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GMAT – MATH SUMMARY

The math test exists out of 37 questions, based on problem solving and data sufficiency. Thesequestions have to be solved in 75 minutes. Scoring: 0 – 60.

CHAPTER 7 – BASIC PRINCIPLES

Integers are all numbers without decimal places. Integers can be positive (1, 2, 3…) or negative (-1,-2, -3…). Zero (0) is also an integer, neither negative nor positive.

There are ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. All integers are made up of digits. Each digit in anumber has a different name. For example: 246,73

2 = hundreds digit4 = tens digit6 = units (or ones) digit

7 = tenths digit3 = hundredths digit

If an integer cannot be divided evenly by another integer, the integer that is left over at the end of division is called the remainder . Remainders must be integers!

Even numbers are integers that can be divided evenly by 2, leaving no remainder. Odd numbers areintegers that cannot be divided evenly by 2.

Consecutive integers are integers listed in order of increasing value without any integer missingbetween. Only integers can be consecutive. Some consecutive even integers: -2, 0, 2, 4, 6, etc. Someconsecutive odd integers: -1, 1, 3, 5, 7, etc.

Distinct numbers cannot be equal, they must have different values.

A prime number is a positive integer that is divisible only by two numbers: itself and 1. Neither 0 or 1is a prime number. 2 is both the smallest and the only even prime number. For example: 2, 3, 5, 7, 11are prime numbers.

Divisible means you can evenly divide the bigger number by the smaller number, leaving noremainder. For example: 10 is divisible by 5. Some useful divisibility shortcuts:

– An integer is divisible by 2 if its units digit is divisible by 2. – An integer is divisible by 3 if the sum of its digits is divisible by 3. – An integer is divisible by 4 if the number formed by its last two digits is divisible by 4. – An integer is divisible by 5 if its final digit is either 0 or 5. – An integer is divisible by 6 if it is divisible by both 2 and 3. – Division by zero is undefined, there is no answer. Any fraction with a 0 on the top is 0. Thus:

4/0 = undefined and 0/4 = 0.

Integer X is a factor of integer Y, if Y is divisible by X. Thus: Y = NX. For example: Y = 10, N=2, X=5.All the factors of 10 are 2, 5, 1 and 10. 10 is a multiple of 5 (2x5), but 15 is also a multiple of 5 (3x5).Most numbers have only a few factors, but an infinite number of multiples.

When a factor is also prime, then it’s called a prime factor . For example: 3 and 5 are prime factors of 15. All positive integers greater than 1 have unique prime factorizations. The prime factorization of 12is 3x2x2.

» Use the factor tree ( page 59).



The absolute value of a number is the distance between that number and 0 on the number line. Theabsolute value is expressed as |x|. For example: |6|=6 and |-5|=5.

CHAPTER 8 – POE AND GMAT MATH

» Read the summary ( page 72).

CHAPTER 9 – DATA SUFFICIENCY: BASIC PRINCIPLES

In data-sufficiency questions you don’t really need to solve the equation; you just need to know thatthe equation can be solved. After all, you just need to know if a statement has sufficient information.

Every data-sufficiency question consists of a question followed by two statements. There are fivepossible answer choices:

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.

– See the graphic view of the answer choices (page 77).

The best way to work data-sufficiency problems is to look at one statement at a time. Look at onestatement, and ignore the other. The most common GMAT data-sufficiency mistake is to put thestatements together too early. Start with the first statement. When you only read statement (1), youcan apply POE. When statement (1) is sufficient, only answers A and D are possible. When statement

(1) isn’t sufficient, answers B, C and E are left.

– Handy flowchart that shows you what to do for any data-sufficiency problems (page 81).



The respons to half of the data-sufficiency questions – if you were going to provide an answer – is anumber. The other half of the data-sufficiency questions, will ask a yes-or-no question instead. Payattention: on a yes/no data-sufficiency problem, it the statement answers the question in either theaffirmative (yes) or the negative (no), it is sufficient. If the answer on the question is maybe, it’s notsufficient.

CHAPTER 10 – ARITHMETIC

There are six arithmetic operations you will need for the GMAT:

1. Addition (2+2) The result of addition is a sum or total.2. Subtraction (6-2) The result of subtraction is a difference.3. Multiplication (2x2) The result of multiplication is a product.4. Division (8÷2) The result of division is a quotient.5. Raising to a power (x²) In the expression x² the little 2 is called an exponent.6. Finding a square root (√4) √4 = √(2x2) = 2

A fraction is just another way of expressing division. In the fraction x/y, x is the numerator and y isthe denominator . To add and substract fractions with different denominators, you must give all of them the same denominator. For example: 1/2 + 2/3 = 1/2 x 3/3 + 2/3 x 2/2 = 3/6 + 4/6 = 7/6.

To multiply fractions, multiply the numerators and multiply the denominators. For example: 2/3 x 6/5 =12/15.

To divide one fraction by another, just invert (omkeren) the second fraction and multiply. For example:2/3 ÷ 3/4 = 2/3 x 4/3 = 8/9. When you invert a fraction, the new fraction is called a reciprocal.

An integer can be expressed as a fraction by making the integer the numerator and 1 the denominator.

For example: 16 = 16/1. Some numbers are a mix of integers and fractions, for example 3,1/2. It’s



easier to work with these numbers if you convert them into fractions. For example: 3,1/2 = 6/2 + 1/2 =7/2.

