the average of all the six countries for the year 1988.
Problem 2 Refer to the table given below to answer these questions. The table shows the number of Items (in thousands) manufactured (M), rejected (R) and sold (S) by five different companies over the years. Company Year 2001 2002 2003 2004 2005 2006
M 136 164 148 156 168 175
A R 1.2 1.7 1.5 2.2 2.5 2.8
S 125 138 136 145 160 168
M 98 115 152 147 138 168
B R 0.5 1.1 2.6 1.8 1.3 2.2
S 90 102 132 140 129 148
M 165 172 169 178 158 180
C R 3.5 2.9 2.3 3.2 1.8 2.4
S 158 166 160 172 152 171
M 158 169 173 166 159 171
D R 1.5 1.9 2.3 2.1 2.0 2.4
S M 149 85 162 96 168 88 159 102 150 86 165 105
E R 0.6 0.8 0.5 0.9 0.7 0.8
S 80 90 83 98 81 101
• What is the percentage (rounded off to two digits after decimal) of items rejected out of the total items manufactured by company B in the year 2003? Select.... • How many items remained unsold out of the accepted items by Company A in 2004? Select....
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• What is the total number of items accepted by all the five companies together in 2002? Select.... • Approximately, what was the average number of items rejected by company D for all the given years? Select.... Problem 3 The following table shows that United States Electricity producers of the year 2009. Electric Producers Coal # 1 149,156 Natural Gas#3 84,098 Nuclear 69,435 Hydroelectric 28,866 Other Renewables 10,667 Wind 4,957 Wood & Wood Derived # 5 3027 Petroleum Liquids # 2 2092 Other Biomass # 6 1420 Geothermal 1170 Petroleum Coke 1159 Other Sources # 8 958 Other Gases #4 864 Solar Thermal, Photovoltaic 94 Hydro Pumped Storage -226 Total 347,069 Sectors
Public Utilities 113,180 32,438 36,633 26,386 965 620 145 1662 101 99 478 48 7 2 -139 211,656
Independents 34,363 45,150 32,801 2291 7424 4337 782 296 1141 1071 567 553 243 92 -87 123,690
Other Producers 90 322 0 10 143 0 2 10 141 0 0 67 0 0 0 642
Number of Producers 1243 6157 0 180 3136 0 2099 125 37 0 114 312 615 0 0 10,881
1. Independents producers in United States used the geothermal resources better than other producers. Yes No 2. Using the resources Natural Gas#3, Nuclear and Hydroelectric, the production capacity of Public Utilities is higher than that of Independent producers. Yes No
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Answers and explanations Sample Problem Answers: Yes, No, No For the first, you must look at the genres it leads in rentals: Documentaries and Romance. Since Mark’s ranks 2nd in Documentaries, the answer is yes, it does not always lead sales. For the second, since Mark’s rents 50% of the Documentaries, all other stores combined can add up to no more than 50%. This does not exceed more than Mark’s, so the answer is no. For the third, the three other stores combined rent 77%. We know that Mark’s is second in this category, so the leader could easily rent over 25% in this genre, so the answer is no. Problem 1 No The maximum decrease happened in America i.e. 483 – 388 = 95. No Nowhere is it mentioned that all the stone produced in a country in consumed in the country i.e. it can be exported also, so it is possible that China exported more stone in 1989 even though the population might have decreased/remained the same. No Average production in 1988: (84.89+38.32+129.28 + 33.50+29.06+19.56)/6 = 334.61/6 = 55.768 So only 2 countries exceed the average production. Problem 2 Rejected items by company B in 2003 : 2.6 Total manufactured: 152 So percentage: 2.6/152 X100=1.71% Unsold items: 156-2.2-145=8.8 thousands i.e. ANSWER = 8800 Number of items accepted by all companies: 162.3+113.9+169.1+167.1+95.2 =707.6 ANS 707600 Total items rejected by D over the years: 1.5+1.9+2.3+2.1+2.0+2.4 =12.2 Avg: 12200/6=2033.33 Problem 3 1. The capacity of production of Independent producers was 1071 while that of Electric producers is 1170 so Electric producers used the geothermal sources in the best way. 2. The production capacity of Public Utilities using Natural Gas#3 is 32,438, using Nuclear resources is 36,633 and using Hydroelectric resources is 26,386 making the whole capacity by these three sources 95,457. The production capacity of Independent Producers using Natural Gas#3 is 45,150, using Nuclear resources is 32,801 and using Hydroelectric resources is 2291 making the whole capacity by these three sources 80,242. Hence, production capacity of Public utilities is higher than that of Independent Producers.
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Two-Part Analysis Two-Part Analysis questions present a brief written scenario or problem and ask you to make two choices related to that information. These choices are connected to each other in some way; for example, they might be two steps involved in solving a problem or two components required to successfully complete a task. In Two-Part Analysis questions you may be asked to, for example, • Calculate the proportions of two different components in a mixture • Determine something that would be lost and something that would be gained in a trade-off • Find the maximum number of two different products that could be purchased within a certain budget • Identify a first action and a second action that together would bring a company into compliance with a new rule TIME: You will have an average of 2 minutes and 30 seconds for each IR question in the section, but some question types are more complicated than others. The recommendation is trying this one for 2 minutes initially, but take the full 2 minutes 30 seconds if you think you need it. Just note that, as you study, you’re going to have to determine your strengths and weaknesses so you can learn to balance your time appropriately.
