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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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]]>**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) 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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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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Below is a scatterplot on which the individuals are countries. Each dot is a country.

On this graph, the x-axis is the GDP-per-capita of the country. The GDP (Gross Domestic Product) is a measure of the amount of business the country conducts: the size of this depends on both the inherent wealth of the country and the population. When we divide that by the population of the country, we get GDP-per-capita, which is an excellent measure of the average wealth of the country. The y-axis is life-expectancy at birth in that country. The sideways L-shape tells the story: For countries with a GDP-per-capita above $20K, life-expectancy at birth is between 70 and 80 years, but for the poor countries, those with a GDP-per-capita less than about $20K, life-expectancy at birth varies considerably, and is in many cases considerably less than the 70+ years that is standard for most of the world.

Now, as an example of a scatterplot with two different marks on the graph, here the same graph again, with some of the points marked differently.

On this graph, the grey circles are countries on the continent of Africa, and the blue squares are countries in the rest of the world. Notice that essentially, the entire continent of Africa is in the “vertical arm” of the L on the left side, while the rest of the world predominantly makes the “horizontal arm” of the L at the top of the graph. In other words, if you are born in Africa, your odds from birth are far worse than if you are born anywhere else on the planet. The international social justice implications of this are staggering, and well beyond what I can discuss here. This does, at least, give a taste of how the Integrated Reasoning section might ask you to draw a politically or ethically important conclusion from a graph. Suffice it to say: displaying data in a scatterplot can make truly important information visually apparent.

This gets to the heart of why mathematician love graphs, and why the GMAT is likely to give you graphs like scatterplots. A scatterplot makes the relationship between two variables, over a potentially large number of data points, visible at a glance. The more you practice with these graphs, the more you will appreciate their astonishing capacity to convey information in visual form.

Where in the real world might you see scatterplots? As with much of the rest of GMAT Integrated Reasoning material, I highly recommend the *New York Times*, *Bloomberg Businessweek*, and the *Economist Magazine* as excellent sources that often display complex and highly relevant information in graphical form. Also, here’s a Magoosh practice question:

1) http://gmat.magoosh.com/questions/2303

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]]>The post Integrated Reasoning Question Type: Bar Charts appeared first on Magoosh GMAT Blog.

]]>This post is a whirlwind overview of what you need to know about the varieties of bar charts in order to be successful with them on the new IR section.

Some sources call a graph with horizontal bars a “bar chart” and a graph with vertical bars a “column chart.” Apparently, GMAC is not interested in that distinction, because the OG 13’s section on IR calls graphs with vertical bars “bar charts”; presumably, if the bars were horizontal, GMAC would still call them “bar charts.”

A little more is at stake here than pure semantics. Typically, when the bars are horizontal, each bar represents a completely different item from some overarching category. For example:

Here, the bars are different fruits. Why these fruits were selected, and not others, is not obvious. The order here is simply alphabetical, as there is no pre-determined way to put fruits into “order”, whatever that would mean. If there is no inherent order to the categories, and the representative chosen do not exhaust the category, then the data typically would be displayed in horizontal bars, what many sources would call a “bar chart.”

If the set has an inherent order to it (days of the weeks, months of the year, etc.) and/or the representative shown constitute all in the category, the data typically would be displayed in vertical bars, what many sources would call a “column chart”, but which GMAC appears to still call a “bar chart.” For example:

Here, days of the week have a well-defined order, in which they are displayed. Assuming this business only operates during weekdays, this is also a complete set of all the days on which they do business. That’s why the vertical columns are used.

This is a more detailed chart of the “sales by day of week” chart given above.

This one gives more nuanced information. Apparently, this company has two divisions, and how each division performs during different days of the week varies considerably. For example, Division 1 clearly has its best days on Wednesdays, while for Division 2, Mondays and Thursdays appear to be close to tied for best days. Here, the individual pieces are displayed as segments of a column because we might be interested in knowing either the revenues of either division separately or the total revenues of the company, which equals the sum of the revenues of the two divisions.

Sometimes we care about the sum of the parts, and sometimes we don’t. If, instead of being two divisions of the same company, those same data were interpreted as the revenues of two different companies competing in the same market, then the sum of the revenues would be virtually meaningless. In this case, the columns or bars are “clustered”, that is to say, displayed side-by-side. For example:

Here, the side-by-side comparison makes it very easy to compare which company outperforms the other on each day of the week.

The following graph shows the annual revenues of two companies, close competitors in the same market, over a recent six year period.

