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]]>Many students have questions about the GMATs Integrated Reasoning (IR) section. “Is integrated reasoning part of the GMAT score?” Well…yes and no. Your IR score will be submitted to schools along with your verbal and quantitative score. However, the IR score is totally separate from the “total score,” which consists solely of the Q & V sections. But nonetheless, admission committees have started giving considerable attention to integrated reasoning GMAT scores, so it’s important to perform well on each section. Continue reading below for specifics on precisely how the IR section scored.

**Fact**: The current version of the GMAT features a Verbal Section, a Quantitative Section, a single AWA essay, and the new Integrated Reasoning (IR) section. The sequence of the new test will be:

1) AWA essay = Analysis of Argument, 30 minutes

2) IR section = 12 questions, 30 minutes

3) optional break, up to 5 minutes

4) Q section = 31 questions, 62 minutes

5) optional break, up to 5 minutes

6) V section = 36 questions, 65 minutes

This the traditional order. As of July 11, 2017, this is one of three possible orders of the sections: students now have some choice about section order.

**Fact**: the IR section consists of four question types —

a) Graphics Interpretation (GI)

b) Two-Part Analysis (2PA)

c) Table Analysis (TA)

d) Multi-Source Reasoning (MSR)

**Fact**: all four question types will appear on *everyone’s* IR sections.

**Fact**: the breakdown by question type will differ from one person’s IR section to another person’s only because of the *experimental questions*.

In other words, everyone will have the same breakdown by question type for the questions that *actually* count toward their score. However, extra *experimental questions* are added in to this baseline, resulting in different IR section breakdowns for different people.

GMAC has revealed neither what that fundamental breakdown is nor how many of the 12 questions will be experimental. Let’s examine a hypothetical scenario just to understand:

Let’s say the graded IR questions consist of 2 GIs, 2 2PAs, 2 TAs, and 2 MSRs, for a total of eight (these are my made-up numbers). For everyone taking the test, let’s say those are the eight questions that are graded. The other four questions would be experimental questions, and will be different for different users. Thus, Abe might get an IR section with 3 GIs, 3 2PAs, 3 TAs, and 3 MSRs. Betsy might get an IR section with 2 GIs, 3 2PAs, 3 TAs, and 4 MSRs. Cathy might get an IR section with 2 GIs, 6 2PAs, 2 TAs, and 2 MSRs.

In each case, only the baseline eight questions count toward the score, and the others are experiments. (The numbers in this example are purely speculative: we have no idea what GMAC has up their sleeve.)

Here’s the kicker, though. As our hypothetical friend Cathy is working through her IR section, she may start to think: “Gee, I’m seeing a lot of 2PA questions! Some of them must be experimental!” Quite true. But the catch is, among those six 2 PA questions, the two that *actually* count could be the first two, or the last two, or any combination. Those comfortable with combinations will see that there are actually 6C2 = 15 different ways that the two that count could be scrambled among the four experimental questions.

As the test taker, even if you do have strong suspicions about which question types the experimental questions were, you will have no way of knowing, as you are working on a particular question, whether it counts or is experimental. Therefore, you have to treat every single question as if it counts, same as on the Q & V sections.

**Fact**: the IR section is ** not** computer adaptive. You are randomly assigned 12 questions as a group, and move through that sequence regardless of whether you are getting questions right or wrong.

**Fact**: The GMAT score report will consist of (a) V score, (b) Q score, (c) Total Score (combination of your V & Q scores), (d) AWA score, and (e) IR score.

**Fact**: the IR score will be an integer from 1 to 8. There is **no partial credit** on the IR section. For example, in a TA question in which there are three dichotomous prompts (e.g. true/false), you must get *all three* right to get credit for that one question. If you get at least one of the three parts wrong, the whole question is marked wrong.

**Fact**: The number of IR questions you get right will constitute a *raw* score. The GMAC, using some arcane alchemy known only to them, will convert that raw score into a *scaled score* (1 – 8), which will be accompanied by percentiles.

Notice: Because of the statistical magic GMAC uses in converting raw scores to scaled scores (on IR, Q, & V sections), what may seem to your advantage or disadvantage may not work out that way. For example, the fact that there’s no partial credit is challenging: it makes it harder to earn points on individual questions. BUT, harder *for everyone* means that lower *raw* scores are needed to get a higher *percentile* grade. By contrast, if all the questions are very easy, that means most people will get them right, which means it will be “crowded” at the top, and much harder to place in a high percentile. Therefore, what matters is *not* how inherently easy or hard the test is—what matters is **how well you perform, compared to other test takers.**

Given your inherent talents, what will maximize your GMAT skills with respect to others taking the GMAT? Sign up for Magoosh, and you will learn all the content and strategy you will need.

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

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]]>The GMAT Integrated Reasoning question formats are highly dependent on technology, and unlike traditional Verbal and Quantitative questions, these would be too compromised in a print format. Therefore, from the beginning, GMAC never put official Integrated Reasoning questions in the GMAT Official Guide: the official questions always have been online. At first, a code in the back of the GMAT Official Guide would give you access to a separate site that just had the official Integrated Reasoning questions.

Starting with the OG 2016, GMAC put all the questions in the OG online, in case you wanted to study them in an online format rather than in print format. When GMAC made this move, logically they put the 50 official Integrated Reasoning questions on the same website with the other questions. The code in your copy of the OG will give you access to that website. The Quant & Verbal questions on that website are identical to those in the printed OG, but going to that website is *the only way* you can practice official Integrated Reasoning questions.

Each IR question is one of four formats:

(1) **Multi-Source Reasoning** (MSR)

(2) **Table Analysis** (TA)

(3) **Graphics Interpretation** (GI)

(4) **Two-Part Analysis** (2PA)

If these are unfamiliar to you, you can read about the basics in the Magoosh IR eBook. The official website and the actual GMAT itself appear to give questions of the four formats successively: that is, all the MSR, then all the TA, then all the GI, then all the 2PA. This is in sharp distinction to the Quant & Verbal sections, in which quant formats (PS & DS) or verbal formats (RC & CR & SC) are freely interspersed.

We do know: eight of the 12 questions will count, and the other four will be experimental questions. We do know: whatever block of 8 questions counts, those 8 questions will have the same distributions of question for all test takers. We don’t know what that distribution is: let’s say, just for simplicity, that it’s 2 MSR questions, 2 TA questions, 2 GI questions, and 2 2PA questions. That mix will count for everyone. Now, the four experimental questions don’t count, so they could be any mix of problems: it could be one of each type, or two of one type and two of another, or all four of a single type. Suppose Fred happens to get an IR section on which all four of the experimental questions are 2PA. In the course of the 12 questions, Fred would see six 2PA questions: if he were counting, he would realize that the experimental questions would have to be 2PA, but think about it. He doesn’t start to realize something is unusually until he gets to his 4th or 5th or even 6th 2PA. At that point, he knows some of those 2PA questions had to be experimental, but he has no way of knowing which two count: the first two? the last two? the third and the fifth? Of course, of six questions, there are 6C2 = 15 different ways the two that count could be distributed among them, and all 15 of those scenarios are equally likely. The upshot is: even if you have an inkling that you are getting more of this question than that, you always have to treat the question in front of you as if it counts.