Format The possible answers and your choices will be given in a table format of the following form: Question #1
Question #2
Options Answer #1 Answer #2 Answer #3 Answer #4 Answer #5
The possible answers are listed in the third column, on the right side of the table. Your choices for the first part and second part of the question will be recorded in the first and second columns of the table, respectively. Remember that you need to make a choice for each of the first two vertical columns of the table – NOT one for each horizontal row. You will mark the answer for Question #1 in the first column and the answer for Question #2 in the second column. It is possible, in some scenarios, for both questions to have the same correct answer. You cannot mark more than one answer in any column. You must get both columns correct to earn credit for the question, as there is no partial credit on the GMAT IR.
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Types of Two-Part Analysis problems The Two-Part Analysis questions can be either mathematical (numerical or algebraic) or completely verbal.
Algebraic Two-Part Analysis problems The algebraic questions are quite similar to Problem Solving questions involving variables in the answer choices. The prompt will be just slightly more involved than a comparable PS prompt, and then two questions, rather than one, will be asked about that prompt. Remember, you can always use pure algebra, or you can plug in different numbers for the different variables and eliminate answers that way. Example 1: Normally, a rabbit runs at a speed of kilometers per hour, but when chased by a tiger, it speeds up to kilometers per hour. The total distance from the starting point to destination is kilometers. If the rabbit sees the tiger at exactly half the distance from its starting point to destination, what will be his time for the whole journey and for the first half of the journey? Time taken by the rabbit for Time taken for the first half the whole journey of the journey
Options D/(C+M) 1/2 D× (C+M)/CM D/(C+2M) D/C D/2C 2×D/(C+M)
Explanation: We know that the total time can be calculated by dividing total distance by the average speed. Since half the distance D/2 is covered with speed C, the time taken for the first half of the journey will be D/2C. Similarly, the time taken for the second half of the journey will be D/2M. The total time taken by the rabbit would be the sum of both the times: D/2C+D/2M=1/2 D(1/C+1/M)=1/2 D×(C+M)/CM. The correct answer is Time taken by the rabbit for Time taken for the first half the whole journey of the journey
Options D/(C+M)
Correct
1/2 D× (C+M)/CM D/(C+2M) Correct
D/C D/2C 2×D/(C+M)
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Numerical Two-Part Analysis problems In the numerical questions, the two numbers might be, for example, the solution values of two related variables, or two percentages that satisfy some specified condition. These are also similar to PS problems with numerical answer, except two questions are asked, so review strategies for the PS Section. You always will be able to solve directly, often using algebra or some formula, and you almost always have the option of back testing from the answers provided. Example 2: Jack and Jill were walking towards each other on a straight road. Initially, they were 2 km apart, and Jill started walking one hour before Jack. If Jill walked at a constant rate of 20 meters/minute, and Jack walked at a constant rate of 60 meters/minute, then how many meters each of them covered before they met? Jack
Jill
Distance in meters 600 800 1,000 1,200 1,400
Explanation: Before Jack started walking, Jill walked 60 minutes at a constant speed 20 meters/minute, therefore she covered metres. Now, distance remaining by the time Jack started walking was equal to meters. Since they are moving towards each other at constant rates 60 and 20 meters per minute, they are approaching each other at meters/ minute. Therefore, they will meet minutes after Jack starts walking. Therefore, the distance covered by Jack was meters, and the distance travelled by Jill was meters. The correct answer is Jack Correct
Jill
Correct
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Distance in meters 600 800 1,000 1,200 1,400
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Verbal Two-Part Analysis problems The purely verbal questions will typically present a paragraph-long prompt, perhaps involving technical terminology, and then the questions will pose two related tasks: first step + second step; biggest advantage + biggest liability; satisfies all conditions + satisfies none of the conditions; something gained + something lost; etc. For verbal Two-Part Analysis problems, read the questions first, and read the entire prompt carefully. Read the questions first, so you know exactly the kind of information that will be relevant, and read with that in mind. Pay attention to what must be true, what could be true, and what absolutely can’t be true. Example 3: The following is an extraction from sport commentator’s speech which discusses fictitious location on the field called Sanura. And now we can see that at final minutes of the match almost all players have gathered near gates in anticipation of scoring a goal and are waiting for the ball to be thrown into the play. Each coach puts one defenseman from his team in Sanura. While until recently controlling Sanura was considered a good idea only when face-to-face game was developing there in the beginning of the game, now it became clear that even in situations like this one, when the play occurs far from Sanura, it is crucial to put some players there. Based on the definition of fictitious word Sanura that can be inferred from the extract above, which of the following game episodes CAN happen in Sanura and which CANNOT? Make only two selections, one in each column. CAN
CANNOT Throwing a ball from the line Getting sports trauma Scoring a goal All members of one team gathering together Members of different teams meeting