1) Company B’s revenues in 2005 were approximately

A) $56,000

B) $85,000

C) $132,000

D) $154,000

E) $217,000

2) Of the years shown, in the first year that Company B’s revenues overtook Company A’s revenues, how much more money did Company B earn that year?

A) $45,000

B) $63,000

C) $91,000

D) $108,000

E) $138,000

3) What was the percentage decrease in Company A’s revenue from 2007 to 2008?

A) 4.5%

B) 11.4%

C) 26.2%

D) 32.2%

E) 55.7%

4) Suppose for each year shown, we calculate the ratio of Company B’s revenues to Company A’s revenues. From 2003 to 2008, by what percent did this ratio increase?

A) 16.7%

B) 109.5%

C) 219.1%

D) 441.7%

E) 1104.4%

1) This first question is a very straightforward question about reading a single value from the chart. We want Company B’s profits in 2005. We look at the red column above 2005, which has a height slightly above $80K, certainly less than $90K, about halfway between them. The only answer in that ballpark is $85000, answer = **B**.

2) This is a slightly trickier question. First, we need to identify the first year in which Company B’s revenues overtook Company A’s revenues. This would be the first year on the chart for which the red column is higher than the blue column. The first time this happens is 2007. In 2007, A made something just above $90K, say $93K, and B made something just below $140K, say $138K. We want to know how much more Company B earned, so we subtract: $138K – $93K = $45K, and this is answer **A**.

3) In 2007, A made something just above $90K, say $93K. In 2008, A made something just above $960K, say $63K. For approximation purposes, let’s just round these to $90K and $60K respectively. If the revenues went from $90K in 2007 to $60K in 2008, that’s a drop of $30K, which is one-third of the starting value $90K. One-third as a percent is 33.3%, so the percentage decrease is going to be something very close to 33.3% percent. The only close answer choice is 32.2%, answer = **D**.

4) This is a very challenging question, about as hard as anything the GMAT is going to ask on the IR section. Notice that the answer choices are very widely spaced, which means we have free rein to approximate in answering this question. First, we have to approximate the two values of the ratio. In 2003, A earns approximately $130K, and B earns just over $20K. I’m going to approximate B’s earnings as $26K, so that both the numerator and denominator are divisible by 13. Then the ratio becomes:

ratio B:A in 2003 = 26/130 = (2*13)/(10*13) = 2/10 = 0.2

Then, in 2008, A earns just over $60K, and B earns something over $150K, so I am going to approximate them as $60K and $150K respectively. Then:

ratio B:A in 2008 = 150/60 = (5*30)/(2*30) = 5/2 = 2.5

According to our approximation, the ratio has increase by a factor of

factor = 2.5/0.2 = 25/2 = 12.5 times

Now, a tricky thing about percent increase. If I multiply by 2 (x becomes 2x), that’s a 100% increase. If I multiply by 3 (x becomes 3x), that’s an increase of 2x, a 200% increase. If I multiply by 4 (x becomes 4x), that’s an increase 3x, a 300% increase. Here, we multiply by 12.5 — x becomes 12.5 x — so that’s an increase of 11.5, a 1150% increase. The only answer even vaguely close is **E**.

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]]>What in Sam Hill is a bubble chart?

A bubble chart is a close cousin to a scatterplot. In a scatterplot, each data point has values in two different variables, and for each data point, its vertical & horizontal position on the graph tells its value in those two variables. For example, here’s a scatterplot:

Each dot on this scatterplot is a company. The vertical position of the dot tells you the 2011 revenue of the company. The horizontal position tells you the year the company was founded. For example, there’s a company founded in 2001 that has revenues under $100K — it appears to have had 2011 revenues of around only $70K, the lowest of the six companies shown. It appears the oldest company did quite well, but then the next two oldest companies have come nowhere close to the success of the older company, while some of the younger companies have done much better. This data makes us curious: after the oldest company, why were the next two companies relatively unsuccessful, but later companies were relatively successful?

The beginning of an answer to this question shows up on the bubble chart. On a bubble chart, the center of the “bubble” is exactly like a dot on a scatterplot — 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.

Below is a bubble chart based on the same data. Notice: the vertical and horizontal variables are identical, so the centers of the bubbles in the chart below are exactly the same as the locations of the dots in the chart above. In this new graph, the size of the bubble introduces a new variable: number of employees.

Just for a sense of scale, I’ll say that Company A (the oldest, founded in 1996) has 78 employees, and Company F (the youngest, founded in 2010) has 12 employees.