Also, let’s talk a little about this word “question”—we say the website has 50 practice “questions” and the IR section has 12 “questions,” but I would argue a more accurate term would be “screens.” The website has 50 screens, and the IR section of the GMAT has 12 screens. Each screen will be one of four formats—MSR, TA, GI, 2PA—and * almost every screen has more than one question on it*. Rather than talk about how many questions within each question, for clarity, for the remainder of this post, I will refer to each “screen” and how many questions on that screen. Here’s a little of what we can glean about the four screen formats from the 50 IR practice screens on the website.

Finally, remember that there is **no partial credit on the GMAT Integrated Reasoning**. If there are multiple tasks on a single IR screen, you must get every single task on the screen correct to earn credit for that screen.

This is the only of the four types in which the same content appears across multiple screens. For every other question format, all the relevant content appears on one screen, and none of that content appears on any other screen.

The information for a bank of MSR questions appears in separate “cards” on the left side of a split screen, and the questions appear on the right side, much like Reading Comprehension. The same set of cards is present for 3-5 MSR screens, again, much like a RC passage. At least one card is all text, and sometimes all the cards are all text. A card may also contain a graph, a chart, a table, or even a mathematical formula relating ideas discussed on other cards. As a general rule, most of the questions can only be answered by combining information from different cards.

Some MSR screens have a single five-choice multiple choice (MC) question: on the whole Integrated Reasoning section, this is the only screen type, the only question type, on which there is only one question on the screen.

The others, in fact, the majority of MSR screens, have what I call Multiple-Dichotomous Choice (MDC) question designs. A dichotomous choice question is one that has only two possible responses (yes/no, true/false, etc.) The GMAT Integrated Reasoning MDC design has three such questions in a table. Here’s an example of a frivolous MDC, just so you can see the design.

Each row is a dichotomous choice: we have to give one of only two choices as a response. Of course, the answers to this playful MDC are “helps” in the first two rows, and “doesn’t help” in the last row. This MDC question depended on general knowledge, whereas the MDC questions that appear in the MSR format will depend on the information on the cards. If the IR screen contains a set of MDC questions, you must get all three correct to get credit for that screen.

Here’s an Integrated Reasoning Multi-Source Reasoning practice question.

Each IR Table Analysis screen contains a verbal prompt and a sortable table, that is, a table you can put into ranked order by any column. Tables typically have 5-8 columns. The GMAT loves to have some columns that give data about ranking: for example, the table could have one column that lists the actual areas, in sq miles, of counties, and another that lists the rank of the area in terms of the world—the United States of America has an area of 3.8M sq miles and rank of 4^{th} in the world.

Every table appears just once, on one screen, with a set of MDC questions, always three individual questions, as above. Once you answer those three questions and hit submit, that particular table is gone forever.

Here’s an Integrated Reasoning Table Analysis practice question.

Each GI screen presents a verbal prompt and a graph. The questions on a GI screen are in the form of two drop-down menus in a fill-in-the-blank format. That is to say, underneath the graph will be one or two sentences, with a total of two blanks: the student “fills in” the blank with a choice from the drop-down menu: the drop-down menus have 3-5 choices.

The graphs can be of several different types, including bar charts (including clustered column and segmented column charts), scatterplots, and bubble charts. One more exotic type of chart is the numerical flowchart. Here’s a post with a single Integrated Reasoning Graphics Interpretation practice question, and here’s a set of IR GI practice questions.

This question format presents some kind of prompt, and then a table. The table has three columns. At the top of the first two columns are the “questions,” and the possible answers to the questions are listed in the third column. The same set of possible answer choices applies to both questions. Often, the two questions are connected, in the sense that one must answer one to figure out the answer to the other.

In some ways, 2PA is the most flexible of the four question formats. Individual 2PA screens can be purely verbal (similar to RC and CR questions) or mathematical.

This post gives a single Integrated Reasoning Two-Part Analysis practice question, and here’s a set of IR 2PA practice questions.

The GMAT Integrated Reasoning questions are hard. Magoosh has a GMAT IR ebook as well as a full bank of lessons and practice questions to prepare you. Together, we can do this! 🙂

See also: Is the GMAT Integrated Reasoning More Important Now?

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

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]]>Now that you know a bit about this question type on the GMAT exam, here are some quick thoughts about what you need to do to prepare for the GMAT Integrated Reasoning question! 🙂

For the most part, the GMAT Integrated Reasoning differs significantly from the rest of the GMAT, but there a few similarities. Here are the principal similarities with the Q & V sections. (a) As with the Quant and Verbal questions, there is no ability to go back to a question. Once you press “submit,” that question is done and gone forever. (b) As with Q & V sections, the GMAT IR section is timed: in this case, you get just 30 minutes for the whole section, which makes this a bit more of a time crunch than the Q & V sections—more on that below. (c) As on the Q & V sections, some of the questions that appear are experimental and do not count toward your score; as you are taking the test, you have absolutely no way to know which questions count and which are experiment, so you have to treat each question you see as the real McCoy. (d) No subscore, whether Q or V or IR, on the GMAT is simple a count of the number you got correct: in all cases, the subscore is a psychometrically determined chimera, the calculation of which need not concern us.

The Verbal Section is, essentially, an ocean of five-choice multiple choice questions. Yes, the tasks differ among SC, RC, and CR, but the question format is identical. One could certainly make the argument that DS is just a five-choice multiple choice question in disguise, and that would make the Quantitative section another ocean of five-choice multiple choice questions.

The Integrated Reasoning is not simply another ocean of five-choice multiple choice questions. This ain’t your granddaddy’s GMAT! The four question types are:

- Multi-Source Reasoning(MSR)
- Table Analysis(TA)
- Graphics Interpretation(GI)
- Two-Part Analysis(2PA)

Here’s a brief primer on these formats.

__Multi-Source Reasoning__

This Integrated Reasoning question format, like the Reading Comprehension on the Verbal, dumps a great deal of information and then asks a few questions in a row. Just as 3-4 consecutive RC questions come with a single passage, 3-5 consecutive MSR questions will come with a single multi-card prompt. As with RC, the thought is that one has to invest a good deal of time to understand all the information in the cards, so it makes sense for a student to multiple questions in a row on all this information.