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Explanation: 1. Wrong. Nothing in the extract implies that the ball can or cannot be thrown in Sanura. We know that players are waiting for it near the gate, and probably, at least in some cases, the ball is thrown in somewhere in that area, but we do not know whether throwing in the ball may take place in Sanura. 2. Trap question. We know from the personal experience that any sport is accompanied with traumas however it is not stated clearly in the extract so it is just our assumption and thus it is wrong 3. CANNOT. The passage decribes a situation when all players are gathered near the gate waiting to score as a situation that occurs far from Sanura, so the gate is obviously not in Sanura, and you cannot score a goal in Sanura. 4. Wrong. Nothing is said if all members can or cannot gather in Sanura 5. CAN. The passage states that each coach puts one defenseman in Sanura in some situation, so members of different teams can meet in Sanura. The correct answer is CAN
CANNOT
Correct Correct
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Throwing a ball from the line Getting sports trauma Scoring a goal All members of one team gathering together Members of different teams meeting
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Two-Part Analysis strategies and tips 6. Read the information given carefully. All of the material presented is designed to be challenging, but if you have familiarity with the subject matter, do not let this knowledge influence your answer choices. Answer the questions only on the basis of what is given. 7. Determine exactly what the question is asking. Do not assume that the headings in the two response columns are complete descriptions of the tasks to be performed. Pay close attention to how the question describes the tasks. Often the headings in the two response columns are shorthand references to the tasks and may lack some details that could help you to better understand what you are supposed to do. 8. Remember that only two choices are to be made. Select one answer in each of the first two columns of the response table. You do not need to make a choice for each row of the table. The third column contains possible answers for the two choices to be made. 9. Do not choose an answer before reviewing all of the available answer choices. Do not assume that you have chosen the best answers in the two columns without reading all of the available options. 10. Determine whether tasks are dependent or independent. Some Two-Part Analysis questions pose two independent tasks that can be carried out individually, and others pose one task with two dependent parts, each of which must be carried out correctly to create a single correct response. With questions of the dependent type, the question asked cannot be answered coherently without making both choices, so be sure to examine your answers in relation to one another. 11. Keep in mind that one answer choice can be the correct response for both columns. If the tasks associated with the two response columns are not mutually exclusive, it is possible that one answer choice satisfies the conditions associated with both response columns.
Sample Problem: A person requires 52 bikes in 4 months with a budget of $25,440. He has taken offers from two companies A and B. Company A can provide him with 8 bikes per month at the rate of $500 per bike. Company B can provide him with 7 bikes per month at the rate of $480 per bike. If the person utilizes both the offers to get 52 bikes in his budget, what will be the number of bikes that he will buy from both companies? Company A
Company B
Number of Bikes 20 24 28 32 36 40
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Home assignment Problem 1 An investor has a chance to put his money on two investment options A and B. If he puts 500 dollars in investment option A, he will get 50 dollars return while in investment option B, he would get 30 dollars return for 200 dollars investment. If the investor has 1,500 dollars, how much return will he get in each of the investments? Make only one selection in each column. A
B
Return on Investment ( in Dollars) 100 125 150 175 200 225
Problem 2 There are two cars A and B. Car A has a maximum speed of 120 km/h consuming 12 liters fuel in one hour at maximum speed and car B has a maximum speed of 100 km/h consuming 8 liters fuel in one hour at maximum speed. Both the cars are 960 km away from each other. These cars must reach at a point in 6 hours by running towards each other. We have a limit of availability of fuel for both cars. The available amount of fuel is 84 liters. How much hours will both the cars will run to meet a point in 6 hours by consuming the limited amount of 84 liters of fuel. Car A
Car B
Number of Hours 6 5 4 3 2
Problem 3 A man covered a distance of 340 kilometers in 5 hours by two modes of transport, bus and car. If the average speed of car is 80km per hour and the average speed of bus is 60 km per hour, what is the duration travelled by each mode of transport? Select only one option in each column. Bus
Car
Hours 1 2 2.5 3 3.5 4
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Answers and explanations Sample problem: Let x be the number of bikes bought from Company A, and y be the number of bikes bought from Company B. So, 500x+480y=25440 or 50x+48y=2544 …………… (1) Total number of bikes bought from both companies should be equal equal to 52: x+y=52 ……… (2) Solving both equations (1) and (2) simultaneously, we get from equation (2): x=52-y. Putting in equation (1): 50(52-y)+48y=2544 2600-50y+48y=2544 20y=560 y=28 So, x=52−y=52−28=24 Hint: Only two pairs satisfy the equation (2): 20 and 32; 24 and 28. You can put them in equation (1) and check. Problem 1 In investment option A, he gets 50 dollars return for every 500 dollars. Hence, for 1,500 dollars, his return would be 1,500÷500×50 = 150 dollars. In investment option B, he gets 30 dollars for 200 dollars investment. Hence, his return on 1,500 dollars would be 1,500÷200×30 = 225 dollars. Hence return for A = 150 dollars and B = 225 dollars. Problem 2 Let number of hours travelled by car A is x and number of hours travelled by car B is y. Car A consumes 12 liters per hour and Car B consumes 8 liters per hour at their maximum speeds. So, 12x + 8y = 84 ………………… (1) Car A travels 120 kilometers in 1 hour and Car B travels 100 kilometers in one hour at their maximum speeds. So, 120x + 100y = 960 or 12x + 10y = 96…………………… (2) Subtracting equation (1) from (2) we obtain: 2y=12 or y=6. Putting the value of y in equation (1), we have 12x+48=84 or 12x=36 or x=3. Hence, Car A will have to travel 3 hours and Car B has to travel 6 hours.