A good shortcut when comparing fractions is the Bowtie; multiply the denominator of the first fractionby the numerator of the second and the denominator of the second by the numerator of the first. Thebiggest number is the biggest fraction (page 96).

A decimal can be expressed as a fraction, and the other way around.

Reciprocals = omgekeerden. For example: 1/5 and 5/1 are reciprocals.

A ratio can be expressed as a fraction and vice versa. For example: the ratio 3 of 4 can be written as3/4 as well as standard ratio format 3:4. There is one difference between ratio and fractions. Thewhole in a ratio is the sum of all parts. If the ratio is expressed as a fraction, the whole is the sum of the nominator and the denominator. For example: The whole is 7 Fraction: 3/7 and Ratio: 3/4.

A percentage is a fraction in which the denominator is always equal to 100. Percent increase =steiging. Percent decrease = daling.

Compound Interest (page 111).

The average = (total sum of the items) ÷ (total numbers of the items). Arithmetic mean is the preciseterm for the process of finding an average. This term will be used in the GMAT questions.

To find the medium of a set of n numbers, reorder the numbers from least to greatest and pick themiddle number. If n is odd, just pick the middle number. If n is even, add the two middle numberstogether and divide by 2.

To find the mode of a set of n numbers, pick the number that occurs most frequently. A set of numbers can have more than one mode.

To find the range of a set of n numbers, take the smallest number and subtract it from the largestnumber. This measures how widely the numbers are dispersed. Another way to measure thedispersion of a set of numbers is the standard deviation, which measures the distance between thearithmetic mean and each of the numbers in that set. Most GMAT questions about standard deviationconcern the difference between standard deviation and the mean.

An exponent is a short way of writing the value of a number multiplied several times by itself. For example: 4³ = 4x4x4. The large number (4) is called the base, and the small number (3) is called theexponent. Rules:

– When you multiply numbers with the same base, you add their components. For example: 6² x6³ = 65.

– When you divide numbers with the same base, you subtract the bottom exponents from thetop exponents. For example: 65 ÷ 6³ = 6².

– When you raise a power to a power you multiply the exponents. For example: (4²)² = 44. – When several numbers are inside parentheses, the exponent outside the parentheses must be

distributed to all of the numbers within. For example: (4y)² = (4)² x (y)² = 16 x y². – x² + x³ ≠ x 5 but it can be written as x²(1+x). – x5 - x² ≠ x³ – If you raise a positive integer to a power, the number gets larger. – If you raise a positive fraction < 1 to a power, the fraction gets smaller. – If you raise a negative number to an odd power, the number gets smaller. – If you raise a negative number to an even power, the number becomes positive. – Any number to the first power = itself.

– Any number to the 0 power = 1.



– Any number to the negative power y is equal to the reciprocal of the same number to thepositive y. For example: 3-2 = 1/32 = 1/9.

The square root (√) of a positive number x is the number that, when squared, equals x . For example:the square root of 9 is 3 or -3 (3x3=9 and -3x-3=9). A number inside the √ is called a radical. Thus,√4=2 4 is the radical and 2 is the square root. The cube root (3√) of a positive number x is the

number that, when cubed, equals x . For example: the cube root of 8 is 2 (2x2x2=8). Rules aboutradicals:

– √x√y = √(xy) √12√3 = √36 = 6. – √(x/y) = √x / √y √(3/16) = √3 / √16 = √3 / 4 – To simplify a radical, try factoring √32 = √16√2 = 4√2. – The square root of a positive fraction less than 1 is larger than the original fraction √(1/4) =

1/2.

CHAPTER 11 – ALGEBRA

New math technique for cosmic problems, that makes even difficult problems easy: Plugging In.

1. Pick numbers for the variables in the problem;2. Using your numbers, find an answer to the problem (target answer);3. Plug your numbers into the answer choices to see which choice equals the answer you found

in step 2. Start with A and E.

Do not plug in the numbers 0 and 1, numbers from the problem or numbers from the answer choices.

There are three kinds of cosmic problems:

1. Variables in the answer choices ( page 130);2. Percents in the answer choices (page 131);3. Fractions or ratios in the answer choices (page 133).

Sometimes a GMAT question includes the words ‘must be’, ‘could be’ or ‘cannot be’. This type of problem can also be solved by Plugging In, but you need to plug in more than one number (trydifferent types of numbers to be shore).

Sometimes is solving (in)equalities faster than Plugging In. You recognize equalities on this sign: =.Inequalities are marked by >, <, ≥ or ≤. You can solve an inequality the same way as an equation,except in one way: If you multiply or divide both sides of an enequality by a negative number,

the direction of the inequality symbol changes. For example: -2x>5 Divide both sides by -2

x<-(5/2).

To solve simultaneous equations, add or subtract the equations so that one of the variablesdisappears (example on page 141).

Quadratic equations come in one of two forms: factored or unfactored. For example: (x+2)(x+5) =x2+7x+10. The first one is factored, the second one is unfactored. When solving a problem thatinvolves a quadratic equation, you first notice which form it’s in. If the quadratic equation is inunfactored form, factor it immediately. If the quadratic equation is in a factored form, unfactor it.