The cards will be on the left side of the split screen. At any one time, only one card will be up front and in view: you will have to use the tabs to bring one of the rear cards forward to view it. These cards will have mostly verbal information, perhaps a table or chart, an occasionally there is some kind of formula or mathematical information on one. You typically will have to combine information from different cards to answer any question.

The questions will appear, one at a time, on the right side of the split screen. There are two question types.

__MSR question #1__: just **a single five-choice multiple choice question**. This is the only place that this format appears on the GMAT IR.

__MSR question #2__: **a set of three dichotomous choice questions**. These will be in a grid, and the top of the first two columns will be some kind of dichotomy: yes/no, true/false, increase/decrease, buy/don’t buy, etc. There may be a verbal prompt before the chart, explaining the dichotomy a bit. Then, in each of the three row of the chart below the top row, there’s a question or statement, and for one, you have to pick the correct column.

You can see examples of these in the practice MSR questions on this blog

MSR practice question about the Whizzo Chocolate Company

MSR practice question about Draw Loss Poker

__Table Analysis__

The centerpiece of a GMAT IR TA question is, of course, the table itself: this is a large table with 4+ columns and typical 20 or 30 rows of data. This table is sortable, in this sense that we can choose any column by which to order the table. The GMAT loves to have at least one column that is a set of ranks: for example, suppose one column were a list of populations of various US states, in millions of people (California‘s entry in that column would be 39.1 and New York‘s would be 19.8); another column might be rank in US state population (CA’s entry would be 1 and NY’s would be 4). Right away, just those two data points tell us that there must be two states that have more than NY, a population higher than 19.8 million, but less than CA, a population less than 39.1 There are all kinds of logical deductions one might have to make from ranking data.

Every TA question comes with just one set of three dichotomous choice questions, the same format that appears on the MSR questions. Once you answer that question and hit submit, you never see that particular table again.

GMAT IR Practice Question: Table Analysis

BTW, in case you are curious, the two US States between CA and NY are Texas (pop. 27.5 million) and Florida (pop. 20.3 million)

__Graphics Interpretation__

As you might expect, each of of these questions presents a graph or chart of some kind. The chart may be a pie chart, a line chart, a bar chart, a scatterplot, a bubble chart, or some more exotic kind of chart. On the question screen, you will see the chart, and then below the chart, two sentences each with a blank: below that blank there will be a drop-down menu for 3-5 answer choices. For example, the sentence might show some sequence of economic data over recent years, and then one of the sentences could be “*The company made its highest profits in* ______.” The drop down menu might contain the choices {2010, 2011, 2012} and using the chart, we would have to select the correct year. These tend to be less time-consuming among GMAT IR questions: as long as the data can be figured out readily from the graph, there are only two questions to answer.

Here is a set of GI practice questions.

One particular unusual GI question involves a numerical algorithm flowchart.

__Two-Part Analysis__

GMAT IR Two-Analysis is the wild card of the Integrated Reasoning section. The basic form includes some introductory material, then a chart with three columns: the top entries in the first two columns are the questions, and set of entries listed down the right-most column are the possible answer choices for the questions. The two questions share the same set of answer choices and often it’s impossible to answer the second question without answering the first question first.

What’s brilliant about this design is that it can be entirely mathematical or entirely verbal. This is the only IR question that could be a pure mathematics question, and it is the only IR question that could be, essentially, a double-barreled Critical Reasoning question.

To get a sense of the variety, see the six practice problems in this set of 2PA practice questions

As you can see, the GMAT Integrated Reasoning section contains a variety of categories of information it will present, a variety of ways of present information, and a variety of question formats. Only the MSR includes the traditional five-choice multiple choice questions as *one* of its possible question formats. The other MSR questions, and all the TA & GI & 2PA questions formats, are entirely new.

Part of success on this section is simply getting as familiar as possible with the format of the presentations and the format of the questions. One way to reduce significantly the challenge posed by this section is to understand, in detail, the simple logistics of the formatting, so that this presents no surprise on test day.

**Fact**: there are 12 questions in the GMAT IR section—more accurately, 12 “screens,” because almost every “screen” consists of 2-3 individual questions. The MSR traditional five-choice multiple choice questions are the only questions in which there is simply one task in the question.

**Fact**: there is no partial credit on the IR. None. Zilch.

Those two facts, combined, have some powerful strategic implications for time-management. Suppose an IR question has multiple parts—for example, a MSR or TA section posing a Multiple Dichotomous Choice Question—this format presents two possible choices (“true”/”false”, “company gains money”/”company loses money”, etc.), and makes three statements: you have to decide the right choice for each statement. Because there’s no partial credit on the IR, you would have to choose the correct option for all three of those statements in order to get any credit for this question.

Well, if you are sure about the first two statements, it would probably be worth investing a little time to figure out the third statement. BUT, if the first two statements completely confused you, and you had to guess, it is not worth investing a ton of time in the third statement in an effort to figure it out. You randomly guessed on the first two, which means your chances of getting any credit for the question have already dropped to 25%. If you can’t answer the third statement quickly, it’s best to cut your losses, guess and get out of that question, so you have more time to devote to later questions.

Some skills demanded on the GMAT Integrated Reasoning are carry-overs from the Quantitative and Verbal sections. Many of the careful reading strategies used on Reading Comprehension and the argument analysis skills used in Critical Reasoning are highly pertinent to the IR. Of course, there’s a lot of math on the GMAT IR, especially reading graphs and interpreting data, so there’s a lot of overlap with what you need to know for the Quantitative section.

What’s new and different on the Integrated Reasoning involves critical thinking and executive function. That latter term, “executive function” is not “executive” in the business world sense; instead, it is a term from neurobiology that refers to the commanding and coordinating role of the prefrontal lobe of the cerebral cortex. While many aspects of prefrontal lobe executive function (e.g. not acting out a socially unacceptable impulse) are more or less irrelevant to GMAT performance, some—those most closely aligned with critical thinking—are vital to the IR. These skills include deciding priorities, weighing benefits vs. liabilities, designing strategy, resolving conflicting values, etc. The term “executive function” comes from neurobiology and has nothing to do with the business world, but ironically, many of these skills are absolutely essential for success as an executive in the modern business world.

How do you learn that stuff? Read how the experts do it every day. You need look no further than the WSJ or the *Economist* Magazine to get myriad examples of successful, and not-so-successful, executives exercising these skills in the real world. If you happen to be friends, or family friends, with someone who is a successful executive, pick their brain: listen to them talk about their craft. How do these folks make decisions and allocate limited resources and assess risks? Learn from the pros.

If you are not a math nerd by nature, you probably need to get more familiar with graphs. Again, both the WSJ and the *Economist* Magazine are wonderful sources: rare is an issue of either than won’t have a couple graphs scattered somewhere amongst its articles. Find those graphs, and practice interpreting them in context. If you understand everything a graph is communicating in a WSJ or *Economist* article, you are well on your way to the level of mastery that Integrated Reasoning expects.