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Problem 3 Let the time travelled by bus be A hours. Hence, the values can be represented as below. Mode
Bus
Car
Speed
60
80
Time
A
5-A
Distance = speed × time
60A
80×(5-A)
Given the total distance is 340 km. Hence, 60A+80(5-A)=340. Solving, A=3 hours. Hence, B=53=2 hours. Hence, the man travelled 3 hours by bus and 2 hours by car.
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Multi-Source Reasoning Multi-Source Reasoning (MSR) tasks are the longest IR tasks to read, so in a lot of ways they resemble RC questions. Of all IR questions, MSR questions require good reading comprehension as they test your ability to handle problems that do not have direct solutions.
Format Data sources (question prompt) Data sources consist of 2 or 3 tabs of information that may include text, charts, or tables. Only one data source can be displayed at a time. To view a different source, select its tab. You can click on the tabs to view any of the sources as many times as needed. Note: Be prepared to see some information that is ambiguous, redundant or incomplete.
Question Most MSR prompts come with 2 or 3 tasks. There are two formats for MSR questions: • Multiple-choice questions You have to select the best of the five answer choices given. • Set of three statements with opposing answer choices (true/false, yes/no) For each of the statements, you need to mark the correct option. The statements in the questions may contain text, numerical values, or algebraic expressions that require an indication as to whether each meets a certain condition. For example, you may be asked whether: • each statement is true, according to the sources • each statement or numerical value is consistent with the sources • each statement or algebraic expression would solve a problem described in the data sources the value of each algebraic expression can be determined on the basis of the data sources Expect 3 sets of tasks based on the same data sources. TIMEING: You will have an average of 5 or 7.5 minutes to read an MSR prompt and complete the accompanying questions.
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How to deal with an MSR task (Strategy): 1. Skim the sources provided in all tabs. You only need to grasp the big picture information: what the text is about, and the scope of topics covered in each tab. You may want to summarize key information - put down the main ideas for each tab. 2. Read the question carefully. Make sure that you understand precisely what is being asked. 3. Refer back to the parts of the information to answer the question. Now you need to focus more closely on the specific information needed to answer the question. Analyze each source of information carefully, because the questions require a detailed understanding of the information presented. 4. Select the answer choices that are supported by the information in the data sources. You may also want to read the question first, and then familiarize yourself with the text in the Tabs, as this will give you some idea of more what the story is about and what kind of data will be presented in the text.
Tips for MSR • Estimate whenever possible Very often, you’ll have to infer based on the information provided in data sources. Use the data provide In the tabs for estimations that help you answer the questions. • Pay attention to numerical information Do not confuse numbers with rates or percentages, and know that some of the numbers may be misleading (for example, they may be given in the data source, but irrelevant to the question). • Be prepared to ignore a major part of the data • Use RC and CR techniques (especially, the techniques advised for Inference questions).
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Multi-Source Reasoning. Example 1 The following are emails exchanged between a computer hardware manufacturing firm’s sales manager Justin and their marketing agent Alex. Mail sent from Alex to Justin Mail sent from Justin to Alex We are glad to hear that someone has shown interest in our Good news! We have received new product! And yes, their offer is very low compared to the first offer for the new motherboard produced by your our sale price. While we understand the nature of negotiacompany. The offer is $500 a piece, and while I know this is tions you described, we are reluctant to end up at a price less than your sale price, it is that’s too low for us. After givcommon for buyers to make ing it some thought, we think an aggressively low bid in an effort to bring down the seller’s that making a counter offer at price. Based on my experi$590 makes sense. This will give us room for further neence, I think you can make a gotiations, if the buyer makes counter offer with a price of another counter offer. Also, $585 per item, and still end there are other concessions up agreeing on a price that is no lower than 10% below your we would be willing to make besides price, if you think sale price. Just let me know those can help us reach a what you would like to do. deal. Please communicate our counter offer to the buyer, and let us know how it goes.
Mail sent from Alex to Justin I talked to the client, and it sounds as though they are willing to negotiate further on the price, although the buyer said that $590 is «a lot more’ than they can afford. I mentioned your willingness to negotiate on items other than price, and they have expressed willingness to make this sale happen no later than mid-August so that they can get everything in place before their college reopens. I expect that, if you offer them a price of $530 and agree to make the deal happen by early August, they will accept your offer. Please let me know how you would like to proceed.
Given the information provided above, for each of the following statements, select Yes if it can be inferred from the data source. Otherwise, select No. Yes
No
The company’s sale price for their motherboards is at least $620 per item. It is possible for the buyer and seller to make a deal in which neither side needs to change its opening offer by more than 15%. Alex is willing to negotiate to get the deal fixed at a lower price than what the company is ready to accept.
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Finding answers Step 0. Read the questions (optional), skim the text in [Tabs 1-3] to get the general understanding of the subject discussed. Note down main ideas if you find that a written summary works for you. The summary could look like this: T1
T2
T3
A.:
J.:
A.:
Customer offer: $500 - too low.
500 – too low!!
Customer said: $590 - too much!!
Suggest counteroff. $585.
Suggest counterof. $590 – better for negotiations
Can agree on price max.10% below sale price.
Also, can consider other things to reach a deal.
If sale in early August and price is 530, they will agree. OK?
