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Integrated Reasoning

© 2012 Veritas Prep

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Analytical Writing Assessment & Integrated Reasoning

The first hour of your GMAT experience will consist of two 30-minute sections, the Analytical Writing

Assessment and the Integrated Reasoning section. This lesson will introduce both exercises and provide

strategies for each. You will find that the skills for each are quite similar to those you have employed in

studying for the Quantitative and Verbal sections. One notable exception pertains to the Graphics

Interpretation question format within Integrated Reasoning, as it more specifically addresses a

candidate’s ability to synthesize information from charts, graphs, and other visual aids. In the pages that

immediately follow, you will complete a Skillbuilder lesson that covers the most common types of

graphics tested on the Integrated Reasoning section. Following that, you will reach the in-class lesson

for Analytical Writing Assessment and Integrated Reasoning.

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Integrated Reasoning

The Integrated Reasoning section of the GMAT, beginning in June of 2012, will stand as its own 30-

minute section between the Analytical Writing Assessment and Quantitative Reasoning sections. Its

mission is true to its name – to integrate the quantitative skills and reasoning with the logic and reading

comprehension skills from the Verbal Reasoning section.

This lesson will help you to draw from concepts and strategies that you have learned in previous lessons,

integrating them toward success on the Integrated Reasoning section. It will also introduce the IR

question types and its unique format, and provide specific strategies to succeed on the nuances of the

new section.

On the Integrated Reasoning section, you will see 12 different problems in a 30-minute section.

Integrated Reasoning problems will take four forms:

1) Table Analysis

2) Graphics Interpretation

3) Multi-Source Reasoning

4) Two-Part Analysis

In the lesson that follows we will break down each of the four types, with examples, and cover

important strategies for each. But while most of the concepts and skills for the Integrated Reasoning

section have already been covered in previous lessons, the Graphics Interpretation questions do require

a skill as yet uncovered – the ability to quickly glean information from graphics. So before the lesson

begins, we recommend that you complete the following Skillbuilder section, whichcovers the most

common types of charts, graphs, and other graphics that appear on the Graphics Interpretation section.

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Skillbuilder - Graphics Interpretation

The Integrated Reasoning section is germane to its name – it integrates skills from the Quantitative and

Verbal section in order to test your reasoning ability. Accordingly, it does not require too many “new”

skills that you are not currently employing on other portions of the exam.

The most (and, really, only) glaring exception relates to the Graphics Interpretation problems, which will

require you to interpret data that is displayed on graphs, charts, and other visual presentations. While

the graphics are largely explained and well-labeled, you will benefit from familiarity with the most

common types of graphs. This includes:

Bar Graph

Bar graphs display data corresponding to categories. One axis will list categories (in the above graph the

x-axis is used to show categories of GMAT test-takers) and the other will display a numerical range.

Each bar will represent the number that corresponds to that category, and the sizes bars will show the

relative values at a quick scan.

When using/viewing bar graphs, be careful not to let the scale distort your interpretation of the values.

Consider the following:

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Veritas Prep Entire Pool Gary's GMATEmporium

Average GMAT Scores by Preparation Method

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Just looking at the bars, one would think that the score on the left is more than twice as high as the one

on the right. But look at the relative scale – the test scores go from 200 to 800, but the scale here goes

from 764 to 782, just enough to make the 770 score look paltry by comparison. When drawing

inferences from bar graphs, recognize that the graph is a way to display the data, but is also just one

interpretation.

Sample Questions from a Bar Graph

By what percent is “My GMAT Score” greater than “Your GMAT Score”?

A) More than 200%

B) More than 100% but less than 200%

C) More than 50% but less than 100%

D) Less than 2%

From the graph, which of the following conclusions are valid:

1. Veritas Prep GMAT students outperform the average student on both the Integrated Reasoning

section and the GMAT as a whole.

2. Veritas Prep does a better job of teaching GMAT concepts than does Gary’s GMAT Emporium

3. Gary’s GMAT Emporium is better at teaching the Integrated Reasoning section than it is at

teaching the GMAT as a whole.

(Solutions: 1) Valid. 2 & 3) Invalid – beware of inferences made from data. The graph only shows the final scores but does not

in any way show evidence that attributes those scores to effectiveness of teaching. Veritas Prep may simply attract more

capable students from the beginning, and those students would score high regardless of the instructional value. (NOTE: While

we at Veritas Prep do believe that we attract high-quality students, we also suggest that you avoid Gary’s GMAT Emporium))

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Line Graphs

Line graphs are most often used to show the trend of data over time. Here, the x-axis shows students’

timeline of GMAT tests, and the y-axis displays their range of scores. Following the lines, one can see

their progress and notice trends in their improvement. As with bar graphs, choice of scale is important

(were the y-axis to extend to 10,000, the lines would look almost exactly flat, and the differences

between the scores would appear marginal).

Sample Questions From A Line Graph

Which of the following conclusions can be drawn from the graph above:

1. The average score improvement for the students surveyed, measured from their pretest to their

official score, was greater than 100 points.

2. Each student improved his or her score from the pretest to the official score.

3. The week 3 practice test featured harder questions than did the week 6 practice test.

4. The average official score for the three students surveyed was greater than 700 points.

5. Over the course of their study, Carmelo showed the greatest total score improvement of the

three students surveyed.