– Unfactor a factored equation: (x+2)(x+5) = x2 + 5x + 2x + 10 = x2 + 7x + 10 – Factor an unfactored equation: x2 + 2x – 15 (x…)(x…) (x + 5)(x-3)

The equation rule: You must have as many equations as you have variables for the data to besufficient. For example: x = y+1 cannot be solved without another distinct equation.



Three types of quadratic equations are almost always included in the GMAT. Remember them!

– (x + y) 2 = x2 + 2xy + y2

– (x + y)(x – y) = x2 – y2

– (x – y) 2 = x2 – 2xy + y2

CHAPTER 12 – APPLIED ARITHMETIC

Rate x Time = Distance T=D/R and R=D/T

Work problems always involve two people, factories or machines working at different rates. In thisproblem the trick is not to think about how long it takes to do an entire job, but rather how much of the job can be done in one hour. Therefore, you use Plugging In.

Any strange looking symbol – like #, *, $ or ∆ - is a function. A function is basically a set of directions.The test writers will also use f(x) to indicate a function.

Basic probability formula = (number of outcomes you want) / (total numbers of possible outcomes).To find the probability of a series of events, you multiply the probabilities of each of the individualevents. Formula:The probability that A and B will both happen = A x B in which A = (number of outcomes you want) /(total numbers of possible outcomes) and B = (number of outcomes you want) / (total numbers of possible outcomes).

The probability that A or B will happen = A + B

The probability that something won’t happen = 1 – the probability that it will happen.

The formula to figure out the odds that at least one thing will happen: Will = 1 – Won’t.

Permutations and combinations For a problem that asks you to choose a number of items to fillspecific spots, when each spot is filled from a different source, you have to multiply the number of choices for each of the spots. For example: At a restaurant you must choose an appetizer, a maincourse and a dessert. There are 2 possible appetizers, 3 possible main courses and 5 possibledesserts. You could order 2 x 3 x 5 = 30 different meals.

Permutations: single source, order matters

For a permutation problem that asks you to choose from the same source to fill specific spots, youhave to multiply the number of choices for each of the spots – but the number of choices keeps gettingsmaller. You can figure out the number of permutations of a group of n similar objects with the formula:n(n-1)(n-2)(n-3)…, also written as n!

Permutations: single source, order matters but only for a selection

For example: If there were 9 baseball teams (n), the total number of permutations of the top 4 teams(r ) would be 9x8x7x6.

Combinations: single source, order doesn’t matter

Formula: (n(n-1)(n-2)…x (n-r +1)) / (r !). Another way to write this formula: (n!) / (r !(n-r)!). For example: if there were 9 baseball teams, the total number of combinations of the top 4 would be: (9x8x7x6) /(4x3x2x1).

Not sure if it’s a permutation or a combination problem? Permutation problems usually ask for

‘arrangements’. Combination problems usually ask for ‘groups’.



CHAPTER 13 – GEOMETRY

Memorize the certain common angles ( page 175 ) and the following approximations: – π ≈ 3 – √1 = 1

– √2 = 1,4 – √3 ≈ 1,7

Important notes: – The diagrams in the GMAT are drawn to scale, unless a diagram is marked as ‘not drawn to

scale’. Not all the diagrams will be drawn to the same scale. – Diagrams marked ‘not drawn to scale’, cannot be measured. The drawings in these problems

are often purposely misleading to the eye. – Drawings in questions using the data sufficiency format of the GMAT are not drawn to scale.

They cannot be estimated with your eye or with a ruler. – Most GMAT geometry problems involve more than one geometric concept.

13.1 DEGREES AND ANGLES

180º rule (part 1): When you see a geometry problem that asks you about angles, always look to seeif tw angles add up to a line, which tells you that the total of the two angles is 180º. This is often thecrucial starting point on the road to the solution.

There are 360º in a circle. The quarter is 90º and the half is 180º.

A line is just a 180º angle. ℓ is the symbol for a line. The part of the line that is between points A andB is called a line segment. A and B are the end points of the line segment.

When two lines intersect, four angles are formed ( page 179). The four angles add up to 360º. Angles

that are opposite to each other are called vertical angles and have the same number of degrees.

Two lines in the same plane are said to be parallel if they extend infinitely in both directions withouttouching. The symbol for parallel is ||. When two parallel lines are cut by a third line, there appear tobe eight different angle measurements, but there are only two ( page 180 ).

If two lines intersect in such a way that one line is perpendicular (= loodrecht) to the other, all theangles formed will be 90º angles, also known as right angles.

13.2 TRIANGLES

A triangle is a three-sided figure that contains three interior angles, which always add up to 180degrees. There are several kinds of triangles: – Equilateral triangle = the three sides are equal in length. Because the angles opposite equal

sides are also equal, all three angles in an equilateral triangle are equal. – Isosceles triangle = two sides that are equal in length. The angles opposite the two equal

sides are also equal. – Right triangle = one interior angle is equal to 90 degrees. The longest side of a right triangle

(the one opposite the 90º angle) is called the hypothenuse.

Some rules about triangles: – The sides of a triangle are in the same proportion as its angles. The longest side is opposite

the largest angle. The shortest side is opposite the smallest angle.

– One side of a triangle can never be longer than the sum of the lengths of the other two sides,or less than their difference.



– The perimeter (= omtrek) of a triangle is the sum of the lengths of the three sides. – The area (= oppervlakte) of a triangle is equal to (height x base) / 2. The base and height must

be perpendicular to each other. In a right triangle, the height also happens to be one of thesides of the triangle.