Now we can go back to each the statements the question and look for the information that helps confirm or deny these statements. Question 1. The company’s sale price for their motherboards is at least $620 per item. Step 1. Let’s look at the question again. To decide if the statement above is true, we need to understand: (a) whether the sale price of the motherboard can be estimated based on the information that is presented in the data sources, (b) and how our estimations for the sale price can be compared against a value of $620. Step2. Now we go back to the data sources to find the relevant information. (a) can be done based on information from Tab1 and Tab 2. From the information presented in [Tab 2], we can infer that the final price is likely to be lower than 590 (Justin writes : “...making a counter offer at $590 makes sense. This will give us room for further negotiations, if the buyer makes another counter offer” . This means that, if the customer makes another counter offer, the company can agree to lower its offer of $590). From the information presented in [Tab 1], we can see that Alex suggests the counter offer of $585 and expresses an opinion that the final price on which the company and the customer may eventually agree is no lower than 10 % below the sale price. Let’s examine this phrase a bit closer. “Final price no lower than 10% below the sale price“ means “Final price anywhere between 90% and 100% of the sale price, but not lower than 90% of the sale price.” If the final price were $585 (which would mean that the customer accepts a very unfavorable offer and agrees to the company’s initial bid of 585), this final price of $585 could be anywhere between
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90% and 100% of the sale price. For (b), let’s try to compare the estimations for the final price with the initial offers: • If $585 is 90% of the sale price, than the sale price is =585/90*100 = 650 (higher than 620). • But if 585 is 99% of the sale price, than the sale price is 585/99*100 = 590 (lower than 620). We have found at least one possible value of the sale price that is lower than $620. So, the answer to Question 1 is No. Question 2. It is possible for the buyer and seller to make a deal in which neither side needs to change its opening offer by more than 15%. 1. We need to find the opening offer for each of the sides, and to figure out a possible price at which the sides could (but not necessarily will) make the deal. Then, we’ll check if this hypothetical deal price can differ from any of the 2 opening prices no more than 15 % 2. Refer back to the data source. • The customer offer is $500 as the customer offer. (Directly stated in [Tab 1]: “We have received the first offer … The offer is $500 a piece”) • The opening offer for the seller is the initial selling price, which we do not know, but from [Tab 1] ]we know that 585 is between 90 and 99 percent of this price, and from Tab 2 we know that 590 must be somewhat more that the initial price. (“ ... a counter offer at $590 makes sense. This will give us room for further negotiations...”). To make the estimations simpler, let’s take 590 as the initial price of the seller. Is it possible to close the deal at a price that is between the customer’s initial offer of 500+15%x500=575 and 590-15%x590=501,5? (The customer will not be paying more than 575, and the company will not accept less than 501,5.) Any value of the final price between 501,5 and 575 satisfies this condition. For example, the price of $ 530 that is suggested by Alex in [Tab 3]: “ ...if you offer them a price of $530 and agree to make the deal happen by early August, they will accept your offer .” So, it is indeed possible for both sides to come up with a price that is accepted both by the company and the customer, and this price will be between $501 and $575. The answer to Question 2 is Yes. Question 3. Alex is willing to negotiate to get the deal fixed at a lower price than what the company is ready to accept. 1. The question is clear. We have to check if this can be inferred from the data source . 2. Refer back to the data source. Alex expresses his personal point of view and asks for Justin’s opinion and instructions on the further course of action: • “Based on my experience, I think … Just let me know what you would like to do.” [Tab 1] • “I expect...Just let me know what you would like to do. “[Tab 3] So, Alex is not likely to either negotiate a particular price, or, furthermore, to fix the price - without Justin’s approval. The answer to Question 3 is No.
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Multi-Source Reasoning with Tables The data sources for MSR may contain not only texts, but also numerical information in form of tables. The tables are not sortable, and are somewhat simpler than the tables you’ll find in Table Analysis tasks. The strategy for dealing with these MR tasks is the same as for all MSR tasks. Notes for MSR taska with Tables • You may need to perform estimations or calculations. • Pay attention to numbers, proportions, dates, etc. To find the correct answer, you may need to convert those numbers to a different scale. For example, note that in in the example below, in [Tab 3], the food consumption is given for a family of 4, rather than per one person.
Multi-Source Reasoning. Example 2. Village Sites [ Tab 1] An archaeological team gas been excavating three ancient village sites – Barras, Agna, and Cussaia – looking in particular at kitchen waste dumps as a way to understand the villages’ dietary patterns and trading relationships. What follows are brief summaries of their findings. Barras: The best data come from stratified finds in this oceanside village, which was inhabited from AD 600 to 1300 and was the only one of the three villages to produce seafood, its main dietary item. Though Barras residents hunted on land and raised crops, this provided relatively small amounts of food. As Barras’s overall prosperity rose, there was more food available per person, and its population increased from an average of 100 residents in AD 600s to 400 residents in the AD 1000s to 600 residents in the AD 1200s. Agna: Agna was established in an inland forest around AD800 and its residents mainly hunted but also are considerable amounts of fruit, nuts, and other forest-vegetable products. They also traded meat to Barras for other goods. With no open fields, Agna grew no grain. Cussaia: Predating Barras, Cussaia depended heavily on raising grain crops and eventually obtained seafood and meat via trade. It traded directly only with Barras, because a mountain range separated it from Agna, though some products may have been traded between Agna and Cussaia via Barras. Additionally, there is no evidence that any other village traded with Barras, Agna or Cussaia prior to AD 1300.