(Solutions: 1) True. 2) True. 3) False. 4) True. 5) True.)

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Scatter Plots

Scatter plots are used to display individual data points in a manner that allows for trend analysis. Each

point on a scatter plot represents one piece of information (in this case, someone’s GMAT score and the

number of hours they spent preparing), and the regression line shows a general trend in the data (in this

case, that the two figures are positively correlated).

Sample Questions from a Scatter Plot

Which of the following conclusions can be properly drawn from the graph above?

1. All students who studied less than 45 hours scored below average on the exam.

2. The students who studied for the longest duration scored the highest on the exam.

3. Of the students surveyed, anyone who studied more than 60 hours scored above the exam

average.

4. Of the students surveyed, the average score for those who studied more than 50 hours was

greater than that for those who studied 50 hours or less.

5. Studying for more than 150 hours is an ineffective use of one’s time.

Solutions: 1. False. 2) False. 3) True. 4) True. 5) False.

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Bubble Charts

In the above chart, the y-axis shows the average starting salary of MBA programs, the x-axis shows the average campus

temperature (in degrees Fahrenheit) during the school year, and the size of the circles denotes the ratio of applications

received to candidates admitted for each school, with the size of the circle directly proportional to the measure of the

ratio.

In the bubble chart above, notice that three dimensions are being represented. The x and y axes display

data similar to how they would in a scatter plot, but unlike a scatter plot the sizes of the “data points”

vary. This third dimension shows the cluster of data points at each x-y coordinate. In this case, the

bubble chart format is helpful in demonstrating how applicants react to the combination of two factors:

do applicants value climate more than they value their earnings potential? The third dimension is

helpful in providing a visual representation of two factors toward a decision; the Integrated Reasoning

question pool is known to include bubble charts in the form of marketing presentations, as they assess

questions like “do consumers value high quality more than they value low price?”.

Sample Questions From A Bubble Chart

Which of the following conclusions can properly be drawn from the graph above?

1. More applicants applied to the schools with the higher average starting salaries than to those

with lower average starting salaries.

2. Schools with average starting salaries above $100,000 deny admission to a greater proportion of

their applicant pool than do those schools with lower average starting salaries.

3. Earnings potential is the greatest factor in an applicant’s decision to apply to a school.

4. Warm-weather schools attract more applicants than do cold-weather schools.

Solutions: 1) False. 2) True. 3) False. 4) False.

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Earnings Potential vs. Climate in MBA Admissions

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Venn Diagrams

A bit of a departure from “graphs”, Venn Diagrams are nonetheless “graphics” and in the pool of

testable graphics for the IR section. Venn Diagrams exist as tools to organize overlapping sets of

information. Consider an example:

In the diagram below, each x represents one MBA applicant from a consulting firm

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x x x x x x x x

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Used an Admissions Consultant Admitted to 1st

choice school

Note a few things about the Venn Diagram:

1) Above the overlapping circles is a group of five data points, representing the “neither” category

that fits in neither set.

2) The overlapping area between the circles (five x’s)represents the “both” group, in this case

people who both “used an admissions consultant” and “were admitted to the 1st choice school”.

3) In the partial circles (four x’s in the left; six in the right), those data points represent the “only”

categories. There are four applicants who “only” used an admissions consultant (but were not

admitted to their top choice schools) and six who “only” were admitted (but did not use an

admissions consultant).

With these Venn diagrams, there are multiple ways to account for the “Total” pool of data:

“Only” circle A + “Only” Circle B” + “Both” + Neither = Total

or

All of Circle A + All of Circle B – “Both” + Neither = Total

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The difference between the two is that, in order to find the “only Circle A” total, one would need to take

the entire Circle A total and subtract out the “both” category. And the same is true for finding “only

circle B”; that would be “All of Circle B” minus “both”. So in the second equation, we subtract “both”

because essentially the top equation subtracts it twice (once to find “only A” and once to find “ only

B”)and add it back only once, for a net of “minus both”.

Sample Questions From A Venn Diagram

1. What percent of applicants from this firm were admitted to their first choice school?

2. Were applicants who used an admissions consultant more, less, or as likely to be admitted to

their first choice school than those who did not use an admissions consultant(assuming that the

baseline “candidacy” of each was the same to begin)?

3. What percent of students who used an admissions consultant were admitted to their top choice

school?

4. True/False: The number of applicants who used an admissions consultant accounted for more

than half the total number of applicants?

Solutions: 1) 60%. 2) More likely. 3) 67%. 4) False.

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Integrated Reasoning

Integrated Reasoning Format

The Integrated Reasoning section lasts for 30 minutes and consists of 12 problems. Note that each

“problem” by the GMAT definition can have multiple questions within it. As we will explain later in the

lesson, the Integrated Reasoning format is attractive to GMAC and to business schools in large part

because it breaks from the traditional multiple-choice format. For example, a problem might supply you

with multiple arguments regarding a topic, and then call out four sentences and ask you to choose the

appropriate function (premise, conclusion, context, etc.) of each. Or a problem could supply you with a

set of data and ask you to calculate/estimate three ratios from that set. Accordingly, you will face 12

problems, or scenarios, but you may click upward of 30 individual answer choice buttons as part of that

section.