– In a right triangle, the square (= kwadraat) of the hypotenuse equals the sum of the squares of the other two sides. This is called the Pythagorean theorem. Formula: a2 + b2 = c2 (in which cis the hypotenuse).The right triangle in the ratio 3:4:5 is the most common Pythagorean triple.Two others you have to remember (show up a lot) are 5:12:13 and 7:24:25.

– A right isosceles triangle always has proportions in the ratio side:side:side√2. ( page 189) – The second special right triangle is called the 30-60-90 right triangle. The ratio between the

lengths of the sides in a 30-60-90 triangle is constant. If you know the length of any of thesides, you can find the lengths of the others. The ratio is always (x):(x√3):(2x). The shortestside is length x, the hypotenuse is 2x and the remaining side is x√3.

13.3 CIRCLES

A line connecting any two points on a circle is called a chord. The distance from the centre of thecircle to any point on the circle is called the radius. The distance from one point on the circle throughthe center of the circle to another point on the circle is called the diameter . Diameter = 2 x radius.

The rounded portion of the circle between points A and B is called an arc ( page 193).

The area of a circle is equal to πr 2, in which r = radius.

The circumference (the length of the entire outer edge of the circle) is equal to 2πr .

A circle cut in half by a diameter is called a semi-circle.

A triangle is said to be inscribed inside a semi-circle when one of its sides is the diameter of the circleitself, with the two other sides meeting at any point on the circle. A triangle inscribed inside a semi-circle is always a right triangle.

13.4 RECTANGLES, SQUARES AND OTHER FOUR-SIDED OBJECTS

A four-sided figure is called a quadrilateral. The perimeter of any four-sided object is the sum of thelengths of its sides.

A rectangle is a quadrilateral whose four interior angles are each equal to 90 degrees. Opposite sitesof rectangles are always equal. The area of a rectangle is length x width.

A square is a rectangle whose four sides are all equal in length.

A parallelogram is a quadrilateral in which the two pairs of opposite sides are parallel to each other and equal to each other, and in which opposite angles are equal to each other. The area of aparallelogram equals base x height . A rectangle is also a parallelogram, but a parallelogram doesn’thave to be a rectangle.

13.5 SOLIDS, VOLUME AND SURFACE ARE A

The volume of a rectangular solid or a cube is equal to length x width x depth.

The volume of a cylinder is equal to the area of the circular base times the depth = πr 2 x depth.



The surface area of a solid is the sum of the areas of all the two-dimensional outer surfaces of theobject. For example: the surface area of a rectangular solid is the sum of the areas of the solid’s sixfaces ( page 199).

13.6 COORDINATE GEOMETRY

Any straight line on the plane can be described by the equation y = mx+b. In which b is the y-

intercept (the point at which the line crosses the y -axis), m is the slope (= helling) of the line and x

and y are the coordinates of some point on that line.

Formula for the slope = (the difference in the y-coordinates) / (the difference in the x-coordinates).

CHAPTER 14 – ADVANCED DATA SUFFICIENCY

Write down the flowchart (choices AD and BCE) on your scrapbook (chapter 9). The answer choicesfor data sufficiency questions are always the same.

In a data sufficiency question, before proceeding to the statements, take stock of the information thatyou already know. Then, see if you can determine what sort of information the statements need toprovide so that you could solve the problem.

In data sufficiency questions, figures are often NOT drawn to scale and the test writers won’t mentionthis. You should base your conclusions about whether you have sufficient information on thestatements rather than any figures.

Important information for solving data sufficiency questions with equations:1. When working with equations, your generally need as many equations as there are

variables in those equations. – A single equation with two variables cannot be solved, – But two distinct equations with the same two variables can be solved, using

simultaneous equations (chapter 11)1. Just because there is only one variable doesn’t mean that an equation has just one

solution.

– Generally, equations have as many solutions as the greatest exponent in theequation.

– Simple equations with a variable raised to an odd power may have only onesolution.

1. Sometimes it’s possible to get an answer even if there is only a single equation with

two variables – IF the problem asks for an expression that contains both variables. – Look for integer solutions if at least one of the coefficients will be a larger primenumber like 11, 17 or 29.

1. Sometimes you can also get an answer if there is only a single equation with two

variables if both of those variables can only take integer values.

Half of the data sufficiency problems you’ll see on the GMAT will be yes/no questions. Plugging In isthe most important strategy for handling these questions. Yes or no Plugging In checklist:

1. Try plugging in a normal number for the variable. The number you pick must satisfy thestatement itself, the number will yield an answer to the question – yes or no.

2. Try plugging in a different number for the variable. You might try one of the ‘weird’ numbers,such as 0, 1, a negative number or a fraction. If the number still answers the same way, then

you can begin to suspect that the statement yields a consistent answer and your down to AD.If you plug in a different number and get a different answer this time, then the statement doesNOT definitively answer the question, and you’re down to BCE.



3. Now, repeat this checklist with statement 2.

Pay attention: anytime that you are tempted to answer a data-sufficiency question in only a fewseconds, you may be about to fall for a Joe Bloggs answer. You should reread the question. Joe’sbiggest problem is going too fast. Several common traps that Joe falls for:

1. Joe thinks answer E means ‘I don’t know’ If you want to pick E on a question that you

find confusing, make sure that you can explain why you don’t have enough information.2. Joe thinks the statements are missing information Sometimes Joe picks answer E

because he’s convinced that the statements need to provide more information. Of course, Joearrived at his conclusion pretty quickly, so it’s likely that he may have missed some way to usethe information provided. Make sure that you take the time to fairly evaluate the information ineach statement.