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Food Variety [ Tab 2] Barras: Percentages, by Estimated Weight, of Dietary Items Consumed per Person per Month
Century 600s 700s 800s 900s 1000s 1100s 1200s
Seafood 65% 65% 60% 45% 45% 60% 55%
Meat 10% 10% 15% 30% 30% 10% 25%
Grains 10% 15% 15% 12% 12% 20% 10%
Other 15% 10% 10% 13% 13% 10% 10%
Food Consumption [ Tab 3] Barras, Agna: Estimated Average Monthly Meat and Seafood Consumption (lb per 4-Person Family) Century 600s 700s 800s 900s 1000s 1100s 1200s
Barras Seafood 240 250 275 258 240 275 265
Agna Meat 37 38 70 172 160 45 120
Seafood Not Applicable Not Applicable 60 66 66 8 45
Meat Not Applicable Not Applicable 240 180 186 240 240
Question 1 Based on the information in the passage and tables, it can be determined that the average monthly meat consumption, in pounds, by the residents of Barras in the AD 1000s was which of the following?
• • • • •
9,600 10,000 16,000 17,400 18,000
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Question 2 Assume that an increase of 5% or more from one century to the next in the amount of a given food consumed by Barras residents is due primarily to a corresponding increase in imports of that food into Barras from other villages. Given this assumption and the information provided, for each of the following select Yes if it describes a food likely imported by Barras during times of increased food consumption, Otherwise, select No. Meat from Agna from the AD 500s to the DA 600s.
Yes
No
Meat from Agna from the AD 800s to the DA 900s. Grain from Cussaia from the AD 600s to the DA 700s. Step 0. Have a look at the question, scan the text, make a summary. Once you’ve scanned Tabs1,2,3, no doubt you’ll get the main idea. • Tab 1 lists what was consumed, when and why. Tab 1 names 3 villages, and provides information about the century when those villages existed; discusses diet composition for these village, explaining why the village population consumed that kind of food (traded, hunted, lived in a forest, etc.). • Tab 2 gives figures of Food Variety for Barras. • Tab 3 lists details of Food Consumption for Barras and Agna, per 4 person family, for different time periods. Note that in Tab 3, the food consumption is given for a family of 4, rather than per person. Step 2. Let’s get back to the questions. To answer Question 1, we need to answer these questions first: (a)How many people lived in Barras in the 1000s? (b)How much meat did they consume? Step3. Refer back to the data sources to find supporting information. (a) [ Tab 1] “… its population increased from an average of 100 residents in AD 600s to 400 residents in the AD 1000s to 600 residents in the AD 1200s. “ How do you like this text fragment? Not particularly readable, is it? If we concentrate a bit, we’ll be able to decipher that there were 400 residents in the AD 1000s. (b) [ Tab 3] From the average meat consumption table, we see that a household of 4 people in Barras in the 1000s consumed 160 pounds of meat per year. It this enough to answer Question 1? Yes. If 4 people consume 160 lbs of meat per year, than 400 people consume 100 times more, that is: 160 * 100= 16,000 The answer to Question 1 is 16,000.
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To answer Question 2, we need to evaluate if Barras could import certain types of food from certain villages, for a given time period. • Meat from Agna from the AD 500s to the DA 600s [ Tab 1] “Agna was established in an inland forest around AD800”. Clearly, nothing could be imported from Agna in the 500s-600s, as Agna didn’t exist at that time. The answer is No. • Meat from Agna from the AD 800s to the DA 900s [ Tab 1] “Agna: … They also traded meat to Barras for other goods.” The answer is Yes. • Grain from Cussaia from the AD 600s to the DA 700s [ Tab 1] “Cussaia: … Predating Barras, Cussaia depended heavily on raising grain crops .... It traded directly only with Barras” The answer is Yes.
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Multi-Source Reasoning with Graphs Some data sources in MSR may include Graphs. Here, the same tips apply as for Graph Interpretation.
Multi-Source Reasoning. Example 3 Height-for-age standards
Weight-for-height standards
The World Health Organization (WHO) has produced a comprehensive set of growth standards for children. These standards are based on studies of children living in 6 nations on 5 continents under optimal conditions with respect to health and nutrition. The table displays the percentile distribution of height, in centimeters, at 3-month intervals, for boys ages 2 through 5 according to the WHO model. In a model population – a large population of boys ages 2 through 5 that conforms to the WHO growth standards – for n = 3, 15, 50, 85, and 97, the nth percentile in height-for-a given age is the unique height among boys of that age that is greater than or equal to n percent, and less than or equal to (100-n) percent, of heights of boys of that age.
The graph shows the percentile distribution of weight, in kilograms, for heights from 80 am to 120 cm, for boys ages 2 through 5, according to the WHO model. In a model population, for n = 3, 15, 50, 85, and 97, the nth percentile in weight for a given height is the unique weight among boys of that height that is greater than or equal to (100-n) percent, of weight of boys of that age. Weight Percentiles for Height for Boys 2-5
Question 1 Yes
No
B is a boy aged 4 years 3 months whose height is 110 cm and whose weight is 19 kg. For each of the following statements, select Yes if, based on the given information, it must be true of B relative to a model population. Otherwise, select No. Approximately 50% of boys at the same weight are shorter than B.