There are four main problem formats that you will encounter on the IR section:

1) Table Analysis

Table analysis questions will provide test takers with a table of data, and ask them to determine

the accuracy of 4-5 statements. The data table is sortable, and requires decisive analysis

techniques to make the most of the information presented.

2) Graphics Interpretation

Graphics interpretation questions will require test takers to read and interpret a graph or other

image, and then complete a handful of response statements using drop-down menus.

3) Multi-Source Reasoning

Multi-source reasoning problems present test takers with a set of tabbed pages, each with

relevant information. Test takers must utilize all of the provided sources to determine the

accuracy of the given statements.

4) Two-Part Analysis

Two-part analysis problems require the test taker to determine the two correct components of

the answer. Answer choices are presented in a table, and all provided options must be

considered.

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Additional Rules of the Game

The Integrated Reasoning section is not computer-adaptive

A single prompt may provide the information to solve several questions, but the questions are independent of one another. Test takers do not have to answer one question correctly to be able to answer another.

Test takers respond to each question before moving to the next question prompt. Once a question has been answered, candidate cannot return and change the answer.

Narrative prompts (text on tabs) are approximately 300 words or fewer.

An on-screen single-function calculator is available for use on the Integrated Reasoning section only. The calculator does not itself perform order-of-operations; for example, typing in 2 + 4 * 5 will elicit the answer 30, having performed 2+4 before multiplying that sum by 5. Be careful when calculating!

Integrated Reasoning Required Skills

As of this print, the Integrated Reasoning format is still largely in development and therefore a

comprehensive list of testable skills does not yet exist. But from the officially-released practice

problems and prompts, the following skills from the current Quantitative and Verbal sections are known

to be testable:

Quantitative

Venn Diagram

Ratio

Weighted Average

Rates & Mixtures

Geometry

Verbal

Critical Reasoning

-Inferences -Strengthen/Weaken -Assumption -Roles in Boldface

Reading Comprehension

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Given the direct transfer of skills and concepts outlined above, test-takers should not think of the

Integrated Reasoning section as a “new” section or even as a “different” section. It is simply a section

that integrates and tests the skills that you will use throughout the GMAT, and does so in a business-

focused context with charts, graphs, emails, and other office-friendly presentations. This is also why,

although the Integrated Reasoning section comes before the Quantitative and Verbal sections, we cover

after we have thoroughly taught those skills. The Integrated Reasoning section is a holistic twist on the

subjects that you have already studied.

Timing on the Integrated Reasoning Section

Work quickly. 12 problems in 30 minutes means that you will almost certainly need to click at least 25

correct answers in that time to complete the exam.

Accordingly, you should use your Arithmetic lesson skills to estimate whenever exact numbers are

unnecessary and to use number properties to select answer choices when you can avoid calculations.

Be careful not to rely too closely on the calculator. Calculations/estimates that you can do in your head

will save time, and the calculator adds a wrinkle: if you mistype the calculation or invert the order-of-

operations, it will produce an incorrect answer.

What is 30 divided by 12? (don’t use a calculator or long division! 30 and 12 are both divisible by 6.

That problem breaks down to 5 divided by 2 – or 2.5) You have 2.5 minutes, on average, per problem.

That is more than enough time to process each prompt and answer the questions, but you have little

time to waste.

Preview questions before you try to interpret data. Charts and graphs are fantastic for organizing

information, but difficult to truly grasp from an initial read without a direct goal.

Similarly, use the “sort” function on the charts to arrange data in ascending/descending order based on

the values that you seek to organize. Charts on the IR section are sortable, and those who take

advantage of this fact will be rewarded with large savings of time.

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Table Analysis

Table Analysis problems assess your ability to interpret tables to draw conclusions based on data. That

sentence may sound bland (“of course table analysis problems would make you analyze data…) but

recognize the importance of your role – you need to determine whether you can draw particular

conclusions. Accordingly, your goal should be to let the conclusions drive the way that you approach the

data. Preview the questions first, then sort the table to analyze each question.

Important Skills:

-Sorting the Data Table

-Critical Reasoning: Valid conclusions MUST BE TRUE

-Calculation Estimates: Most calculations do not need to be performed to completion. Use your

knowledge of divisibility, fractions, and ratios to make quick determinations and calculate only when

necessary.

Let’s take a look at a Table Analysis problem:

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Before looking at the questions, note a few things about this table:

1) There is quite a bit of data. Reading the table without looking at the questions first is a lost

cause; you simply cannot process all of this in 3 minutes. Be question driven!

2) The values are quite specific (to the tens digit for 8-figure numbers). You do not want to

calculate these numbers – even with the on-screen calculator – unless absolutely necessary.

Use estimates and logical determinations of when you need to truly calculate, as we will discuss.

3) The “sort by” button at the top of the screen will be dynamic on a computer – you can change

the organization of the table. Currently the table is sorted by Units Sold. But notice that the %

Change totals (for both Unit and Dollar Sales) are all over the place; if a question asks about

those, you can re-sort the column to better organize your search for the pertinent information.

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This problem can contain several questions. Here are some examples:

1. The product with the highest unit sales in 2010 also had the highest dollar increase in price since

2009.

2. Every orange scented product experienced growth in unit sales from 2009 to 2010.

3. No product experienced growth in dollar sales but a decline in unit sales from 2009 to 2010.

4. The highest-priced product in 2010 was also the highest-priced product in 2009.

5. Spray bathroom cleaners generated more dollar sales than any other single type of bathroom

cleaner in 2010.