Click the image below to read our eBook, which features strategies and practice content to help you improve your GMAT IR score!

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

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]]>**Fact #2**: In the months leading up to that date, thousands of GMAT test-takers accelerated their plans, taking the GMAT early to avoid the IR section. This produced a glut of pre-IR GMATs

**Fact #3**: Once a GMAT is taken, the score is valid for five years.

**Fact #4**: GMAC, the folks who write the GMAT, has done extensive research on the IR and has extensive data demonstrating the statistical validity of the IR section.

The four facts above are objective and uncontested. What is considerably more intriguing is what they imply.

You see, a couple years ago, business school adcoms were seeing a large percentage of GMAT scores coming in from the pre-IR period. Since some applicants had an IR score and some didn’t, the adcoms were in a position in which they really couldn’t use IR as a valid means of assessment.

At this point, the game has changed. Now, GMAT scores from before June 2012 technically would be valid, but scores from such an old GMAT are rarities. Virtually all GMAT scores submitted to adcom now have an IR score included. This makes the IR a viable possible assessment tool for adcom, in a way that it wasn’t a couple of years ago.

Fact #4 looms large in this context. After all, the point of the GMAT overall is as an assessment tool, a predictor for how well an applicant might handle the academic work at business school. Well, GMAC has extensive data demonstrating that the IR section has a predictive validity that is independent of the Q and V scores: in others, it provides extra assessment information that the other parts of the GMAT do not.

All this would tend to make us predict that, as time goes on, as IR scores with GMAT become the norm, that adcom would start to place more emphasis on the IR score. In fact, as this article points out, that is exactly what is happening. The GMAT IR section is becoming more important in admissions.

Right now, all we can say is that the importance of IR is growing. It makes sense to do your best on the IR section, just as you strive to do your best on the other parts of the GMAT. You can’t afford to ignore any part of the exam. But how important is the IR? The data that is in seems to suggest the typical and frustrating answer: *it depends*.

For folks who already excel at math, who studied something mathy in undergrad, who are in the upper percentiles of the Quant sections, the IR appears somewhat less predictive. In other words, we generally expect these folks to do well in the IR also. A low IR might raise questions for such a candidate, but a high IR is sorta what is expected.

By contrast, a verbal person, someone who majored in, say, literature or history in undergrad, someone who is lackluster in math but in the upper echelons of the Verbal sections—for this person, a strong IR score would be an extremely powerful statement. It may be, for some verbal people, the Quant section will always present difficulties, but the IR sections might be something these folks can master; if so, this mastery could speak volumes to adcom.

Right now, adcoms are starting to take IR seriously. How far will this go? Right now, many schools are still accepting the GRE as an alternative to the GMAT. The GRE Quant & Verbal are rough analogs of the GMAT Quant & Verbal, but the GRE has nothing like the IR section. It’s certainly possible that, if business school adcoms come to rely on the IR as an essential assessment tool, they may grow more reluctant to accept the GRE. Of course, that’s exactly the conclusion that GMAC would like business schools to draw. Of course, what ETS is hoping is that, once they get their GRE foot in the door at business schools, the business schools will be loath to roll that back. Big multi-million dollar players with very different agendas: you might want to grab some popcorn, sit back, and watch this one play out! The long-term implications are anyone’s guess! If you are talking an exam for an application in a couple months, you are fine with either exam. If you are taking an exam *now* for an application a few years from now, be cautious. The GMAT, of course, would always be a safe bet for business school admissions.

The moral of the story is: don’t neglect the Integrated Reasoning section. If you are going to take the GMAT, do everything you can to master IR (here are some great tips for that) as well as everything else associated with the GMAT. Among other things, remember that Magoosh can help you!

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]]>Hello! 🙂 GMAT’s newest section, IR, has some confusing (inaccurate?) instructions that you should definitely be aware of. This will help you budget your time much better and give you a sense of what to expect out of this section, so you can focus on doing well and not be distracted by surprises. Let us know if you found this video helpful, and whether you have any questions for us. Enjoy!

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]]>

1) The graph below shows the different commuting options chosen by commuters in the Farview City metropolitan region in 1995 and in 2005.

1a) The commuting mode whose ridership increased by approximately 29% from 1995 to 2005 is __________________.

1a) Assume the graph above shows all commuters in the two relevant years. In 2005, the car commuters were _______ percent of all commuters.

2) In a certain academic competition, there are three rounds, and three possible results in each round. The folks who “lose” acquire no commendations and do not advance to the next round. The folks who “place”, acquire a set of commendations for that round, but do not advance to the next round. The folks who “win” acquire a set of commendations for that round, and, in the case of the first two rounds, advance to the next round; in the case of the third round, the “win” means winning the entire competition. The following chart shows, on average, the percentages of participants who achieve the three results in each of the three rounds.

2a) If 100,000 participant start this process, and if all the percentages in the chart are correct, _______ people of them would win the entire competition.

2b) Exactly _______ % of participants who start acquire exactly two sets of commendations.

3) For years, the Bethel Company had Gamma division. The year 2008 was the first year that Rho division was in operation. The chart shows the profits generated by these two divisions. Assume these two divisions were the only source of profits for the Bethel Company during these years.

3a) In 2010 and 2011 combined, Rho division accounted for _____ % of Bethel’s profits.

3b) From 2008 to 2011, Rho division increased by ______%

4) The charts below show the breakdown for the 2010 revenues for Goliath Corporation, a major supplier of food and food preparation materials. The pie chart shows the breakdown of sales to grocery stores. Assume these two charts contain all the revenue for Goliath Corporation.

4a) The revenue from foreign export sales is __________ the revenue from grocery stores in the Northeast.

4b) Revenue from governmental contracts would have to increase by ________% to equal the revenue from grocery sales in the Midwest.

5) The graph below shows the population & land areas for eight major US cities. The area of the circle indicates the size of the GDP for the city’s extended metropolitan region.

The city abbreviations are **ATL** = Atlanta, GA; **BOS** = Boston, MA; **CHI** = Chicago, IL; **DAL** = Dallas, TX; **HOU** = Houston, TX; **LA** = Los Angeles, CA; **NYC** = New York City, NY; **PHI** = Philadelphia.

5a) Population density is the ratio of population/land area. Among the eight cities shown, __________ is the city with the lowest population density.

5b) According to this graph, the population of a city is ________________ with the size of the GDP of the metropolitan region.

6) Apex Appliances is a regional appliance retailer with multiple store through seven states. The graph below shows their performance over two calendar years, 2011 and 2012. Each dot is one month, and shows the total number of store visitors and the sales revenue from that month. The six dots with the highest numbers are store visitors are the “fourth quarter” months, October – December, of each year.