No more than 15% of boys at this age are taller than B. B’s height is greater than or equal to that of 50% of boys aged 5 years 0 months.
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• Approximately 50% of boys at the same weight are shorter than B. [Tab 1] contains Height-for-age standards, and [Tab 2] contains Weight-for-age standards, neither of which provide a distribution of height on the basis of weight. Therefore, we cannot tell what proportion of boys weighing 19 kg have height that is lower than 110cm. The answer is No. • No more than 15% of boys at this age are taller than B. [Tab 1] If the 85th percentile in height for boys aged 4 years 3 months is 109.5 cm, it means that 15% of boys aged 4 years 3 months are taller than 109.5 cm. So, 15% of boys who are 4 years 3 months old are taller than B. The answer is Yes. • B’s height is greater than or equal to that of 50% of boys aged 5 years 0 months [Tab 1] The 50th percentile for boys aged 5 year 0 months is 110.0 cm - the same height as B’s. So, B’s height is greater than or equal to that of 100-50%= 50% of boys aged 5 years 0 months. The answer is Yes.
Sample Problem: Company PR Ltd had undertaken a project to complete a 24 km road in 80 days. Following are the mails exchanged between the on site manager Adam and his boss Evelyn. Evelyn: Hi Adam, please update me on the status of this project. We are running out of time here and half of our allotted days have already passed.
Yes
Adam: Hi Evelyn. Because of the terrain peculiarities and bad weather conditions, we are running behind the schedule and completed only one third of the expected work. The current team of 40 men and 20 women is not sufficient to complete the project in time. Each of these workers invariably works for 8 hours each day and all are equally efficient.
Evelyn: Please increase daily working hours to 10. I will also be hiring 20 more women to join the group. At any cost, we must have the job done on time.
No After hiring 20 more women and increasing daily working hours, the company will be able to complete the project on time. (Assume all workers work at the same constant rate). Evelyn will need to hire 8 more men/women on top of the 20 additional women she already hired to complete the project on time If Evelyn does not hire any additional workers, the project will take 24 days more than the estimated duration.
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Home assignment Problem 1 Three sources of information are three letters below. Letter 01 05/04/2012 To: The Finance Manager
Letter 0 01/04/20122 To: The Marketing Manager
From: The Marketing Manager From: The Chief Executive Officer Re: Strategy for product proRe: Strategy for product promotion motion Our company is going successful in its chosen strategic direc- In pursuance of our policyto promote our core product, ention. However, to maintain the strategic direction right, Market- hance funds allocation for the ing department needs $75000 product concerned. You may for the promotion of product X, consult finance manager for as the product Y is not perform- the funds. However, it needs no emphasis that the strategy ing well. The product Y is the focus of our strategy being our to avoid direct competition will continue its implementation in core product. We want to get the future for our complemenbetter results: a higher sale of tary products X and Product Y. Y. This budget is in addition to the budget at the disposal of Marketing Department.
Letter03 06/04/2012 To: All the marketing staff From: The Marketing Manager Re: Strategy for product promotion You are well aware of our policy to focus sales of product X. The target sale of the product has been increased by 25%. I have increased the funds for the promotion of the product X. You are directed to ensure target achievement up to 31, December 2012.
Consider each of the following statements. Does the information in three letters support the inference as stated? Yes
No
Statement It is likely that the finance manager will not release funds for the product X. It is not the core product. Marketing manager is not implementing the right strategy. Promotion of product X also promotes product Y.
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Problem 2 Introduction Electronics Board designing Company has the policy that if for two successive months the production efficiency of Product Manager is less than 80%(The efficiency corresponds to faults other than the machinery faults) then the Product Manufacturing Manager is fired. In the month of June, the Product Manufacturing Manager had the production efficiency of 78% (lot of boards were wasted). In the month of July the There was a problem in the manufacturing machine. Email from Boss to Product Manufacturing Manager
Email from Product Manufacturing Manager to Boss Sir in last month (July) we produced 1000 circuit It has come into my notice that our producboards, as we do every month. Out of which the tion of circuit boards has been reduced in manufacturing machine wrongly produced (wastlast month(July). We always maintain above ed) 300 boards and 210 were wasted due to bad 85% efficiency in the production and manuwork. There was a fault in the machine mechanical facturing of the circuit boards but last month part such that it was not routing the circuit boards progress is not good for our Company. Send well so that’s why 300 circuit boards were wasted. me the progress report of last month (July) But in this current month (August) I have noticed and reason for decline in efficiency of prodthe fault in the machine and I got it right now. uct. Hopefully this will not happen again. 1. What is the total probability of choosing a wasted board in July?
2. What is the efficiency of Production Manager in July?
(A) (B) (C) (D) (A) (B) (C) (D)
0.3 0.51 1 0.21 64% 74% 70% 82%
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Problem 3 Memo #1 from the Chief Operations Officer of Jackson’s Auto Company to Quality Control on March 23, 2011.
Memo #2 from the VP of Quality Control to the COO on March 24, 2011.
Memo #3 from COO to VP of QC on March 25th, 2011.
I am concerned about the wiring of the front seat adjustment system in our POGO X3 car. We currently have 8500 cars that were made before upgraded components began to be installed. Should the wire system on these cars have additional tests run to ensure proper functioning? If so, what tests need to be run and on how many cars?