6. Half of the bathroom cleaners that experienced a drop in average price from 2009 to 2010 were

aerosol cleaners.

7. Ultra Shine brand bathroom cleaners experienced greater total unit sales growth from 2009 to

2010 than did Deluxe brand bathroom cleaners.

8. No orange-scented bathroom cleaner sold more units in 2009 than in 2010.

Through these questions, you should see several critical skills emerge:

1) Sort-and Scan. Several questions ask you to make a determination about either a leader in a

category (e.g. “the product with the highest unit sales”) or an entire segment of a category (e.g.

“no orange-scented cleaner”). Sort by that category and then scan the other relevant column

for the data that you need. Remember this theme from the algebra lesson? The GMAT loves to

provide you with “an inconvenient truth” and force you to take information and make it

convenient to your purpose. On Table Analysis problems, making information convenient is

perhaps the most important skill for your success.

2) Relative math. None of the questions in this set require you to perform calculations, but several

necessitate that you process numbers to draw a conclusion. When questions ask, as does #4,

whether one particular item was the greatest (or least) in a certain category you do not usually

have to calculate. Just scan the other choices to see if one is clearly greater, and at that point

you have your “false” answer. And if you cannot find one, then you can test the item in

question against the next-most-likely to be certain.

3) Interpreting wording. Much like word problems on the quantitative section, IR problems are

often worded such that you need to slow down and make certain that you understand exactly

what is being asked so that you don’t hastily fall into a trap. Question 4 is a good example. The

highest-priced product from 2009 isn’t directly given on the table, but the percent change from

2009 to 2010 is. And the “winner” has a negative change from 2009 to 2010…meaning that it

was higher-priced in 2009 and has since decreased. In a question that asks for the “highest”,

seeing a negative number in the percent change field may not feel right, but if you properly

interpret what you are looking for you can successfully navigate this wording.

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4) Drawing Conclusions. The instructions ask you to indicate which statements are true or false, so

in effect you are simply using the table as a set of premises for Critical Reasoning problems. Is a

conclusion perfectly valid, or can you find an exception that makes it not necessarily true?

Breaking down these questions:

#1) Question 1 is a classic Sort-and-Scan. Sort by Unit Sales, then scan the Price Increase to see whether

there are any products with higher price increases than the Unit Sales leader. As it turns out, there is –

Deluxe Orange Spray. Accordingly, the answer is “False”.

#2) This is again a classic Sort-and-Scan. Sort by Fragrance to align all of the Orange products together,

and then scan them along the Percent Change column. All signs are positive, so none of the Orange

products experienced a decline in Unit Sales. The answer is “True”.

#3) Eerily similar to question 2, this question requires you to sort for one category (in this case % Change

in Dollar Sales) and then scan part of that category (those with an increase) for a decline in Unit Sales.

Four products fit the bill, so the answer to “no products…” is “False”.

#4) As mentioned above, this question requires some interpretation. First, sort by the Average Price to

find the most expensive product. Then, you want to determine whether that product was the highest-

priced product the previous year. The -$0.05 in the $ Change column means that you need to ADD five

cents to the current price to find last year’s price, meaning that it was even more expensive last year.

Scan the $ Change column to determine that no products in the current ballpark of price were even

more expensive last year, and you can confidently answer “True”.

#5) This question is a fantastic example of using Relative Math. While it does ask whether spray

cleaners had a higher total sales number than that of any other category, you need not calculate that (or

any other) total! Only perform actual calculations, and here it’s not necessary. Because this is a Relative

Math problem it actually makes most sense to sort by Dollar Sales so that your scan goes in order of

dollar amounts. Consider the chart below in that form:

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The single-biggest seller is a powder cleaner at ~$34 million. But scan the list for the next few highest

revenue generator – none is a powder. Powder cleaners simply will not be the largest segment in dollar

sales. The next two highest totals belong to spray cleaners at $33 million and $27 million. If you think of

this as a horse race, spray cleaners have jumped out to a huge lead. Aerosols come next, at $22 million

and $21 million, but by now sprays have around a $17 million lead. As you consider the back-and-forth

from sprays and aerosols, you can find that as the total values of each product dwindle down to a small

fraction of the spray “lead”, there’s simply no reason to do the math. Spray cleaners have a visibly

insurmountable “lead” and the answer must be True.

#6) This problem is another Sort-and-Scan. Sort by Price Change and you will find that six cleaners

experienced a decrease in price. Scan the Type column to find that only two are aerosols, and the

correct answer must be “False”.

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#7) Similar to #5, this question is another great example of Relative Math. Sort by Brand to align the

Deluxe and UItra Shine cleaners. Although you only have Unit Sales for 2010 and Percent Change (not

Unit Change), you do not need to calculate the percentages. Just scan to note that the Ultra Shine

products have both greater volumes and greater percent changes, and that the Deluxe brand has one

major negative change. Even without doing the math, you can quickly conclude that the Ultra Shine

brands experienced a much larger unit sales increase, so you can efficiently answer “True”.

#8) This is a Sort-and-Scan problem. Sort by Fragrance to align the Orange products together, scan the

Percent Change in Unit Sales column, note that no Orange cleaner experienced a decline, and select

“True”.

