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GMAT MATH


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GMATClub contributingtoeachotherslearning

Percent

Whatisthepercentformula?

Howmuchis15percentof20?

MATH:ARITHMETIC

1

Percent|Answers

PercentFormula:

Part=PercentxWhole

Forexample,15%of20is:15

20 300

3

2


Percent2

Whatistheformulaforperce

IfJackgotaraisefrom$15p

perhour,whatwastheperce

3

Percent2|Answers

PercentChangeFormula:

JacksRaise:

4


5/121


Percent3

Iftheproductionofhybridcarstripledlastyear,by

howmanypercentdiditincrease?

100%

200%

250%

300%

333%

MATH:ARITHMETIC

5

Percent3|Answers

ThecorrectanswerisB increasedby200%

Forexample,ifproductionwas10cars,andit

tripledto30cars,theincreasewas20cars,which

is200%of10

6


Percent4

50%of25is25%ofwhic

7

Percent4|Answers

Thereare2solutionstothispro

Longone:

50%of25is12.5

12.5*100=x*25

x=50

8


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Odd/EvenRules

CheckyourknowledgeofOdd/Evenrules

Odd+Odd=?

Odd Even=?

Even+Odd=?

OddxOdd=?

Odd Even=?

OddxEven=?

Hint: trypickingnumbers

MATH:ARITHMETIC

9

Odd/EvenRules|Answers

Odd+Odd= 1+1=2(Even)

Odd Even=3 2=1(Odd)

Even+Odd=2+1=3(Odd)

OddxOdd= 3x3=9(Odd)

Odd Even = 3 2 = 1 5 (Not an integer!)

10


Odd/EvenRules2

Is0oddoreven?

11

Odd/EvenRules2|An

0(zero)isEven

12


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Odd/EvenRules3

Ifb isanoddnumber,whichofthefollowing

mustbeeven?

A. 2 3

B.

C.

1

D. 2

E. 2 2

MATH:ARITHMETIC

13

Odd/EvenRules3|Answers

Usetheplugnumbersmethodtocheckeach

answerchoice.Letstake1:

A. 2*1 3= 1(Odd)

B.

=0(Even) however,justincase,letstry3.

1 (Odd).Itusuallyisagoodideatorun

14


Odd/EvenRules4(Ult

IsA+B+Cevenorodd

A C B iseven

isodd

15

Odd/EvenRules4|An

Statements(1)and(2)combine

ConsiderA=6,B=4,andC=2(the

andA=0.5,B=0.3,andC=0.2(th

Donotassumethatthenumbethequestiondoesnotmention

16


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DivisibilityRules

Is54780divisibleby2?

Is1671divisibleby3?

Is5632divisible by4?

Is3830divisibleby5?

Is2658divisibleby6?

Is396divisibleby9?

MATH:ARITHMETIC

17

DivisibilityRules|Answers

Yes.Divisibilityby2 lastdigitofanumberiseven

Yes.Divisibilityby3 sumofalldigitsisamultiple

of3

Yes.Divisibilityby4 last2digitsisamultipleof4

Yes.Divisibilityby5 thelastdigitiseither0or5

18


Divisibility2(Hard)

Isinteger divisibleb

xisanintegerdivisibleby

xyisanintegerdivisibleby

19

Divisibility2|Answer

Thebestwaytoapproachthisq

inseveralsetsofnumbers

Manyaretemptedtoplug3for

theonlyvalueycanhaveis3;inanswerisYes.

20


9/121


NumberProperties

Whichofthefollowingintegersrepresentsasum

of3consecutiveevenintegers?

200

303

400

554

570

MATH:ARITHMETIC

21

NumberProperties|Answers

Toanswerthequestion,checkwhichintegeris

bothdivisibleby3(sincethereare3integers)and

iseven.Theonlynumberthatfallsintobothof

those2categoriesis570. CorrectanswerisE

22


NumberProperties2(

If 5, 2,

2,

x>0

y=4

23

NumberProperties2

Substitutex,y,andzintheoriginafollowing: 2 3 0;Thesequationarex=1andx=3.

Statement

1

is

sufficient.