Notice how much more nuanced the story becomes now. Company A was founded first: it’s the oldest, with the largest 2011 revenues and the second largest number of employees. The next two companies were also relatively large companies, and they didn’t do well. By contrast, the fourth company, founded in 2002, is a very small company, and it has almost caught up to Company A in terms of revenue. We don’t know how this small company manages to do what it does with so few employees — a vastly superior product? the brilliant use of technology? Obviously, there’s more to the story, but notice how the size of the bubbles added a whole other dimension to the story.

Here’s are some practice IR questions, along similar lines:

The graph below shows the development of Company XYZ, founded in 2001. The vertical axis shows the average number of employees each year, and the size of the dots represents the annual revenues that year.

1. In what year did the company have the highest revenue?

A. 2006

B. 2007

C. 2009

D. 2010

E. 2011

2. What was the percentage decrease in the number of employees from 2007 to 2008?

A. 41.6%

B. 58.3%

C. 85.7%

D. 171.4%

E. 240%

3. Which is a clear trend for Company XYZ during the years 2003 – 2007, before the subprime mortgage crisis?

A. number of employees decreases; revenue decreases

B. number of employees stays about the same, revenue stays about the same

C. number of employees stays about the same; revenue increases

D. number of employees increases, revenue stays about the same

E. number of employees increases, revenue increases

4. Which is a clear trend for Company XYZ during the years 2008 – 2011, in the aftermath of the subprime mortgage crisis?

A. number of employees decreases; revenue decreases

B. number of employees stays about the same, revenue stays about the same

C. number of employees stays about the same; revenue increases

D. number of employees increases, revenue stays about the same

E. number of employees increases, revenue increases

1) This is a simple read the graph question. Revenue is given by size of the bubble, so we are simply looking for the biggest bubble. The biggest bubble on the graph occurs at 2007, so the answer is **B**.

2) For percentage decrease, it’s important to remember the formula is:

Percent Decrease = x 100%

For anything you can count, like number of employees, it’s impossible to have a percentage decrease greater than 100%. A percentage decrease of 100% would mean employees went to zero: the company went out of business. You can’t have a negative number of employees, so the percentage decrease can never be more than 100%. Theoretically, one could talk about more than 100% decrease in something monetary, like assets or profits —- more than a 100% decrease would mean one started “in the black” and ended “in the red.”

Here, the start is about 120 employees, and the difference, the loss of employees, is about 120 – 70 = 50. Notice that 50 is less than half of 120, so this is less than a 50% decrease. The only possible answer is **A**.

3) During the years before the subprime mortgage crisis, from 2003 – 2007, the bubbles rise vertically year after year, indicating that employees are increasing. The size of the dots also increases steady during that five-year period, so revenues are increasing as well. This scenario is described by **E**.

4) During the years following the subprime mortgage crisis, from 2008 – 2011, the bubbles all hover around the same height — a little up, a little down, but not really leaving that 60-80 range. The number of employees appears rangebound, which is another way of saying: they are staying about the same. Notice, though, that starting with a small bubble in 2008, the size of the bubble steadily gets bigger, until 2011, which appears to be the third largest bubble on the chart. Revenues are definitely increases. Apparently, the wake of the subprime mortgage crisis, Company XYZ figured out how to “do more with less.” This scenario is described by **C**.

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]]>The chart above shows the technology capabilities of the 20 existing high schools in Grangerville.

1) If a Grangerville high school is chosen at random, the probability that it will be public high school with a dedicated computer lab is:

(A) 20%

(B) 33.3 %

(C) 40%

(D) 42.9%

(E) 44.4%

2) If a Grangerville high school with either a dedicated computer lab or a computer in every classroom is chosen, the probability that it will be a public school is:

(A) 20%

(B) 33.3 %

(C) 40%

(D) 42.9%

(E) 44.4%

3) If a Grangerville high school with a dedicated computer lab is chosen, the probability that it will be a public school is:

(A) 20%

(B) 33.3 %

(C) 40%

(D) 42.9%

(E) 44.4%

4) If a Grangerville high school with a dedicated computer lab and without a computer in every classroom is chosen, the probability that it will be a public school is:

(A) 20%

(B) 33.3 %

(C) 40%

(D) 42.9%

(E) 44.4%

5) Which of the following statements is true?

I. Independent schools constitute the high percentage of high schools in Grangerville with both a dedicated computer lab and a computer in every classroom

II. Public Schools are tied for the highest percentage of high schools of Grangerville with a dedicated computer lab.

III. Public Schools constitute the highest percentage of high schools of Grangerville with either a dedicated computer lab or a computer in every classroom.