Table Analysis Summary

Table Analysis problems typically rely on your abilities to:

Sort-and-Scan

Draw Conclusions

Perform Relative Math

Interpret Wording

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Graphics Interpretation

Sample questions:

1. The number of cities that had at least 20 auto thefts per 1,000 is closest to ____% of the total

cities measured.

A) 16% B) 33% C) 50%

2. Every city with a population of no more than 600,000 had no more than _________ auto thefts

per 1,000 people.

A) 10 B) 20 C) 30

3. There is a _______________ relationship between a city's population and its number of auto

thefts per 1,000 people.

A) Positive B) Negative C) Equivalent

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Problem Takeaway – Graphics Interpretation

For question 1, segment the graph. You are only interested in data points that are on or to the right of

the vertical line rising from “20” on the x –axis. Here, relative math is again a key. The text to the right

of the math says that there are 35 data points, and there are 12 points to the right of that line. 12/36

would be exactly 1/3, so 12/35 is closest to 33%. Note also this: The answer choices are spread apart

enough that you may not even need to count the data points. Clearly less than half of the points are to

the right of that line, and 7/35 would be 20%, so once you can see that there are significantly more than

7 points there, but significantly less than half, you can eyeball that it’s closest to 33%.

For question 2, again you want to segment the graph. You are only interested in data points below the

600,000 line. Right below that line at the right-hand side of the graph you should notice a data point

quite close to the 30 thefts per thousand mark. Accordingly, the correct answer must be 30.

For question 3, look at the graph as a whole, and at the regression line. The data shows a trend – the

regression line has a positive slope, showing a positive relationship between city size and auto theft

rate. Accordingly, the correct answer is “positive”.

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Multi-Source Reasoning

Multi-Source Reasoning problems will feature prompts with 2-4 tabs on the left hand side of the screen,

allowing you to toggle between different sources of data. Those tabs can include email memos, charts,

short articles, and other pieces of correspondence that will each relate to the others involved in that

problem. From that data, you will need to answer multiple questions that will appear to the right of the

data field; problems will include between 3-6 questions, and should generally be of the “Inference” or

“True/False” variety.

As you should with the other Integrated Reasoning types, you should be question-driven when you

approach the data. First, familiarize yourself with the contents of each tab with a quick scan of what

type of information is available. Shortly thereafter, however, you should read each question and return

to the data to answer. Keep in mind that the standard for Inference or True/False questions is that a

true statement / correct inference “Must Be True”. In assessing each question, make that Must Be True

standard your criteria for answering; if the data does not guarantee a conclusion, it is not a valid

inference.

Multi-Source Reasoning problems will primarily test your logical reasoning abilities, but will often also

include math. Continue to rely on your Relative Math skills to determine when the calculations are close

enough to that border between true/false that you should employ the calculator or pen/pad to be

certain. Note that most such problems that involve math will primarily test logic; for example when you

are faced with the calculation of a percentage, the logical setup (do you need the percentage of the

wholesale or retail price, for example) is likely to be where the authors embed the “trap”, and the

authors will reward savvy test-takers for minimizing the time they spend on needless calculations.

Consider an example:

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Which of the following inferences can be drawn from the prompts above?

1) The home sellers' asking price for their home is at least $380,000.

2) For the buyers, the ability to complete the purchase before mid-August is more important than

the final price of the home.

3) It is possible for the buyers and sellers to make a deal in which neither side needs to change its

opening offer by more than 15%.

4) The sellers' real estate agent is more likely to accept a lower final price of the home than are the

sellers themselves.

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These questions rest on the following skills:

1) Relative Math

2) Interpreting Wording

3) Drawing Conclusions / Reasoning

The reasoning emphasis of these questions should be evident in question #1. Notice that the $345,000

price quoted in Message 1 is not the proposed “end up agreeing upon…” price. So while $345,000 is

10% off of approximately $383,000, we cannot be certain that the original asking price is $383,000 or

higher. The “…and still end up agreeing on a price” caveat suggest that the negotiations might go lower

than $345,000, leaving room for the sellers’ asking price to be lower than $380,000 (for example – if

they settle at $340,000, that’s 10% off of about $378,000).

Note that, in question 1, the math is more of a double-check of the logic than it is a necessity, and one

who quickly tries to calculate using the $345,000 and $380,000 numbers will miss the logic that

$345,000 is not a final price. Stress logic and Relative Math in your assessment of these questions!

In question 2, the conclusion is certainly plausible but not necessarily true. The message states that “a

mid-August closing date appeals to the buyers” but not that it is their most important concern.

Remember – Inferences on the GMAT “Must Be True”, and in this case that standard is not met.

Question 3 demonstrates another application of Relative Math and logic. We are told that the buyers

initially offered $300,000, so a 15% compromise for them would be $345,000. And the sellers' agent has

noted that, at $345,000, the sellers would receive a price that at maximum would reflect a 10%

reduction from their opening price. Accordingly, since that leaves a full 5% further down for the sellers

to go, even assuming the highest-possible asking price, there is indeed room for each to reach a price

within 15% of their initial offer. This math shouldn’t require a calculator (15% of 300 ought to be a

mental calculation for you by the time you reach test day), so what looks like a math problem really is

more of a logic/setup question. Expect to see plenty of these on test day!