If

x>0,

thisx=3.Theresultis27+16+6=49,w7

24


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NumberProperties3

Howmanydistinctintegersare

therebetween1and21inclusive?

MATH:ARITHMETIC

25

NumberProperties3|Answers

MostoftenGMATquestionswillsayinclusivebutsometimestheydont needtoremembertocheck

The

formula

for

calculating

the

number

of

integers

betweentwonumbersis:NM+1

Therefore the answer is: 21 1 + 1 = 21

26


Multiples

Whatisamultiple?

Is5amultipleof55

multipleof5?

27

Multiples|Answers

Themultiple ofanum

productofthenumber

otherwholenumber.(F2,4,6,8aremultiplesof

28


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Multiples2

Is0(zero)amultipleof100?

MATH:ARITHMETIC

29

Multiples2|Answers

Yes,0(zero)isamultipleof

everything However,itisunlikelythatGMAT

30


Multiples3

HowtofindaLeastC

Multiple(LCM)?

31

Multiples3|Answers

Option1:

Step1:Findtheprimefactorsof

Step2:Multiplytheuniquefacto

duplicates)

Option2:

32


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Multiples4

WhatistheLeastCommon

Multipleof18and24?

MATH:ARITHMETIC

33

Multiples2Answers

Option1

Findthefactorsof18and24:

18=3x3x2

24=3x2x2x2 Multiplytheuniquefactors:3x3x2x2x2=72

O ti 2

34


Translate

Theproductofthreeandfou

fiveandthenincreasedbyth

betweentheoriginalproduct

35

TranslateAnswers

3x4=12

12 5=7

12 8=4

7 + 4 = 11

36


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ArithmetictoMemorize

=

MATH:ARITHMETIC

37

ArithmetictoMemorize|Answers

50%

25%

40%

38


ArithmetictoMemori

75%=

20%=

16

%

87

%

39


8.33%

87.5%

75%

75%=

40


14/121


ArithmetictoMemorize3

2 =

2

2

2

2

2

MATH:ARITHMETIC

41

ArithmetictoMemorize3|Answers

2 =4

2 8

2

16 2 32

2 64

42


ArithmetictoMemori

3 =

3

3

3

4

4 4

43


3 =9

3 27

3

81 3 243

4

44


15/121



5 =

5=

11 =

12 =

13 =

14 =

15 =

16 =

MATH:ARITHMETIC

45


5 =25

5=125

11 =121

12 =144

13 = 169

46


ArithmetictoMemori

Completethefollowing:8,16,24,32,40,160

12,24,36. 120

15,30 150

47


Completethefollowing(A

8,

16,

24,

32,

40,

48,

56,

64,

72112,120

48


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2

3 =

625

169

ListallPrimesbetween1and50

ExtraHard&ExtraCredit

2

125

243

MATH:ARITHMETIC

49


2 1.4

3 =1.7

625 25 169 13

P i 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47

50


Reciprocal

Whatisareciprocal?

51

ReciprocalAnswers

Reciprocalforanumber,d

,isanumberwhichwhen

yields.Thereciprocalofafragetthereciprocalofanumbe

52


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AbsoluteValue

Whatisthe3 stepapproachtosolving

equationsandinequalitieswithabsolute

value?

MATH:ARITHMETIC

53

AbsoluteValue|Answers

Step1: Openmodulusandsetconditions.Tosolve/openamodulus,youneedtoconsider2situationstofindallroots:

Positive(orrathernonnegative)

Negative

54


AbsoluteValue2

If|x1|=4,whatist

x?

55

AbsoluteValue2|An

Step1:Findpositive/negativero

1 0 inourcase, 1 4

1 0 inourcase, 1

Step2:Solvetheequations

x=5

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AbsoluteValue3

WhatisthevalueofxIf|x 5|=10?

MATH:ARITHMETIC

57

AbsoluteValue3|Answers

|x 5|=10

Wemustevaluateboththepositiveandnegativeoutcomesincetheabsolutevalueremovesthe

negative

sign Thus,wehave2equations: X 5 10

58


AbsoluteValue4

IsM


19/121


Factors

Howmanytotalfactorsdoes462

have?