(A) I only

(B) II only

(C) III only

(D) I and II

(E) I and III

6) If a public high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

7) If a public high school in Grangerville is chosen at random, the probability that it has a computer in every classroom is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

8 ) If a public high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab and does not have a computer in every classroom is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

9) If a parochial high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

10) If a parochial high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab and does not have a computer in every classroom is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

11) If an independent high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

12) If an independent high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab and does not have a computer in every classroom is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

(1) **A**; (2) **D**; (3) **B**; (4) **E**; (5) **E**; (6) **B**; (7) **A**; (8) **B**; (9) **E**; (10) **D**; (11) **E**; (12) **B**.

1) There are twenty school total. Of those twenty, only four are in the category “public school with a dedicated computer lab” – the four red squares in the Venn circle on the left. 4/20*100 = 20%. Answer = **A**.

2) There are 14 schools in one of the two Venn circles – those are the schools either with dedicated computer labs or a computer in every classroom. Of those schools, 6 are public: the four red squares in the left Venn circle, and the two in the right Venn circle. 6/14*100 = 42.9%. Answer = **D**.

3) There are 12 in the left Venn circle (including the overlap region) – those are the schools with dedicated computer labs. Of those, four are public schools – the four red squares in the Venn circle on the left. 4/12*100 = 33.3%. Answer = **B**.

4) When the overlap region is subtracted from the left Venn circle, the resultant lune holds the high schools with a dedicated computer lab and without a computer in every classroom. There are nine schools in this region, of which 4 are public: the four red squares in that left-most lune. 4/9*100 = 44.4% Answer = **E**.

5) Evaluate the statements one by one. Statement I: *Independent schools constitute the high percentage of high schools in Grangerville with both a dedicated computer lab and a computer in every classroom*. Schools with both a dedicated computer lab and a computer in every classroom are the overlap region of the two Venn circles. There are three schools in that region, and two are independent, so independent schools constitute the majority of that region. Statement I is true.

Statement II: * Public Schools are tied for the highest percentage of high schools of Grangerville with a dedicated computer lab*. The schools with a dedicated computer lab are the left Venn circle, the whole of the circle including the overlap region. In this circle, there are 12 schools —- 5 parochial, 4 public, and 3 independent. Therefore, parochial schools only constitute the highest percentage of that region, and public schools are a clear second. Statement II is false.

Statement III: *Public Schools constitute the highest percentage of high schools of Grangerville with either a dedicated computer lab or a computer in every classroom*. Schools with either a dedicated computer lab or a computer in every classroom constitute the combined area of the two Venn circles. There are 14 schools in that region —- 6 public, 5 parochial, and 3 independent. Public schools constitute the majority of that region. Statement III is true.

Answer = **E**

6) There are 12 public high schools – the 12 red squares throughout the diagram, including those at the top. Of these, four are in the left Venn circle, which represents having a dedicated computer lab. 4/12*100 = 33.3%. Answer = **B**.

7) There are 12 public high schools. Of these, two are in the right Venn circle, which represents having a computer in every classroom. 2/12*100 = 16.7% Answer = **A**.

8 ) There are 12 public high schools. Of these, there are four in the left-most Venn lune (i.e. the left circle with the overlap subtracted). This region represents the schools that have a dedicated computer lab and do not have a computer in every classroom. 4/12*100 = 33.3%. Answer = **B**.

9) There are 5 parochial schools in the diagram – the five blue circles. All five of these are in the left Venn circle, which represents having a dedicated computer lab. 5/5*100 = 100%. Answer = **E**.

10) There are 5 parochial schools in the diagram. Of these, four of them are in the left-most Venn lune, which represents the schools that have a dedicated computer lab and do not have a computer in every classroom. 4/5*100 = 80%. Answer = **D**.

11) There are 3 independent schools in the diagram – the three green triangles. Of these, all three are in the left Venn circle, which represents having a dedicated computer lab. 3/3*100 = 100%. Answer = **E**.

12) There are 3 independent schools in the diagram. Of these, only one is in the left-most Venn lune, which represents the schools that have a dedicated computer lab and do not have a computer in every classroom. 1/3*100 = 33.3%. Answer = **B**.

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]]>- The following is a Multi-Source Reasoning practice problem, which will be part of the new Integrated Reasoning section on the GMAT.
- You are allowed to use a calculator on this section, because you will be given an on-screen calculator for Integrated Reasoning questions on the real GMAT
- Here, the three “cards” will simply appear one after the other. On the real GMAT, they will be clickable cards all in the view of one window on different tabs.