Question 4 is a classic example of the “Must Be True” logical standard (and in this case that standard is

not met). While the sellers' real estate agent seems more willing to drop prices in negotiation, it is not

necessarily true that he will accept a lower price in the end. Email #2 mentions that the sellers are

willing to counteroffer at $350,000 in part because that higher price gives them "room to negotiate"

underneath, so we do know that the sellers are willing to accept a price lower than $350,000. And the

real estate agent explains in Email #3 that he feels that a settling price of $330,000 is possible. Because

we do not know whether this price is considered too low by the sellers, we cannot determine whether

either party's intent is to sell for lower than the other is willing to accept, and this statement is not

necessarily supported by the given information.

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Multi-Source Reasoning Summary

Multi-Source Reasoning problems typically rely on your abilities to:

Draw Conclusions

Perform Relative Math

Interpret Wording

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Two-Part Analysis

Two-Part Analysis problems take a new twist on the multiple-choice question format, using the broader-

reaching IR format to ask you two questions at once using the same prompt. Problems can take various

proportions on the math/logic spectrum, with some problems looking almost exactly like Problem

Solving quantitative problems and others looking just like Critical Reasoning questions. Consider these

examples:

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Notice that the first question is almost exclusively a Problem Solving question. It provides one equation

with two variables, and then asks you to assess the answer choices seeking a combination that satisfies

the equation. The second is almost exclusively a Critical Reasoning question, using the IR form to ask

you two Assumption questions off of the same prompt.

For the Problem Solving question, note that the answer choices are as much a part of the problem as

they are in many PS problems. While you are only given one equation, the answer choices limit your

options by only featuring multiples of 5,000. This allows you to significantly decrease your workload. As

always, you should employ divisibility rules and concepts to make for quicker math, so:

25a + 30b = 1,000,000

Can become:

5(5a + 6b) = 1,000,000

5a + 6b = 200,000

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And since all of the answer choices are multiples of 1,000 and so is the right-hand side of the equation,

you can strip off all of the “,000”s and say that 5a + 6b = 200, looking at only the ten-thousands and

thousands digits of the answer choices to find a fit. When b is 25, that means that 5a must be 50, and a

could be 10. So a = 10 and b = 25 satisfies the equation and is therefore correct.

On the second problem, the Critical Reasoning format should look familiar. These are assumption

questions, so you can employ the Assumption Negation Technique:

Joseph argues that growing health insurance premiums can be controlled by reducing the number of

unnecessary tests performed by doctors. He says this because many tests that are performed, and then

billed to insurance providers, are unnecessary. But note the assumption -- while this practice may relate

to **some** excess expenditure, the argument assumes that it's enough excess spending that, if it were

cut, the health care industry could save quite a bit. Accordingly, the second assumption, that "tests and

diagnostic procedures DO NOT make up an insignificant portion of the bills to insurers", is required.

Without it -- if we could then say (via the Assumption Negation Technique) that these tests DO

represent an insignificant portion of the bill, then their presence or absence does not matter.

Accordingly, Joseph's argument requires that fact.

Ronald argues that, if patients are allowed to make decisions instead of doctors doing so, the number of

unnecessary tests will decline. He believes this because of the stated fact that doctors are purposely

selecting expensive tests to perform. However, his conclusion is a two-part conclusion -- it's not just that

"doctors shouldn't be making these decisions", it's that "patients should, instead". And so his argument

assumes that patients will make better decisions. That corresponds with the fourth choice, that

"patients are NOT just as likely as doctors to choose the most expensive diagnostics and tests". If that

assumption is not true -- if patients ARE just as likely to choose the expensive tests, then Ronald's

proposal does not reach his stated aim, to succeed in reducing the number of tests.

With Two-Part Analysis questions, the skill-set includes those for Problem Solving and Critical Reasoning

questions, with the twist that you will have to levy multiple answers for each problem. The main

difference is the format itself – each problem will have more “moving parts”, so your ability to cut

directly to the questions themselves to structure your approach will be important to time and resource

management.

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Integrated Reasoning Summary – 2012

To understand the Integrated Reasoning section best, put it in context:

1) As of 2012, the Integrated Reasoning section is a new addition to the GMAT and to the score

reports that schools will receive. Accordingly, for the 2012-13 admissions cycle GMAC is

assessing the validity of the questions themselves just as much as it is assessing your ability.

And schools, similarly, will be analyzing the importance of the IR scores more than relying upon

them for admissions decisions. Do your best on the IR section – a high score is still an asset to

your candidacy – but do not let the experience weigh you down or shake your confidence. Until

the format is in full-swing and the scores have demonstrated validity to admissions officers,

small fluctuations in IR scores will not have great influence on your admissions chances.

2) The IR section will come second, after the AWA and before the Quantitative section. For the

foreseeable future, your Quant/Verbal scores will remain the driving standardized-test forces

behind your candidacy. Pace yourself and ration your stamina and stress levels accordingly;

you’re in for a 4-hour experience on test day, so don’t let the IR section sap your strength too

early in the game.

3) The IR section tests many of the same skills that the Quant and Verbal sections test. The IR

section is a fantastic warm-up to get your mind primed for the Relative Math, logic, problem

solving, and wordplay puzzles that you will perform for the rest of the test. Currently, the IR

section exists as a great opportunity for you with little downside; until the validity of the IR

section is proven, a “qualifying” score should suffice to keep your application held in high

regard, and the mere function of taking this section will help you succeed on the rest of the

exam. Do not look at IR as a threat to your candidacy; until further notice, it exists as a great

opportunity for you to set yourself up for success.