MATH:ARITHMETIC

61

Factors|Answers

Advancedmethodforfindingthenumberofallpossiblefactors:

Writeouteachprimefactorandtheirpower,forexample,12canbewrittenasfollows:

2

3

5 t ( ll th i ill h )

62


Factors2

Dointegersusuallyhav

evennumberoffactors

63

Factors2|Answers

Vastmajorityofintegershavea

factorssuchas12forexample:

Thuswhenfindingthetotalnum

make

sure

it

is

an

even

number Theonlyintegersthathaveano

f f ( h

64


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Average

Iftheaverageof5consecutiveintegersis

12,whatistheaverageoftheevenonly

integers?

10

12

13.518

36

MATH:ARITHMETIC

65

Average|Answers

First,findtheconsecutiveintegers.Since

thereare5,theremaybeeither2or3even

integers.Theseintegersare10,11,12,13,14.

Theaverageoftheevenintegersis12aswell

(10+12+14=36.Divide36by3andyouwill

66


Average2

Theaverageof10consecutiv

Then,9isdeductedfromthe

number,8isdeductedfromt

deductedfromthethird,and

lastnumberwhichremainsu

isthenewaverage?

A)55 B)50 C)6

67

Average2|Answers

Youdontneedtofindeachoft

Instead,youhavetwooptions,y

averageofnumbersbetween0

trap

though,

there

should

be

10than9andtheaverageis4.5,no

find the sum of consecutive inte

68


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Ratios

Whatistheratioofatodif

2a=3b,

b=2c, and3c=d?

A)1:2 B)2:1 C)2:3 D)4:3 E)1:5

MATH:ARITHMETIC

69

Ratios

Withquestionslikethese,unlessyoucanspota

shortcutrightaway,theeasiestwaytosolveisto

plugnumbers:letspicka=6,sincethereisa2and

3

involved 2*6=3b;b=4

70


Powers

2 2 2 2

A)2 2

B)2

C)2 2

D)2

E)30

71

Powers|Answers

2

2

2

2 ? Therearenorulesforadd

bt ti Thi

72


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Powers2

2 2 2 2 2 ?

A)2

B)32

C)2

D)2E)62

MATH:ARITHMETIC

73

Powers2|Answers

2 2 2 2 2 2

Whenpowerswiththesamebase(2

inthiscase)aremultiplied,thepowers

aresummedandthebaseisheld

74


Powers3

?

75

Powers3|Answers

2

Divisionofpowerswitht

76


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Powers4

3 ?

MATH:ARITHMETIC

77

Powers4|Answers

3 3

Whenanumbertakentoapoweris

taken to another power, you need to

78


Powers5

3

=?

79

Powers5|Answers

3

3 Startoperationsfromoutsidean

80


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Powers6

2

2

2

2

?

MATH:ARITHMETIC

81

Powers6|Answers 2

2

2

2

2

Negativepowersturnanumbertoareciprocal number taken to that power

82


Powers7

5

?

83

Powers7|Answers5

1

Anynumber(positivnegative)takentoth

84


25/121


Powers8

4

?

MATH:ARITHMETIC

85

Powers8|Answers

4

4 2 Fraction powers are interpreted as

86


Powers9(UltraHard)

Ifm andn arepositiveintegers,

largerthantheremainde

m>n

Theremainderof

is2

87

Powers9|Answers

Statement(1)byitselfisinsufficie10 ,thesumofdigitsof10

thevalueofn thatdeterminesthe.Ifyoupluginm=2,n=1 (theansw

n=2 (theansweris"no"). Statement(2)byitselfissufficient

is 2 as S2 states then is 2 5 or

88


26/121


Percentiles

Lenasfirsttestscorewasatthe80th percentilein

a classof120students.Onanothertest,24outof

200studentsscoredbetterthanLena.Ifnobody

hadLenasscore,whatisLenaspercentileafter

thetwotests?

MATH:ARITHMETIC

89

Percentiles|Answers

Takeeachtestresultseparately:

Test1:120x80th =96(shescoredbetterthan96

students)

Test2:Shescoredbetterthan176students(200 24) Sumuptheresults:

90


ConsecutiveNumbers

Whatisthesumofconsec

8,9,7,6,5,4,3,2,1,0,1

91

ConsecutiveNumbers

Sumofconsecutiveintegerseq

multipliedbythenumberofter

consecutiveintegers 8,9,7,6,

3 (meanequ

ofthefirstandlastterms),soth

92


27/121


EvenlySpacedSet

Whatisthesumofallmembersof

theset9,12,15,18,21,24?