6a) During this two-year period, Apex Appliance had ________ non-fourth-quarter month(s) with higher sales revenue than the fourth-quarter month with the lowest sales revenue.

6b) In Apex’s accounting system, the “yield” of a month is the ratio of sales revenue to number of customers in that month. In the month show here with the highest yield, Apex earned _________ in monthly sales revenue.

AS a general IR rule — yes, you get a calculator. *Make it your goal to touch that calculator as little as possible*. You will see: we can do all of these questions without the calculator!!

1)(a) Well, we can estimate this one. A 29% increase is an increase of a little more than a quarter. Bikes tripled, so that’s way more than a quarter increase — that’s not correct.. The category “subway & bus” when from 3 to 5 million, more than a 50% — that’s not correct. Cars decreased, so that’s not correct. Even without looking at “commuter trains”, we can easily eliminate the other three. Notice “**commuter trains**” increased from 7 M to 9M, a 2M increase which is slightly more than one quarter of 7. That’s the answer, and we didn’t need the calculator.

1(b) In 2005, there were 8M car commuters, and 3 + 5 + 9 + 8 = 25M commuters total. That means, car users were 8/25. Multiply this fraction by 4/4 to get 32/100 = **32%**.

2)(a) Suppose 100,000 start. In the first round, 40%, or 40,000 are able to “win” and advance to the second round. In the second round, 20% of 40,000 = 8,000 are able to “win” and advance to the third round. In the third round, 10% of 8,000 = **800** win the entire competition.

2)(b) How are the people who win exactly two sets of commendations? They form two groups. One group are the people who win the first round and place in the second, thus winning two commendations and not advancing. The others are the folks who win the first round, win the second round, but lose the third round, thus earning only two sets of commendations even though they advanced to the third round.

Folks who (1st = win, 2nd = place) = (0.40)*(0.40) = 0.16 = 16%

Folks who (1st = win, 2nd = win, 3rd = lose) = (0.40)*(0.20)*(0.70) = 0.056 = 5.6%

Add these: 16% + 5.6% = **21.6%**

3)(a) The numbers are spread out, so this suggests we can estimate. Profits were $40M for 2010 and $51M for 2011, for a total profit of $91M over the two years. That’s our denominator. Rho accounted for $18M in 2010 and $21M in 2011, for a total contribution of $39M — that’s our numerator. What is 39/91 as a percent? Well, 30/90 = 33%, so this has to be more than 33%, and 45/90 = 50%, so this has to be less than 50%. That immediately leaves only one possible answer, **42.4%**, and we didn’t have to touch our calculator.

3)(b) From 2008 to 2011, Rho increased from $7M to $21M, a three-fold increase. Be careful, though: when something triples, that’s NOT a 300% increase. No, it started at 100% ($7M), then increased by 100% (another $7M) and then another 100% (another $7M) — a **200%** increase. Tripling is always a 200% increase.

4)(a) The revenue from foreign export sales is $124K. The revenue from grocery stores in the Northeast is 26%, about a quarter of $793K. Well, estimate that as $800K – about a quarter would be $200K, and $124 is much **less than** $200.

4)(b) The current revenue from government contracts is $67K. The revenue from grocery stores in the Midwest is 17% of $793K — estimate the number up to $800K and the percent down to 15%. The, 10% of $800K is $80K, and half of that, 5% is $40K, so add those: 15% of $800 is $80K + $40K = $120K, very approximate. That is exactly the double of $60K, and therefore close to the double of $67K. If something doubles, it increases 100%, so we want a percentage increase close to 100%. The closest is **101%**.

5)(a) We will estimate this visually. For a low population density, we want the numerator, population (the vertical coordinate), to be relatively small, and the denominator, land area (the horizontal coordinate), to be relatively large. First, let’s look at Boston vs. Atlanta. Boston appears to have a higher population than Atlanta, with a lower area, so it definitely will have a higher population density than Atlanta — Boston is out as a possibility. Atlanta has a population about 0.4M and a land area about 130 sq mile. Houston has a population of about 2.2M and a land area very close to 600 sq mi. In going from the Atlanta fraction to the Houston fraction, the numerator would have to multiplied by something between 5 & 6 (from 0.4M to 2.2M) while the denominator will be multiplied by something between 4 & 5 (from 130 to 600), so in going from the Atlanta fraction to the Houston fraction, we will multiply by a fraction that has a bigger numerator than denominator, i.e. a fraction greater than 1, which makes the second fraction, the Houston fraction, bigger. Thus, the Atlanta fraction, and **Atlanta** has the lowest population density. (*A bit dicey without the calculator, but we did it*!)

5)(b) Population is the vertical scale on the graph. GDP of the metropolitan area is not a scale, but corresponds to the area of the “bubbles” on this “bubble graph”. Ignore the left-right variation — that’s irrelevant to this relationship. Notice that, as a general pattern, smaller circles are on the bottom — the bottom five circles are very close in area — and clearly the last three circles all increase in area as they increase in height. This is enough to say that: as population of the city increases, on average the GDP of the metropolitan area increase. Thus, the two are **positively correlated**.

6)(a) The fourth-quarter months are the six dots on the right, marked in light green. The lowest of these is surrounded by a red circle, and a horizontal line extends through this lowest point. That line marks the monthly revenue earned by this month, the lowest earning fourth-quarter month.

Notice, of the non-fourth-quarter points, the ones that remain black in the diagram, only three are above this horizontal line. Those three earned more in revenue than that lowest earning fourth-quarter month. **Three**.

6)(b) The orange point, circled with a red circle, is clearly the point with the highest yield. First of all, this point garnered more in revenue than all the other non-fourth-quarter points on the left. If we look at the three fourth-quarter points that are more than it — they earned only 10%-20% more profit, but had more than 4 times as many visitors —- if the numerator (revenue) is multiplied by 1.2, and the denominator (visitors) is multiplied by 4, the whole fraction gets smaller. That’s why all those four-quarter points must have a smaller yield than the circled point.

That circled point has a monthly revenue around $7.5M, or **$7,500,000**.

To find out where graphics interpretation, AKA data interpretation, sits in the “big picture” of GMAT Quant, and what other Quant concepts you should study, check out our post entitled:

What Kind of Math is on the GMAT? Breakdown of Quant Concepts by Frequency

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]]>1) Chair P, from Design Solutions, cost $60 per chair. Chair Q, from Seat Unlimited, costs $90 per chair. An office manager often has to buy several chairs to stock the floor space of new offices. On one occasion, she orders p of chair P, and q of chair Q. The average cost of a chair would be

In the table, select a value for p and a value for q corresponding to an average cost per chair of $70. Make only two selections, one in each column.