3. Joe thinks that confusing statements are not sufficient When an easy statement isfollowed by a complicated statement, Joe picks A. He doesn’t want to say that he doesn’tunderstand the second statement. However, when the test writers match an easy statementwith a statement that is wordy and confusing, the harder statement is also sufficient. If thehard statement didn’t work, the question would be an easy problem (guessing theory).

4. Joe thinks too many problems are easy Remember that most data-sufficiency questionsare not as easy as they seem.

5. Joe makes bad assumptions Data-sufficiency questions try to get test takers to make badassumptions. The test writers often write the questions to take advantage of the assumptionsthat people routinely make. When a problem seems too easy, go back and reread theinformation. Are you assuming something?

6. Joe remembers statement 1 when evaluating statement 2 Joe sometimes tries to useinformation that he learned in statement 1 while evaluating statement 2. To avoid this trap,always evaluate the statements independently. Use the AB/BCE approach.



GMAT – VERBAL SUMMARY

CHAPTER 15 – SENTENCE CORRECTION

Sentence corrections make up a little more than one-third of the 41 questions on the verbal part. To dowell on sentence corrections, you will have to learn GMAT English.

Use POE to narrow down the choices, before you have to start reading the answers carefully. Try tospot the error in a sentence, go through the answer choices and eliminate any that also contain thaterror. Then decide among the remaining choices.

How to use POE?A. Read the original sentence and look for a specific error that the test writers like to test. As

soon as you spot an error, you can eliminate any answer choice that repeats this error. Thenread the remaining choices carefully to see which is best.B. If you don’t spot the error, then go straight to the answer choices to look for clues. The

differences in the answer choices are excellent hints as to what kind of error you might belooking for in the original sentence.

The first of the answer choices is always a repeat of the underlined part of the original sentence. Aboutone-fifth of the sentence correction sentences are fine just the way they are. You can tell that asentence is correct by the absence of any of the other types of errors.

BASIC TERMINOLOGY (DON’ T NEED TO KNOW FOR GMAT)

– Noun = word that’s used to name a person, place, thing or idea. – Verb = word that expresses action. – Adjective = word that modifies (= wijzigt) a noun. – Adverb = word that modifies a verb, adjective or another adverb. – Preposition = word that notes the relation of a noun to an action or a thing. – Phrase = group of words acting as a single part of speech. A phrase is missing either a

subject or a verb or both. – Prepositional phrase = group of words (phrase) beginning with a preposition. – Pronoun = word that takes the place of a noun. – Independent clause = group of words that contains a subject and a verb and can stand by

itself (it contains the main idea of the sentence).

– Dependent clause = group of words that contains a subject and a verb and can’t stand byitself.

THE 8 MAJOR ERRORS OF GMAT ENGLISH

You don’t have to memorize the terminology that’s used. You simly have to recognize a GMAT Englisherror when you see it.

1. Pronoun errors

– Pronounce reference It has to be absolutely clear who is being referred to by a pronoun.‘Samantha and Jane went shopping, but she couldn’t find anything she liked.’ ‘Samantha and

Jane went shopping, but they couldn’t find anything they liked’



– Pronoun number (singular or plural) The pronoun has to be similar to the noun in terms of the number (singular or plural). ‘The average male moviegoer expects to see at least one

scene of violence per film, and they are seldom disappointed. ‘The average male

moviegoer expects to see at least one scene of violence per film, and he is seldom

disappointed’

See the list of common pronouns (page 256). Every time you spot a pronoun, you shouldimmediately ask yourself the following two questions:1. Is it completely clear who or what the pronoun is referring to?2. Does the pronoun agree in number with the noun it is referring to?

1. Misplaced modifiers

The modifying phrase modifies the wrong noun or pronoun. – Participal phraseWhen a sentence begins with a participal phrase (starts with a verb

ending in –ing), that phrase is supposed to modify the noun or pronoun immediately followingit. ‘Coming out of the department store, John’s wallet was stolen.’ (False because the wallet

was not coming out of the department store; John was). ‘Coming out of the department

store, John was robbed of his wallet’

– Adjectives ‘Frail and weak, the heavy wagon could not be budged by the old horse.’ (Falsebecause it’s the old horse that’s frail and weak, not the heavy wagon). Frail and weak, the

old horse could not budge the heavy wagon’

– Adjectival phrases ‘An organization long devoted to the cause of justice, the major awarded

a medal to the American Civil Liberties Union.’ (False because it’s not the major who’s theorganization). ‘ An organization long devoted to the cause of justice, the American Civil

Liberties Union was awarded a medal by the mayor’

Whenever a sentence starts with a modifying phrase that’s followed by a comma, the noun or pronoun after the comma should be what the phrase is referring to. Every time you see a sentencethat begins with a modifying phrase, check to make sure that it modifies the right noun or pronoun.If it doesn’t, you’ve spotted the error in the sentence. The correct answer choice will either changethe noun that follows the modifying phrase (preferred method) or change the phrase itself into anadverbial clause so that it no longer needs to modify the noun.