MATH:ARITHMETIC

93

EvenlySpacedSet|Answers

Thesumofelementsofevenlyspacedsetisgiven

bytheformula

Sum

Therefore,

6 99

94


RecurringDecimal

Express0.393939inafr

95

RecurringDecimal|A

Toconvertarecurringdecimalto1.Separatetherecurringnumberfraction2.Annexdenominatorwith"9"as

lengthoftherecurringnumber3.Reducethefractiontoitslowes

96


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Fractions(ExtraHard)

Ifa,b,andcarepositivedistinct

integers,is

aninteger?

c=2

a=b+c

MATH:ARITHMETIC

97

Fractions|Answers

StatementIisinsufficientsinceitdoesnotprovide

enoughinformationaboutborc

Statement

II:

We

can

rewrite

as

NowpluginthevalueforafromS2:

98


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29/121


Algebra(Hard) Ifeachexpressionunderthesquarerootisgreater

thanorequalto0,whatis 6 9 2 3?

2

2 6 2

2 3

2 6 2

2

MATH:ALGEBRA

1

Algebra|Answers Basedonthesetup(andMathprinciplestestedon

theGMAT),2 hastobe 0.Therefore 2.

6 9 3 3

Because 2, 3 0

2


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Average

Iftheaverageof5consecutiveintegersis

12,whatistheaverageoftheevenonly

integers?

10

12

13.518

36

MATH:STATISTICS

1

Average|Answers First,findtheconsecutiveintegers.Since

thereare5,theremaybeeither2or3even

integers.Theseintegersare10,11,12,13,14.

Theaverageoftheevenintegersis12aswell

(10+12+14=36.Divide36by3andyouwill

2


Average2 Theaverageof10consecutiv

Then,9isdeductedfromthe

number,8isdeductedfromt

deductedfromthethird,and

lastnumberwhichremainsu

isthenewaverage?

A)55 B)50 C)6

3

Average2|Answers Youdontneedtofindeachoft

Instead,youhavetwooptions,y

averageofnumbersbetween0

trapthough,thereshouldbe10than9andtheaverageis4.5,no

find the sum of consecutive inte

4


31/121


Mean

HowtofindtheMean?

MATH:STATISTICS

5

Mean

Arithmetic

Mean

=

Average

=

6


Median

HowtofindtheM

7

Median|Answers Arrangeallnumbersin

from

the

smallest

to

thMedian willbethemid

8


32/121


Mode

Howtofindthemode?

MATH:STATISTICS

9

Mode|Answers TheModeofanarrayisthenumberthat

appearsmostoften.Forexample,inan

array1,2,3,3,4 theMode is3.Itappeared twice In the array 1 2 3 3 4 4

10


Range

HowtofindtheRa

11

Range|Answers Rangeisthedifferenceb

smallest

and

largest

elemarray.Ifyouhavetofindm

i i l d

12


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StandardDeviation

HowtofindtheStandard

Deviation?

MATH:STATISTICS

13

StandardDeviation|Answers YouwonthavetocalculateSDontheGMATbut

youneedtounderstandtheconceptofSD

StandardDeviationmeasureshowspreadoutthe

members

of

the

array

are.

To

find

the

Standard

Deviation:

Find the mean

14


StandardDeviation2 Whichofthesetshasahighers

SetA

15

StandardDeviation2 SetAhasthehigherStandardD

theelementsaredistributedfur

mean

16


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StandardDeviation3 Whatisthefastestwaytoestimatestandard

deviation(withoutcalculatingit)?

Thereisaset{67,32,76,35,101,45,24,37}.Ifwe

createanewsetthatconsistsofallelementsof

theinitialsetbutdecreasedby17%,whatisthe

change

in

standard

deviation?