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Relative Math

Let’s begin our discussion of Relative Math with a “Relative Math” problem. The IR section will present

you with 12 “problems”, each featuring multiple “questions” in 30 minutes. What does that mean for

your pacing?

Using Relative Math, you should notice that you’ll have between 2 and 3 minutes per problem – a quick

scan of the numbers should show that 24 minutes would be 2 minutes/problem and 36 minutes would

be 3 minutes/problem, so as it turns out you have exactly 2.5 minutes per problem. And since “multiple

questions per problem” means, at a minimum 2 question per problem but maybe more, you’re looking

at something like a minute or less per question.

What does that mean for your approach? You have to be prepared to employ Relative Math to solve

problems – you won’t have the time to calculate each possible value related to the problem. Instead,

you will want to:

-Determine which values are relevant to a correct answer

-Estimate those values whenever possible

-Calculate values only when the estimates are too close to call

-Remember that the logical setup for the values is typically the crux of the question, not the calculation

itself

As an example, consider the question:

City Amount Saved Total Budget

Andersonville $8,225 $47,975

Bronxtown $16,750 $142,950

Chadwick $3,925 $20,325

Dodgeville $3,350 $16,275

Edgewater $13,100 $51,675

The table above shows the 2010 annual budget for the Sanitation Departments of five cities, and the

amount of money that each was able to save over that budget for the 2011 fiscal year. Which city had

the lowest percentage savings on the basis of the previous year’s budget?

(A) Andersonville

(B) Bronxtown

(C) Chadwick

(D) Dodgeville

(E) Edgewater

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Note that a calculator might be tempting in this case, but that each calculation requires you to key at

least nine digits – a time-consuming process that raises your potential for typo-based error. An eye for

both logical setup and Relative Math can guide you through this process efficiently and confidently.

First, note the correct relationship – the lowest percentage savings, or the lowest savings-to-budget

ratio. Your goal, then, is to test the ratios of left column to right, looking for the smallest ratio. Your

“baseline” for Andersonville is approximately 8/48 or 1/6. And in relation to 1/6, you know that the

numerator is a little over 8 and the denominator is a little less than 48, so the overall ratio is going to be

slightly greater than 1/6. You can denote this quickly on your noteboard with a + sign or a > sign to help

you recognize the direction of your estimates.

A) >8/48, so >1/6

B) <20/140, so < 1/7 (the current “leader” in smallest ratio)

C) <4/20, so < 1/5

D) >3/16, and since you’re comparing against 1/7 (or 3/21) you know that this is greater

E) >13/52, so >1/4.

The answer must be B, and if you’ve employed the above estimates you won’t have had to perform any

true calculations to get there. Bronxtown had the lowest percentage savings.

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Min/Max Scenarios

Consider this situation:

Darryl is seeking to finish his basement and can use his tax return to make one improvement this spring,

and then will spend the summer taking on consulting projects to save up for the rest. If he wants to

make the cheapest of his remaining improvements this spring, which should he choose?

Darryl’s options are to install wood paneling on each of the walls; install carpeting along the floor; and

to hook up a surround sound system and HDTV. His square floor measures 256 square feet, and the

walls are each 10 feet high. From soliciting vendors, he finds that the costs would be:

Sure Wood™ wood paneling

$2.50 per square foot

Woodson™ wood paneling

$125 project fee + $1.99 per square foot

Fluffy Floor™ carpet $8 per square foot

Rugs-on-Rugs-on-Rugs™ carpet

250 square feet for $400, plus $5 per square foot thereafter

Ivy League AV™ $1000 for an HDTV with free surround sound installation

Note here that your goal is to minimize the cost. Accordingly, you really only need to consider the

cheaper options, and the HDTV situation is already denoted as exactly $1000. If a project will cost over

$1000, then it need not apply.

The Sure Wood project, at $2.50 per square foot for four walls of 160 feet each will be far greater than

$1,000; even a quick estimate of $2/square foot shows you that it’s over $300 per wall, and there are

four of them. The same, then, holds true for Woodson.

For carpet, you should see that the Rugs-on-Rugs-on-Rugs option will be considerably cheaper, as $250

square feet for $400 is less than $2 per square foot, compared with $8 for Fluffy. With add-on Rugs

square footage at $5, still less than $8, there is no scenario in which Fluffy would be the cheaper option.

So the only true comparison to be made is Rugs-on-Rugs vs. the HDTV system. And with 256 square feet

and the first 250 at $400, the Rugs product is much, much less than $1,000. And so without calculating

each product type but more focusing on your goal – to find the absolute cheapest, minimum-price

option, you can much more effectively decide on Rugs-on-Rugs-on-Rugs.

The takeaway? When problems ask for maximum or minimum amounts, you can save yourself quite a

bit of work by only considering those options that are likely to fit the objective. If you can make a quick

in-category comparison as you can here, you can avoid even considering certain choices. And if you’re

given easy-to-calculate benchmarks, you can use those to determine whether other calculations are

even worthy of your time. Calculations on IR are more about strategy – when are the calculations worth

the ROI of your time – and less about your ability to perform the math.