Pay attention: while modifying phrases need to refer to the word they are modifying, modifyingclauses (which have a subject and a verb) are a different story. ‘Before designing a park, the

public must be considered ’ (modifying phrase) is wrong, while ‘ Before an architect designs a park,

the public must be considered ’ (modifying clause) is perfectly correct.

1. Parallel construction

– A sentence that contains a list or has a series of actions set off from one another by commasWhen a main verb controls several phrases that follow it, each of those phrases has to beset up in the same way. ‘Among the reasons cited for the city councilwoman’s decision not to

run for reelection were the high cost of a campaign, the lack of support from her party, and

desiring to spend more time with her family.’ This sentence is false. Has to be: and the desireto… The construction of each of the three reasons is supposed to be parallel.

– A sentence that’s divided into two parts ‘To say that the song patterns of the common robin

are less complex than those of the indigo bunting is doing a great disservice to both birds.’ If the first half of a sentence is constructed in a particular way, the second half must beconstructed in the same way: ‘To say that the song patterns of the common robin are less

complex than those of the indigo bunting is to do a great disservice to both birds.

Every time you read a sentence correction problem, look to see if you can find a series of actions,a list of several things, or a sentence that is divided into two parts.

1. Parallel Comparison



– Faulty comparison sentences ‘The people in my office are smarter than other offices’ iswrong. It compares two dissimilar things. You need to make the comparison clear or parallel:‘The people in my office are smarter than the people in other offices. The people can also bemodified in a pronoun: those. This is also correct. The correct answer to a parallel comparisonquestion on the GMAT almost invariably involves the use of a pronoun (that or those) rather than a repetition of the noun.

– Comparing two actions Parallel comparison problems also come up when you compare twoactions: ‘ Synthetic oils burn less efficiently than natural oils’ . In this type you don’t compare theoils, but how the oils burn. It has to be: ‘Synthetic oils burn less efficiently than do natural oils’

Look for sentences that make comparisons. These often include words such as than, as, similar

to, and like. When you find one of these comparison words, check to see whether the two thingscompared are really comparable.

1. Tense

In general: if a sentence starts out in one tense, it should probably stay there. ‘When he was

younger, he walked three miles every day and has lifted weights, too.’ The clause when he was

younger puts the entire sentence firmly in the past. In this sentence has lifted is inconsistent with

the rest of the sentence. It has to be: ‘When he was younger, he walked three miles every day and

lifted weights, too.’

Exceptions: – A sentence that contains the past perfect By definition, any action set in the past perfect

must have another action that comes after it, set in the sample past. ‘He had ridden his

motorcycle for two hours when it ran out of gas.’

– One action in a sentence clearly precedes another If the sentence clearly refers to twodifferent time periods, you can use more tenses. ‘The dinosaurs are extinct now, but they

were once present on the earth in large numbers.’

Tenses that come up on the GMAT: – Present (He walks three miles a day) – Simple past (When he was younger, he walked three miles a day. – Present perfect (He has walked three miles a day for the last several years) past till now

(and further). – Past perfect (He had walked three miles a day until he bought his motorcycle past till a

moment in the past. – Future (Hewill walk three miles a day, starting tomorrow)

Look for changes in verb tense in the sentence or in the answer choices. If the answer choices giveyou several versions of a particular verb themselves, then you should be looking to see which one iscorrect.

1. Subject-verb agreement errors

A verb is supposed to agree with its subject. GMAT test writers like to separate the subject of asentence from its verb with several prepositional phrases. ‘The number of arrests of drunken

drivers are increasing every year.’ ‘The number (of arrests of drunken drivers) is increasing

every year.’

Cover up the prepositional phrases between the subject and the verb of each clause of thesentence so you can see whether there is an agreement problem. Also be on the lookout for nouns that sound plural but are in fact singular ( page 269).

2. Idiom

Idiomatic errors are difficult to spot because there is no one problem to look for. There are norules, each idiom has its own particular usage. If you’ve gone through the first six items on your



checklist – pronouns, misplaced modifiers, parallel construction, faulty comparison, tense andsubject-verb agreement – and still haven’t found an error, try pulling any idiomatic expressions outof the sentence so that you can see whether they’re correct. ‘I’m indebted for my parents for

offering to help pay for graduate school.’ ‘I’m indebted to my parents for offering to help pay for

graduate school.’

See the idioms most commonly tested on the GMAT ( page 272 )

3. Quantity words

Below are the comparison words that come up on the GMAT most frequently:

If two items If more than two items

BetweenMoreBetter Less

AmongMostBestLeast

Another type of quantity word that shows up on the GMAT involves thing that can be counted asopposed to things that can’t:

Countable items Uncountable items

Fewer Number Many

LessAmount, quantityMuch

Look for quantity words. Whenever you see a ‘between’, check to see if there are only two itemsdiscussed in the sentence. Whenever you see ‘amount’, make sure that whatever is discussedcannot be counted.

CHAPTER 16 – READING COMPREHENSION

There are three types of passages on the GMAT:1. The social science passage (concerns a social or historical issue)2. The science passage (describe a scientific phenomenon)3. The business passage (discusses a business-related topic)

There are two types of questions in Reading Comprehension:1. General questions (about the main idea and/or the structure of the passage)2. Specific questions (about a specific piece of information in the passage)

GMAT READING: THE PRINCETON REVIEW METHOD

Step one – Read for the main idea Read the first sentence of a paragraph carefully. It’s often thekey to understand the entire paragraph. Once you know what the paragraph is about, you don’t needto pay a lot of attention to the other sentences in the paragraph. The goal is to spend no more than

two minutes ‘reading’ the passage. Then you have to know what the main idea is of the passage andwhat the structure is.