MATH:STATISTICS

17

StandardDeviation3|Answers Wedon'tneedtocalculateasdecreaseinall

elementsofasetbyaconstantpercentagewill

decreasethestandarddeviationofthesetbythe

samepercentage(theaverageisdecreasedby17%aswellasthedifferencebetweenaverage(mean)

and all elements or their squares Thus the

18


StandardDeviation4WhatistheStandardDev

ofconsecutiveeveninteg

(1)Thereare39elements

(2)themeanofthesetis

19

StandardDeviation4 BeforereadingDataSufficiencysta

wesayaboutthequestion?What

findstandarddeviation?"consecu

meansthatallelementsstrictlyre

Ifweshiftthesetbyaddingorsub

itdoesnotchangethestandardde

20


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StandardDeviation5 SetAconsistsof19integerswithmean4and

standarddeviationof3.IfanewsetBisformedby

adding2moreelementstothesetA,whattwo

elementswilldecreasethestandarddeviationthe

most?

A)9and3

B) 3and3

C)6and1

D)4and5

E)5and5

MATH:STATISTICS

21

StandardDeviation5|Answers Solution:Theclosertothemean,thesmaller

thestandarddeviation,andtherefore,the

greaterthedecreaseinstandarddeviation.D

has4(equaltothemean)and5(differsfrom

meanonlyby1).

22


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CompoundInterest

MATH:WORDPROBLEMS

If$20,000isinvestedat12%annual

interest,compoundedquarterly,whatis

thebalanceafter1year?

1

CompoundInterest|Answers CompoundInterestformula:

1

whereC isthenumberofperiods

20 000 1 .

20 000 1 03

2


Mixtures

14litersofapplejuiceismixe

juice.Iftheresultingmixcon

cranberryjuice,howmanylit

wereproduced?

3

Mixtures|Answers Mixtureproblemsrequireatten

boththeinformationgivenand

Weknowthatthe14litersofap

(100%65%)ofthenewmixture ConstructanX:

4


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WorkProblems

MATH:WORDPROBLEMS

Whatistheformulaforawork

problem?

5

WorkProblems|Answers Thekeytosolvingtheworkproblems,issettingthe

equationcorrectly.Theworkformulaisbasedontheprincipleofworkrates(inverseofthetimeitwouldtaketocompletethejob).Theratealmostalwayswill

be ,,

Formula: Sum ofthe Rates ofWorkers = the combined

6


WorkProblems2Robertworkingalonecan

in8hours.Doug,ontheo

unloadthesametruckin

arehiredtogether,howm

take

Robert

and

Doug

to

utruckworkingtogether?

7

WorkProblems2|An UsingtheWorkformula:

C

3 4 hours (approximate

8


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GroupProblems

MATH:WORDPROBLEMS

Outof90conferenceattendees,50registered

forthebasicworkshopand60signedupfor

theadvancedworkshop.If20attendeeshave

notsignedupforaworkshopyet,howmany

signedupforbothadvancedandbasic

workshops?

9

GroupProblems|Answers Thebestandeasiestapproachtosolvingthistype

ofproblemsisusingtheboth/neitherformula(alternativeoptionisaVenndiagram).

Group1

+

Group2

+

Neither

Both

=

Total 50+60+20 Both=90

130 Both = 90

10


GroupProblems2 Theofficeof120issplitbetwee

employeesattheratioof3:5.If

employeesaremarriedand20o

employeesintheofficearemen

womenworkingintheofficeare

11

GroupProblems2|A Toanswerthisquestionthefast

tabletogether:

Male Female

Married 20 X

Single X 3 X 75

12


39/121


Volume/MixtureProblems(Hard)

MATH:WORDPROBLEMS

Ifafarmersells15ofhischickens,hisstockoffeedwilllastfor4moredaysthanplanned,butifhebuys20morechickens,hewillrunoutoffeed3daysearlierthanplanned.Ifnochickensaresoldorbought,thefarmerwillbeexactlyonschedule.Howmanychickensdoesthefarmerhave?

12

24

48 55

60

13

Volume/MixtureProblems|Answers Veryhardproblem.Severalsolutionsexist;thisone

isprobablynotthemostcorrectbutthequickest:

LetXbethenumberofchickensandYbethedays

they

can

survive

on

the

current

feed: (x15)(y+4)=(x+20)(y3)

14


CountingProblems(U Inagameofchess,themoveso

alternatewithwhiteshavingthe

achesstournament,whiteshav

movesaltogetherwhileblacksh

moves.Ifinanygamethesidet

movedidnotlose,whichofthe

trueaboutthetournament?