On small initial tests previously conducted, the old wiring works properly in 75% of cars tested. This was done on a small sample however. In my opinion, the pass rate should be close to the original, and we should randomly test around 30% of the cars, fixing those that fail.
The cost to uninstall the old components and upgrade them is around $200 per car if done here in our factory. The cost to repair this component in the field will exceed $500, as well as damage our image. However, this is not a safety issue and we are also losing money as they are being tested. Test 25% of the cars.
Consider each of the following statements. Does the information in the three memos support the inference as stated? Yes
No The COO believes that the cost to upgrade the wiring is worth it for the reputation of the company and safety of the owners. Quality control feels that around 2100 cars will have problems with their wiring. The COO does not feel that the risk of leaving the old wires outweighs the safety concern.
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Answers and explanations Sample problem 1. No. From the very beginning, the number of workers is 40 men + 20 women = 60. They spent half of the scheduled time or 80/2=40 days working. As the result, 1/3 of work was done. On all work this team needs 3×40=120 days. So, 60 workers have to work 120-40=80 days more with 8 working hours a day, or we need to have done 60×80×8 working hours to finish the job. If additional x people are added to our team it would contain (60+x) persons. Then work can be completed in (60×80×8)/(60+x) hours. If each person spends 10 hours a day at work, we need (60×80×8)/((60+x)10) working days to finish the job. There are 40 days left: (60×80×8)/(60+x)10=40 (6×2×8)/((60+x))=1 Multiplying each side of the equation by (60+x) we get 96=60+x. So, x=36, or we need 36 additional persons to have work done on time. 20 additional persons won’t help us. 2. No. Refer above. 20+6=26 additional persons are still not enough. 3. Yes. 20+6=26 additional persons are still not enough. As told above, each person in the former case has to complete 80×8 working hours to finish the job. If each person spends 10 hours a day at work, we need (80×8)/10 =64 days to finish the job. So, subtracting 40 days that are left in schedule, we need 64-40 =24 days more. Problem 1 1. No.
2. No.
3. Yes.
The company is selling Y as an attached or complementary product of X. By increasing sales of X, it gets higher sales of Y avoiding direct competition. Even, product Y may not be sold in the name of the company itself. Problem 2 1. Option (B) is correct. In the month of July, the total number of wasted boards is 510. 300 of them were wasted because of fault in the machine and 210 of them were wasted because of bad word of Product Manager. Hence, the probability of wasted boards in month of July = 510/1000 = 51/100 = 0.51 2. Option (C) is correct. Efficiency of product Manager is related to the faults other than the machinery fault. In July, 300 boards were wasted because of fault in machine so these did not affect the efficiency of the manager. So, there are total 1000-300 = 700 boards which will be included in calculating the efficiency of the Product Manager. The other 210 wasted boards will affect the efficiency of the Product Manager. So, Efficiency of Product Manager in month of July = (700-210)/700 ×100 = 70%
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Problem 3 1. No.
2. Yes.
3. No.
For the first, in Memo #3, the COO states that although it may damage the image, since it is not a safety concern, budget was more of a concern. For the second, in Memo #1, 8500 cars were cited as having a problem. In Memo #2, quality control feels that around 75% of the cars will not have problems with their wiring. 8500*.75=6375. These are the cars that are fine, so 8500-6375=2125, or around 2100. The third is similar to the first. It may be easier to ask yourself the opposite of the question, “Does the COO feel that the risk of leaving the old wires outweighs the safety concern.” The answer to this from Memo #3 is Yes. Since the question asked is the opposite of that, the correct answer is No.
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Vocabulary list for IR axis
a line drawn through the center of a figure a sequence of marks, usually along a line, used in making measurescale ments one variable is proportional to another if the ration of corresponding valproportional ues remains constant to estimate a value by following a pattern and staying within the values interpolation already known to estimate a value by following a pattern and going beyond the values extrapolation already known have measurements that are distinct, periodic, and unconnected bediscreet variable tween data points (e.g. the distance an athlete throws a discus) measurements are uninterrupted and connected between data points continuous variable (e.g. growth of a plant) scatter plot a graph that relates data from two different sets line of best fit slope the angle made by a straight line with the x-axis a line on a scatter plot which can be drawn near the points to more trend line clearly show the trend between two sets of data relationship between two sets of data; the trend will show a positive cortrend relation, a negative correlation, or no correlation. positive correlation both sets of data increase together negative correlation one set of data decreases as the other set of data increases no correlation the two data sets are not related weak correlation when the data is not clustered along an obvious line when the data is clustered along an obvious line (can be positive or strong correlation negative) lower extreme minimum data value upper extreme maximum data value range upper extreme minus lower extreme cluster a particular segment of the population gaps spaces in the data set without a segment of the population outlier a point separted from the main body of the data point within the range about which the rest of the data is considered balcentral tendency anced the most frequently observed value of the measurements in the sample. mode There can be more than one mode or no mode. the sum of all the results included in the sample divided by the number mean of observations the middle value of all the numbers in the sample; for an even number of median values, the median is the average of the middle two values; for an odd number of values, the median is the middle of the all of the values. lower quartile separates the first 25% of the distribution from the remaining 75%. upper quartile separates the first 75% of the distribution from the remaining 25%.
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