2) A contractor is hired to construct two concrete retaining walls for the city: Harrison Wall and Jackson Wall. As part of his budget, he needs to calculate the cost of the concrete he will use. For raw materials for the concrete, he has to pay $9.75 per cubic meter of concrete. Harrison Wall will be 35 cm thick, and will have dimensions of 11.5 m long and 8.1 m high. Jackson Wall will be 50 cm thick, and will have dimensions of 31.0 meter long 11.8 m high.

In the table, select the value that the closest to the cost of the concrete for Harrison Wall as well as the cost of the concrete for Jackson Wall. Make only two selections, one in each column.

3) Among the teachers at Ashcroft High School, English and History teacher have the heaviest grading burden. In addition to the smaller daily assignments that all other teachers must grade, English and History teachers, especially of junior and senior students, must grade lengthy writing assignments a few times a semester — literary essays in English and term papers in History. Therefore, since English and History teachers grade more, they should be paid more than the teachers of other subjects.

Select Strengthen for the statement that would, if true, most strengthen the argument, and select Weaken for the statement that would, if true, most weaken the argument. Make only two selections, one in each column.

4) The area of a triangle, in square meters, is 7/3 times the height in meters, and it is also 13/5 times the base, in meters.

In the table below, select a value for the height and value for the base, where both are measured in meters, so that the two values are jointly consistent with the information provided. Make only two selections, one in each column.

5) On planet K, there is essentially no atmosphere, so objects in freefall experience no air friction. At time t = 0, an object released from rest accelerates downward at a uniform rate: it’s downward speed uniformly increases. At time t = 2 second, the object has fallen a distance D in meters from its original height. At time t = 5 second, the object is 75 meters below its original height, and is moving at a downward speed of v in meters per second.

In the table below, select values of D, the distance below the initial height at t = 2 seconds, and v, the downward speed at t = 5 seconds, that are consistent with the information provided. Make only two selections, one in each column.

6) Highway commissioner: at the present time, the forty mile stretch of interstate highway from the town of Hillsborough to the city of West Fredericksport is clogged every weekday with commuter who live in Hillsborough and work in West Fredericksport. Our department is considering increasing the lanes in this stretch of the interstate highway, and the town of Hillsborough could benefit its citizens by contributing to this highway improvement.

Mayor of Hillsborough: we could contribute much more to the well-being of citizens of Hillsborough by investing that same money in a stimulus package to increase the number of jobs here in Hillsborough.

Suppose that the highway commissioner’s and mayor’s statements express their genuine opinions. Select statements (1) and (2) as follows: the highway commissioner would likely disagree with (1), and the mayor would take (2) to present logical support for (1). Select only two statement, one per column.

1) We know the average is $70, so set the fraction expression equal to 70.

The WRONG approach would be to start trying to figure out what pairs of numbers would satisfy the fraction in this form. That would take more than ten minutes! Instead, algebraically simplify. First, multiply by the denominator (p + q)

70(p + q) = 60p + 90q

70p + 70q = 60p + 90q

10p + 70q = 90q

10p = 20q

p = 2q

Right there, that’s the simple relationship we need. The number p has to be double of the number q. The only pair of numbers in this set that fit this relationship are **p = 56** and **q = 28**.

2) This is a problem *screaming out* for estimation. Don’t touch the IR calculator at all — the calculator will be a HUGE waste of time on this question. Here’s our estimation:

cost of concrete ≈ $10 per cubic meter of concrete

Harrison Wall =

cost of Harrison = **$320 **

Jackson Wall =

cost of Jackson = **$1800**

3) Choice **(A)** is irrelevant. The focus of the question is about time spent grading, so time spent meeting with students is outside of the focus of the question.

Choice **(B)** is irrelevant. We have absolutely no indication that teaching different grade levels would involve more or less time spend grading papers, so there is no clear connection between this statement and the thrust of the argument.

Choice **(C)** is vague, making an appeal to what most schools do. If most of the other schools have equal pay for teachers of all subjects, then maybe those schools are doing things the fair way, and this argument is wrong; or maybe the argument about Ashcroft recognizes a fundamental inequity that is not recognized at most other school, and Ashcroft will, by its shining example, usher in a new era of workplace equality. Just because one place is considering doing things differently from the way everyone else does them does not necessarily indicate who is right.

Choice **(D)** points out a flaw. If Science teachers spent a great deal of time grading lab reports, then it definitely wouldn’t be fair for English and History teachers to get more pay for grading, but not the Science teachers. This is a **weakener**.

Choice **(E)** is irrelevant. If one pay system or another is the fair and right thing to do, it doesn’t matter who makes the decision to implement it. Furthermore, it sounds as if the union is interesting in basing pay on “merit”, which is a different criterion than the one supported in the argument.

Choice **(F)** is a strengthener. If this is true, then indeed, pay reflects hours of work, and so if the English and History teachers do work many more hours because of all the grading they have, then they would get paid accordingly. This is a **strengthener**.

**strengthener** = **(F)**

**weakener** = **(D)**

4) The first statement, in math symbols:

The second statement, in math symbols:

5) We will solve for the second column first. The object has fallen 75 meters in 5 seconds, which is an average speed of 75/5 = 15 meters/second. This speed, the average for the entire five seconds, would be the average of the initial speed and the final speed. The initial speed is zero.

That is the speed at time t = 5 seconds. The object has been increasing speed at a uniform rate from 0 to 30, so for the *speed* at t = 2 seconds, we can set up a proportion.

If that’s the speed at time t = 2 seconds, then the average speed over the first two seconds is

If the object moved downward at an average speed of 6 meters/second for 2 seconds, then it covers **12 meters**.

**v = 30**

**D = 12**

6) For statement (1), we need a statement that is simultaneously one with which the highway commissioner would clearly disagree, and which the mayor would clearly support.

Choice **(A)**: the highway commission would clearly disagree with this, but it’s not at all clear that the mayor would agree. It’s a very extreme statement: even if expanding the highway is not the very best option for the citizens of Hillsborough, that doesn’t mean it will be harmful.

Choice **(B)**: the mayor would clearly agree with this, but it’s not very clear that the highway commissioner would disagree: nothing in what the highway commissioner says gives any clear indication that he would disagree with this.

Choice **(C)**: not directly relevant: it is unclear whether either speaker would agree or disagree with this.

Choice **(D)**: not directly relevant: it is unclear whether either speaker would agree or disagree with this.

Choice **(E)**: this opposes the substance of the highway commissioner’s argument, and in some ways, it is a paraphrase of the mayor’s objection to the highway commissioner. It is clear that the highway commissioner would disagree, since it contradicts his position, and it is clear that the mayor would support this, since it is completely consistent with what she said. This is a good candidate for Statement (1).

Choice **(F)**: not directly relevant: while the highway commissioner might agree, it is unclear whether the mayor would agree or disagree with this.