Step two – Look for structural signposts Certain words instantly tell you a lot about the structureof the passage. Some structural signposts to look out for on the GMAT:

– Trigger words Trigger words always signal a change in the direction of a passage. Atrigger word at the beginning of any paragraph is a sure sign that this paragraph will disagreewith what was stated in the preceding one. Trigger words that often appear on the GMAT: but,

although (even though), however, yet, despite (in spite of), nevertheless, nonetheless (= toch),notwithstanding, except, while, unless, on the other hand.

– Continuing-the-same-train-of-thought words Some structural signposts let you knowthat there will be no contradiction, no change in path: first of all, in addition, by the same

token, likewise, similarly, this (implies a reference preceding sentence), thus (implies a

conclusion).

– Parentheses Sentences or fragments that appear inside parentheses often containinformation you’ll need to answer a question.

– Yin-Yang words One of the test writers’ favorite type of passage contrasts two opposingviewpoints, and certain words immediately give this away. Yin words with the yang wordsinside the parentheses: generally (however, this time…), the old view (however, the newview…), the widespread belief (but the in-crowd believes), most scientist think (but Doctor Xthinks…), on the one hand (on the other hand…).

Step three – Attack the questions Use POE to find the right answer. It’s easier to eliminateincorrect answers than to select the correct answer. General questions have general answers, soeliminate any answer to a general question that focuses on only one part of the passage or is toospecific in some other way. Also eliminate answers that cite information that’s not in the passage at all.Specific questions have specific answers. Every specific question gives you a clue where to look for the answer. When a question seems to be specific but is not highlighted, look for a catchy word or phrase in the question and find this in the passage.

Inference questions This question asks you to draw an inference. GMAT inferences go at most atiny bit further than the passage itself. Two traps that you can eliminate:

– The answer is far too much – The answer was never said in the passage

Disputable answer choices The test writers want their answers to be indisputable so that no onewill ever be able to complain. In general, an answer choice that is highly specific and unequivocal isdisputable and is therefore usually NOT the best answer. An answer choice that is general and vagueis indisputable and is therefore often the correct answer. For example:

– Shaw was the greatest dramatist of his time. = DISPUTABLE – Shaw was a great dramatist, although some critics disagree. = INDISPUTABLE

Indisputable answer choices often include these words: usually, sometimes, may, can, some, most.

Disputable answer choices often include these words: always, must, everybody, all, complete, never.

Respect for professionals It’s very unlikely that the test writers would create a right answer thatimplies anything negative about a professional (doctor, scientist etc.).

Moderate emotion The test writers avoid using passages that convey strong emotions. If they askfor the author’s tone and you see strong words in an answer choice (like overly enthusiastic , scornful

and envious), it’s probably the wrong answer.

Minority groups (the diversity passage) Most of the time, GMAT introduces a diversity passagein one of the Reading Comprehensions. This passage is invariably positive in tone. Any answer choicethat expresses negative views of the marginalized group in question is almost certainly wrong.



CHAPTER 17 – CRITICAL REASONING

Critical Reasoning passages are quite short (20-100 words) and you should read them carefully.Immediately after the passage there will be a question. Always first read the question before the pas-sage. The question contains important clues where you have to look for when you read the passage.

Most critical reasoning passages are in the form of arguments in which the writer tries to convince thereader of something. There are three main parts to an argument:

1. Conclusion What the author is trying to persuade us to accept. Look for conclusions at thebeginning and end of the passage (first and last sentence). Look for signposts. Worlds like thefollowing often signal a conclusion: therefore, thus, so, hence, implies, indicates that .

2. Premises The pieces of evidence the author gives to support the conclusion. Words likethe following often signal a premise: because, since, in view of, given that .

3. Assumptions (= veronderstellingen) Unstated (= onuitgesproken) ideas or evidencewithout which the entire conclusion might be invalid.

Most argument structures are: premise, premise, premise, conclusion OR conclusion, premise,

premise, premise .In the Critical Reasoning section, it’s easy to think too much. The test writers describe this as goingoutside the scope of the passage. The two most common reasons that an answer choice is wrong are:

– The answer choice goes too far. – The answer choice is outside the scope of the argument (is not included in the passage).

8 TYPES OF CRITICAL REASONING QUESTIONS

1. Assumption questions

These questions ask you to identify an unstated premise of the passage from among the answer choices. When you read the passage, you have to look for a gap in the underlying logic of theargument. There are three kinds of assumptions: – Causal assumptions Causal assumptions take an effect and suggest a cause for it. For

example: ‘Every time I wear my green suit, people like me. Therefore, it is my green suit that

makes people like me.’ This argument relies on the assumption that there is no other possiblecause for people liking him. Whenever you spot a cause being suggested for an effect, askyourself if the cause is truly the reason for the effect, or if there might be an alternate cause.

– Analogy assumptions An argument by analogy compares one situation to another,ignoring the question whether the two situations are comparable. For example: ‘Use of this

product causes cancer in laboratory animals. Therefore, you should stop using this product.’