**Card #1**

Whizzo Chocolate Company in Chicago, IL, makes a wide variety of exceptionally high quality confections. Each one of their products can be classified into one of 5 groups. (Weights include all necessary packaging for shipping.)

1) 12-piece assortments (1.5 lbs, $14.99), some of which require refrigerated shipping and some of which do not.

2) 20-piece assortments (2.0 lbs, $24.99), some of which require refrigerated shipping and some of which do not.

3) a small chocolate-covered fruit basket (12 lb, $39.99), which requires refrigerated shipping

4) a large chocolate-covered fruit basket (30 lb, $59.99), which requires refrigerated shipping

5) an all-chocolate chessboard with white & dark chocolate chessmen (25 lb, $149.99), which requires refrigerated shipping

**Card #2**

Whizzo Chocolate Company uses only the following shipping methods

Western Food Sender

a) WFS non-refrigerated service: $50 plus $10 times each pound

b) WFS refrigerated service: $80 plus $15 times each pound

**Card #3**

If a single order is a “mixed order”, that is, it contains both items that require refrigerated shipping and items that do not require refrigerated shipping, it does no harm to the latter items to ship them in refrigerated shipping. If a single order is a mixed order, customer has a choice:

a) only items requiring refrigerated shipping sent via refrigerated shipping , and all other items sent without refrigeration

b) all items, regardless of type, sentvia refrigerated shipping

When a customer places a mixed order, the Whizzo sales representative will make this choice clear to the customer, and make clear that absolutely no damage will occur by refrigerating those items which don’t require refrigeration.

1) If a person in Pennsylvania has a total of $500 to spend on a Whizzo order, which of the following orders could he afford, including the cost of shipping?

five 12-piece assortments, all requiring refrigerated shipping |
Yes |
No |

two large chocolate-covered fruit basket |
Yes |
No |

the all-chocolate chessboard with white & dark chocolate chessmen |
Yes |
No |

2) For each of the following “mixed orders”, each containing twenty items total, which shipping option will be less expensive?

**Option A**) only items requiring refrigerated shipping sent via refrigerated shipping , and all other items sent without refrigeration

**Option B**) all items, regardless of type, sent via refrigerated shipping

fifteen 12-piece assortments requiring refrigerated shipping and five 12-piece assortments not requiring refrigerated shipping |
A |
B |

ten 12-piece assortments requiring refrigerated shipping and ten 12-piece assortments not requiring refrigerated shipping |
A |
B |

five 12-piece assortments requiring refrigerated shipping and fifteen 12-piece assortments not requiring refrigerated shipping |
A |
B |

(1) Yes; No; No; (2) B, A, A;

1) Base cost of five 12-piece assortment = 5 x $14.99 = $74.95.

Combined weight = 5 x 1.5 = 7.5 lb.

Refrigeration required.

Shipping cost = 80 + 15*75 = $192.50

Total cost = $74.95 + $192.50 = $267.45 -> affordable

Base cost of two large chocolate-covered fruit basket = 2 x $59.99 = $119.98

Combined weight = 2 x 30 = 60 lb

Shipping cost = 80 + 15*60 = $980 -> way over budget

Base cost of all-chocolate chessboard = $149.99

Weight = 25 lbs

Shipping cost = 80 + 15*25 = $455 -> over budget

2) Suppose you have a mixed order and it is all going to be sent via refrigerated shipping. That cost $80 + $15*(# of pound). Suppose some items, not requiring refrigeration, are removed from that shipment, and a non-refrigerated shipment is created. The additional cost is the $50 base cost of a non-refrigerated shipment. The savings per pound is the difference in the per pound rates: $15/lb – $10/lb = $5/lb. When will this saving exceed the additional $50 cost? When the total weight of the non-refrigerated shipment exceeds 10 lbs.

The first order has five 12-piece assortments not requiring refrigerated shipping: 5 x 1.5 = 7.5 lbs of goods not requiring refrigerated shipping. That is not enough to justify a separate non-refrigerated order.

The second order has ten 12-piece assortments not requiring refrigerated shipping: 10 x 1.5 = 15 lbs of goods not requiring refrigerated shipping. That is enough to justify a separate non-refrigerated order.

The third order has even more weight not requiring refrigerated shipping, so this one will also justify a separate non-refrigerated order.

BTW, the name “Whizzo Chocolate Company” is my homage to a classic Monty Python skit. 🙂

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