The best choice for statement (1) is **(E)**.

To support (E), the only remaining statement that’s relevant and with which the mayor wholeheartedly would agree is **(B)** — that has to be statement (2).

Statement (1) = **(E)**

Statement (2) = **(B)**

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The flowchart represents a mathematical algorithm that takes one positive integer as the input and returns a positive integer as the output. Processes are indicated in the rectangular symbols in the flowchart. Each process is represented by an equation, such as p = p + 1. In this particular process, one is added to the current value of p, and the sum becomes the new value of p. For example, if p = 8 before the process, p = 9 after the process.

1a) A value p = 50 is initially entered. When S first has a value of S = 10, p has a value of _____________.

(On the real GMAT, this little “answer chart” would be a drop-down menu in the blank spot of the question!)

1b) An initial entry that reaches an output in the fewest number of steps is ________.

A full solution will follow this article.

For mathematical and computer science folks, a flowchart diagraming a mathematical algorithm might be one of the most enjoyable games the GMAT provides. For less mathy folks, though, this questions type could be a living nightmare. How does someone not adroit at mathematical reasoning even begin to make sense of this?

Notice for the first question, and often for the first question on such a problem, all the question is asking us is to plug in an initial value and follow it step-by-step through the process. From what I can tell, this is standard on the GMAT: if the mathematical algorithm involves more than a couple steps, then the first of the two question will simple be of the form — “Here are the plug-in numbers: can you follow the step-by-step process a couple steps?” Don’t be intimidated. All you have to do is follow the arrows, one step at a time, and keep track of what each variable equals at each point.

Sometimes the other question also involves plugging in some input, perhaps going a few more steps ahead. Sometimes, though, the other question, like the second question here, involves no so much plugging in a bunch of different numbers, but getting a sense of the patterns. For example, particular loops that repeat several times are very important patterns to notice —- why they repeat, and what changes on each repetition. I will discuss this more for this particular flowchart in the solutions below.

Keep in mind that the actual math involve will just be ordinary arithmetic. Keep in mind that every individual step is something you are most certainly able to do. The biggest challenge, in many ways, is simply keeping all the information organized. I will show how I do this in the solution below.

If the discussion above gave you any insights or “aha’s”, you may want to take another look at what those questions are asking. If you would like to share anything or ask a question, please let us know in the comments section below.

1) OVERVIEW: Without plugging in any particular number, I am going to just follow the process step-by-step and see what I notice.

At the start, S = 12, and p can be any number I enter. The first thing that happens is the question: is p even or odd? If it’s even, we add one, making it odd. The only other place in the entire charge where p can change is the “p = p + 2” box — once p is odd, adding 2 will just produce another odd number, so what happens to p — if it’s even, it is made odd, and once it’s odd, it just moves up by 2, through the odd numbers consecutively.

If p is not prime, the number simply repeats that upper loop — not prime, add 2, is it even? no, not prime, repeat. While going around that loop, S doesn’t change. The only opportunity for S to change is if p is a prime number.

What happens when p gets to an odd value? Then we move down to the decision diamond “Is p < S?” That’s a crucial place. Since S only starts at 12, most of the time, the answer will be no, S will decrease by one, and if it’s not zero, it returns to that same upper loop. Thus, usually, S decrease by one every time p hits a prime number, so p will keep rising until it hits its twelfth prime number value.

BUT, if the input is small, and p actually is smaller than S, then S decrease by p — that is to say, S decreases not just by one but by several notches all at once: the process accelerates significantly, and it will take far fewer steps to complete the entire process.

Notice, also, the output, the final value of p, will have to be prime number, because the only way that we break out of that upper loop and get to the lower half of the flowchart is when p is prime. The output is always prime.

Those are all the things I notice just scanning the flowchart, without plugging anything in.

Question 1a) I will use ordered pairs of the form (p, S) to discuss this. I recommend ordered pairs (or triplets) for keeping track of how numbers change as we move through the steps.

Enter p = 50, so at that point we are at (50, 12). Is p even? Yes, so add one: (51, 12). Is p prime? No (51 = 3*17), so we go around the upper loop — add two to p: (53, 12), then p is odd, and now, 53 is in fact prime.

Drop down to the lower decision dimension: p = 53 is not less than S = 12, so subtract one from S: (53, 11). We see S is not zero, so back up to the upper loop. Add two to p: (55, 11). Is p even? No. Is p prime? No (55 = 5*11). Around the upper loop. Add two to p: (57, 11). Is p even? No. Is p prime? No (57 = 3*19). Around the upper loop. Add two to p: (59, 11). Is p even? No. Is p prime? Yes, 59 is in fact prime.

Again, drop down Drop down to the lower decision dimension: of course, p = 59 is not less than S = 11, so subtract one from S: (59, 10). That’s it. S now has a value of 10, so the value of p at this point is p = 59. That’s the answer. **(D) 59**

Question 1b) Here, the analysis we did above really helps us. For most numbers, larger numbers, S will decrease one notch at a time, and we will have to move p through twelve different prime numbers to reach an output. BUT, if we can have a p get down to the lower half that’s less than S = 12, then we can reduce S by a whole lot at once, and vastly accelerate the process.

Reject p =31 — too big. Even p = 12 will not work: that’s even, so immediately, it will be nudged up to p = 13 at the very beginning, and then it’s already bigger than S. That doesn’t work.

Suppose we start with p = 10. Also even, so immediately it nudges up to p = 11, which is prime. That would go to the lower loop, and in one fell swoop, **S would go down from S = 12 to S = 1! ** **WOW**! That’s huge! That means there would only one more trip around the upper loop, p goes up to p = 13, also prime, back to the lower half, S goes to zero, and the process outputs p = 13 and is done. That’s a lightning fast conclusion! It only goes all the way around that upper loop once!

The smaller starting values, p = 1 (which is NOT prime) and p = 3 will require more than two circuits in the upper loop, so they will take more steps. Of these five answers, nothing else would reach an output as quickly as p = 10. **(C) 10**

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1. Player A initially draws three-of-a-kind and chooses not to discard at all on the discard round. Player B initially draws three-of-a-kind, discards the remaining two cards. For the following final card combinations of Player B, tell whether Player A outscores Player B.

2. Suppose player J draws two pair and chooses not to discard any cards. Suppose player K draws three-of-a-kind and choose not to discard any cards. Which of the following discard choices and final card combination would have a higher point value than player J’s hand but not than player K’s hand?

(A) discard 1 card, three of a kind

(B) discard 2 cards, flush

(C) discard 2 cards, straight

(D) discard 3 cards, full house

(E) discard 4 cards, full house

3. Player G received the following cards on the initial five-card draw: 2 of Clubs, 5 of Diamonds, 8 of Hearts, 8 of Spades, and King of Diamonds. Player G will choose to discard exactly two cards, the 2 of Clubs and 5 of Diamonds. Over all possible hands that could result, what is the range of the possible point values of Player G’s final hand?