33

GMAT Final Preparations

Test Day Strategies

Do not be stubborn

Many an exam has been ruined become the test-taker spent several minutes on a question and cost

himself valuable time that would have been useful for several questions to come. Research shows that

a test-taker’s likelihood of answering correctly actually declines after spending about 3 minutes on a

problem, so undue time spent on a problem not only hurts your chances of getting the next one right, it

doesn’t tend to help you on the current problem, either.

You’ve heard the phrase “won the battle but lost the war”, and on the GMAT this is a problem that can

befall even the most capable of examinees. If you’re struggling through a difficult problem, you may just

need to let it go. Based on the adaptive scoring engine, you’ll likely receive a more manageable problem

next, and give yourself another shot at a harder problem that just may “click” a few questions later.

Time management on the GMAT is crucial – don’t throw it away on any one problem.

If you can get a question right, get it right

On the flip side, some questions will take you significantly longer than 2 minutes. And that’s okay – your

pacing job isn’t to spend 1:45 per verbal question and 2:00 per quant question, it’s merely to average

that. And if you know that you’re on the right track to answering correctly but that your chosen method

will be a bit labor-intensive, that’s a good use of an additional 30-45 seconds. Similarly, spending a few

extra seconds per problem to double-check that you haven’t made a silly mistake is also a good

investment.

Particularly with the GMAT’s scoring algorithm, you will lose more by missing an easy question than you

will gain by correctly answering an impossible question. At the upper end, the test will “find you out” by

continuing to challenge you with harder questions. If you’re spending undue time getting them right,

eventually the pacing will be your undoing. But on the lower end, by missing questions that you should

have gotten you’re wasting opportunities to push your ceiling – you’re spending too much time crawling

out of a hole to get back to “normal”. Through random and educated guessing, you should provide the

test with “false positives” on about 25% of the questions above your ability level; by the same token,

you shouldn’t give away many “false negatives” by missing questions you should have gotten right.

Simply put, make sure that you don’t hastily leave holes in your floor because you’re concerned with

chasing your ceiling.

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Punting for Pacing

Your goal should be to finish all the questions in the time allotted, but many students will find that doing

so accurately is a challenge. If you find that you can answer most, but not all, of the questions

comfortably and with high accuracy, you may want to simply plan on 3-4 “punts” (planned guesses)

spread through either section. The logic? If you know that you’ll struggle with perfect pacing, you’ll be

better off just plain missing (or guessing correctly) on a question here or there than rushing through all

of the questions and being more vulnerable to silly errors. And the psychological benefit: if you’ve

decided in advance that you’ll give yourself a few punts, you won’t feel overwhelmed when you use

them – it’s a strategy, not a desperation move.

When a Question Looks Easy…

Do not despair, or think that it’s evidence that you are performing poorly (and that the CAT algorithm

thusly sent you an easy question). Many a test-taker has unraveled because she thought an “easy”-

looking quantitative question was evidence that she had blown the test already, only to find after

tanking the verbal section as a result that her quant score was actually quite high.

Students often psyche themselves out by reading into their perceived difficulty rating of a question. But

when a question looks easy, there are two quite-plausible reasons that do not mean that “you’re not

doing well”:

1) The question is, in fact, below your ability level, but it’s an unscored, experimental question.

The algorithm needs to test its questions across multiple ability levels, and so the computer will

at times show, for example, a 90th percentile test-taker a 60th percentile question, to ensure that

those at the top of the curve do, in fact, get it right nearly all the time. Here, it’s an “easy”

question for you, but it in no way means that you’re not performing well.

2) The question looks easy, but in fact it’s not. There’s an old quote that “the greatest trick the

devil ever pulled was convincing the world he didn’t exist”. Well, in a similar way, the greatest

trick the GMAT has is convincing you that the difficulty in a hard problem doesn’t exist. Often

hard problems look easy if you miss the subtlety; you’ve likely seen several already in your

GMAT prep – Data Sufficiency questions in which C is “obvious” but the answer is actually B, or

Inference questions in which the test baits you into proudly drawing a probably-but-not-

necessarily-true conclusion. In many cases, a question that looks too easy is actually evidence

that you’re doing extremely well, as those are often the most challenging questions for the

higher scorers.

As hard as is to avoid, do not read into the difficulty levels of the questions that you see on the test.

There’s very little benefit, but a huge risk to many who let that doubt inhibit their efficiency the rest of

the way. Take each question as it comes, and trust that your preparation will carry you to a score that

you deserve.

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See the Value in Anxiety

Have you ever been nervous when buying a lottery ticket? Probably not, and the reason is that although

the stakes are high you have no expectation of actually winning. On the other hand, you have probably

been nervous going into a performance review with a promotion on the line, or asking an attractive

classmate to meet you for happy hour. In those cases, you have a reasonable and probably a high

expectation of success. When you have trouble sleeping the night before the GMAT or feel those

butterflies in your stomach as you read the first question, know this: those nerves are evidence that you

have a right to expect success.

Your body releases adrenalin in these situations to provide you with an additional energy boost. And

maybe that energy is better suited to the historically more prevalent stressful situations of your

ancestors (evading predators, mainly), but that doesn’t change the fact that adrenaline is a good thing –

it’s your body’s way of preparing itself for peak performance. So take it as a positive thing: you’re only

nervous because you’re deserving of success and because your body is getting itself ready for a

challenge.