This argument relies on the assumption that because this product causes cancer in laboratoryanimals, it will also cause cancer in humans. Whenever you see a comparison in a Critical

Reasoning passage, you should ask yourself: ‘Are these two situations really comparable?’ – Statistical assumptions A statistical argument uses statistics to prove its point. For example: ‘Four out of five doctors agree: The pain reliever in Sinutol is the most effective

analgesic on the market today. You should try Sinutol.’ The author’s conclusion is based onthe assumption that four out of every five doctors will f ind Sinutol to be wonderful. This may becorrect, but we do not know for sure. Whenever you see statistics in an argument, always besure to ask yourself: ‘Are these statistics representive?’

You recognize an assumption question on the following sentences: – Which of the following is an assumption on which the argument depends? – The argument above assumes which of the following? – The claim above rests on the questionable presupposition that…

Guidelines for spotting assumptions among the answer choices: – Assumptions are never coming straight from the passage.

V e

r yi m p or t an t t o an sw er C r i t i c al

R e a s oni n g q u e s t i on s! ! !



– Assumptions support the conclusion of the passage, they make the conclusion stronger. – Assumptions frequently turn on the gaps of logic (causal, analogy and statistical).

Look at the example of an assumption question ( page 315 )

1. Strengthen the argument questions

Like assumption questions, strengthen-the-argument questions are really asking you to find thegap and then fix it with additional information. Some guidelines for spotting strengthen-theargument statements among the answer choices: – The best answer will strengthen the answer with new information. – The new information will support the conclusion of the passage, it makes the conclusion

stronger. – Strengthen-the-argument questions frequently turn on the gaps of logic we’ve already

discussed (causal, analogy, statistical).

Strengthen-the-argument questions are generally worded in two ways: – Which of the following, if true, most strengthens the author’s argument? – Which of the following, if true, most strongly supports the author’s hypothesis?

1. Weaken the argument questions

Like assumption questions and strengthen-the-argument questions, weaken-the-argumentquestions really ask you to find a hole in the argument. This time, however, you don’t need to fixthe gap. All you have to do is expose it.

Some guidelines for finding weaken-the-argument statements among the answer choices: – The statement you look for weakens the conclusion of the passage. – Weaken-the-argument questions frequently trade on the gaps of logic that we’ve discussed.

Weaken-the-argument questions are usually worded in one of the following ways: – Which of the following, if true, most seriously weakens the conclusion drawn in the passage?

– Which of the following indicates a flaw in the reasoning above? – Which of the following, if true, would cast the most serious doubt to the argument above? – Which of the following most accurately describes what might be a questionable…

1. Inference questions

Inference questions often have little to do with the conclusion of the passage; instead they mightask you to make inferences about one or more of the premises. You’ll look for a statement thatseems so obvious that it almost doesn’t need saying. The most answer choices are going too far with their statements.

Inference questions are typically worded in one of the following ways:

– Which of the following can be inferred from the information above? – Which of the following must be true on the basis of the statements above? – Which of the following conclusions is best supported by the passage? – Which of the following conclusions could most properly be drawn from the information above?

Very difficult! Look at the examples! (from page 324)

1. Resolve/explain questions

These questions ask you to resolve an apparent paradox or explain a possible discrepancy. In thiscase, the passage will present you with two seemingly contradictory facts. You have to find theanswer choice that allow both of the facts from the passage to be true.

Resolve/Explain questions are usually worded in one of the following ways: – Which of the following, if true, resolves the apparent contradiction presented in the passageabove?



– Which of the following, if true, best explains the discrepancy described above? – Which of the following, if true, forms a partial explanation for the paradox described above?

1. Evaluate the argument questions

These questions will ask you to pick an answer choice that would help to evaluate or assess partof an argument. Like assumption questions, evaluate-the-argument questions revolve aroundunderstanding the unspoken gap in the logic of an argument.

Evaluate-the-argument questions are generally worded in one of the following ways: – The answer to which of the following questions would be most useful in evaluating the

significance of author’s claims? – Which of the following pieces of information would be most useful in assessing the logic of the

argument presented above?

1. Identify the reasoning questions

These questions will ask you to identify a method, technique, or strategy used in the passage, or to identify the role of a bolded phrase in the passage. The best strategy to answer these rare

questions is to identify the conclusion and the premises and think about how they’re related.

Identify-the-reasoning questions are generally worded as: – The bolded phrase plays which of the following roles in the argument above? (bolded phrases

always refer to an identify-the-reasoning questions) – The argument uses which of the following methods of reasoning?

1. Parallel the reasoning questions

These questions ask you to recognize the reasoning in a passage and follow the same line of reasoning in one of the answer choices. ‘If A, then B.’

Parallel-the-reasoning questions are usually worded as:

– Which of the following most closely parallels the reasoning used in the argument above? – Which of the following supports its conclusion in the same manner as the argument above? – Which of the following is most like the argument above in its logical structure?

It’s unlikely that the test writers would use the same subject matter for the correct answer to theparallel-the-reasoning question.

8 question types:

1. Assumption questions2. Strengthen-the-argument questions

3. Weaken-the-argument questions

4. Inference questions

5. Resolve/explain questions

6. Evaluate-the-argument questions

7. Identify-the-reasoning questions

8. Parallel-the-reasoning questions

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