(A) 588

(B) 598

(C) 1794

(D) 3588

(E) 3598

4. Suppose player S draws a straight on the first five-card draw and choose not to discard any cards. Player T initially draws the following five cards: 4 of Diamonds, 4 of Hearts, 6 of Hearts, 7 of Hearts, 7 of Clubs. Which of Player T’s discard choices and final results will outscore Player S?

1. Three-of-a-kind = **A outscores B**

Full House = **A does not outscore B**

Four-of-a-kind = **A does not outscore B**

2. C

3. B

4. first row = **T does not outscore S**

second row = **T outscores S**

third row = **T outscores S**

1) Player A draw three-of-a-kind (worth 60 points), and does not discard, so A’s hand is worth 60 points. In all three cases, B discards two cards, for a reducing factor of 1/6.

(a) B’s final hand = three-of-a-kind, which is (60)*(1/6) = 10 points. **A outscores B**.

(b) B’s final hand = Full House, which is (720)*(1/6) = 120 points. **A does not outscore B**.

(c) B’s final hand = Four-of-a-kind, which is (3600)*(1/6) = 600 points. **A does not outscore B**.

It wasn’t relevant in any of these scenarios, but notice the exact wording — if A and B were tied, the answer would be “A does not outscore B.”

2) Player J, with two pair and no discards, has 36 points. Player K, with three-of-a-kind and no discards, has 60 points. We want a combination worth more than 30 points but less than 60 points.

(A) discard 1 card, three of a kind = (60)*(1/2) = 30. Less than 36, no good.

(B) discard 2 cards, flush = (540)*(1/6) = 90. Higher than 60, no good.

(C) discard 2 cards, straight = (300)*(1/6) = 50. This could work.

(D) discard 3 cards, full house = (720)*(1/10) = 72. Higher than 60, no good.

(E) discard 4 cards, full house = (720)*(1/60) = 12. Less than 36, no good.

**(C)** is the only hand & discard combination that is in the required range.

3) The five original cards in Player G’s hand are: 2 of Clubs, 5 of Diamonds, 8 of Hearts, 8 of Spades, and King of Diamonds. Player G discards the 2 of Clubs and 5 of Diamonds, leaving two 8’s and a king. We know that Player G’s reducing factor for this hand will be 1/6.

The highest possible hand would be four-of-a-kind, in the unlikely scenario that G picked up the other two 8’s. That would result in (3600)*(1/6) = 600 points, the maximum.

The lowest possible hand would be if G picks up garbage and just has the two 8’s. That would result in (12)*(1/6) = 2 points, the minimum.

The range of any set is the max minus the min. Range = 600 – 2 = 598.

Answer = **(B)**

4) Player S’s hand is worth 300 points. That’s fixed. Now, we have to compare T to that 300 point total. discard 4 of Diamonds & 7 of Clubs, winds up with a flush

Scenario #1: discard 4 of Diamonds & 7 of Clubs, winds up with a flush. Flush is worth 540, times the reducing factor of 1/6, for a point value of 540*(1/6) = 90, which is less than S. **Player T does not outscore player S**.

Scenario #2: discard 6 of Hearts, winds up with a full house. Full house is worth 720, times reducing factor of 1/2, for a point value of 720*(1/2) = 360, which beats S. **T outscores S**.

Scenario #3: discards 4 of Diamonds & 4 of Hearts & 6 of Hearts, winds up with four-of-a-kind. Four-of-a-kind is worth 3600, times a reducing factor of (1/10), for a point value of 3600*(1/10) = 360, which beats S. **T outscores S**.

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When the points on a scatterplot lie more or less in a straight-ish line, that 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 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. Here’s an example of a graph with a very strong positive correlation.

Notice, the points are not perfectly in a line, but the upward trend is unmistakably clear. In the real world, examples of variables that are positively correlated are the price of crude oil per barrel & the price of a gallon of gasoline; the number of automobiles in a municipality & the number of traffic lights in that municipality; daily temperature & daily ice cream sales; etc.

Here’s another example graph, with a very clear negative correlation.

Again, the points do not line in a perfect straight line, but the downward trend is clear: when the x-axis variable goes up, the y-axis variable does down. In the real word, examples of variables that are approximately negatively correlated are the unemployment rate & the Dow Jones average; the torque of a car’s engine & its fuel efficiency; a baseball pitcher’s career ERA & his number of career shutouts; etc.

Those two graphs were, by statistical standards, quite “pretty”: the pattern is very clear, and little of real-world messiness is evident. Here’s some real-world data, exploring that last baseball point: a baseball pitcher’s career ERA vs. his number of career shutouts.

This graph only includes career leaders (in the top 1000) in both stats. It’s much messier than the previous graphs, which is typical of real world data, but the negative trend is still apparent. BTW, that single dot way up at the top, with Career Shutouts = 110 and a career ERA = 2.17, is the great Walter Johnson, easily one of the finest pitchers of all time.

For the first two graphs, we can easily imagine the straight line that would go through these points and summarize them. It’s somewhat less clear exactly where it would lie on the third “messy graph. This line, which summarizes the implicit linear trend in a scatterplot is called alternately a “trend line” or a “line of best fit.” The official name in statistics is a “least square regression line”, but the exact details about how it is calculated and all its technical properties are well beyond what you need to understand for the GMAT.

Here’s the second graph again, with a trendline.

The trend line moves through the center of the linear pattern. Here, the points are negatively correlated, so the trendline has a negative slope.

Here’s the baseball graph with its trend line.

The trendline allows us to make prediction of a typical data point. For example, here, if a pitcher has a career ERA of about 3.50, we would expect that pitcher to have, on average, about 20 career shutouts. Pitchers above the trendline had more shutouts than expected for their ERA, and pitchers below the trendline had fewer shutouts than expected for their ERA. Making a predicted y-value for a hypothetical x-value, or judging whether an individual point has a higher or lower “typical” y-value, given its x-value — this is about all the trendline analysis the GMAT will expect of you.

This caution, about the meaning of correlation, may be more relevant to GMAT Critical Reasoning that it is to Integrated Reasoning. To say A and B are positively correlated is to say: when A is a relatively big number, so is B; and when A is a relatively small number, so is B. A and B “go together.” What it does ** not** mean is: A causes B. If A causes B, or if B causes A, then the two variables will have a high correlation, BUT the converse is not true. As the canonical saying in the social sciences goes:

Here’s a free practice question involving a scatterplot with a trendline.

1) http://gmat.magoosh.com/questions/2305

The post GMAT Integrated Reasoning: Correlation and Trend Lines in Scatterplots appeared first on Magoosh GMAT Blog.

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