I.Blackslost5games

II.Blackswonmoregamesthanw

III.Allgamesendedinadraw

15

CountingProblems|A Fromthestemitfollowsthattherew

whichwhiteshadthelastmove.Theresponsibleforthedifferenceinthetmadebywhitesandblacksduringth

know

that

these

4

games

were

not

wcouldwellhaveendedinadraw).Allcouldhavebeenwonbyblacksoren

16


40/121


Distance(UltraHard)

MATH:WORDPROBLEMS

Aswimmermakesaroundtripupanddownthe

riverwhichtakesherXhours.Ifthenextdayshe

swimsthesamedistancewiththesamespeedin

stillwater,whichtakesherYhours,whichofthe

followingstatementsistrue?

X>Y

X


41/121


Rate

MATH:WORDPROBLEMS

Acertainbacteriacolonydoublesinsizeeveryday

for20days,atwhichpointitreachesthelimitofits

habitatandcannolongergrow.Iftwobacteria

coloniesstartgrowingsimultaneously,howmany

dayswillittakethemtoreachthehabitatslimit?

6.33

7.5

10

15

19

21

Rate|Answers Weknowthatthebacteriacolonydoublesinsize

everydayfor20days.Thereforeonthesecondday

itisdoublethesizeofthefirstday,andsoon.

Similarly,

on

the

20th

day,

it

is

at

100%

of

capacity,

therefore,onthe19th day,itwillbeat50%.Since

we have 2 colonies both will be occupying half of

22


42/121


Triangles

SumofanglesofANYtriangleequals?

Whatcanwesayaboutsidesofatriangle?

Whatistherighttriangle(isthattheone

thatsnotwrong?)

MATH:GEOMETRY

1

Triangles|Answers

Sumofallanglesinanytriangleisalways180

Onesideisalwayssmallerthanthesumofthe

othertwoandisalwaysgreaterthanthedifference

oftheothertwo Arighttriangleistheonethathasa90degree

2


Triangles2

Listallmethodsforfin

ofatriangle.

3

Triangles2|Answers

1.Area=

2.Herosformula:

wherea,b,c aresidesofatriangle

perimeter

4


43/121


Triangles3

Theseare2sidesofarighttriangle,findthethird

side:

3,4,x

6,8,x

5,12,x

12,16,x

7,24,x

MATH:GEOMETRY

5

Triangles3|Answers

GMATreliesontheseeasytriangles.Ifyou

memorizethesecombinations,itwillsaveyoutime

ontheGeometrysection

3,4,5 6,8,10

6


Triangles4

Whatistherelationshipb

arightisoscelestriangle?

Whatistherelationshipb

angles?

7

Triangles4|Answers8

2


44/121


Triangles5

Nameasmanyproperties,

relationships,andformulasasyou

knowaboutanequilateraltriangle

MATH:GEOMETRY

9

Triangles5|Answers10

Allsidesareequal

Allanglesareequal(60degrees)

Allheights,bisectorsandmediansareequal:2

3s


Triangles6

Whatcanyouderivefromthisf

(Misthecenterofacircle)

A

B

CM

11

Triangles6|Answers12


45/121


Triangles7

Whatisthevalueofsidesina

306090triangle?

MATH:GEOMETRY

13

Triangles7|Answers

In306090triangle,thesidesarex,x 3,

andthehypotenuseis2x(doublethe

sizeofthesmallestside)

14


Triangles8(Hard)15

Onthepicturebelow,isthearea

ABCgreaterthan1?

1.AngleABC


46/121


Rectangles

Nameasmanyproperties,relationships,and

formulasasyouknowaboutarectangle.

MATH:GEOMETRY

17

Rectangles|Answers

Oppositesidesareparallelandequal

Thediagonalsbisect(divideintotwoequalparts)eachother

Thediagonalsareequal

Asquareisaspecialcaseofarectanglewhereallfoursidesarethesamelength.

Thetwodiagonalsareequal(samelength). Eachdiagonalbisectstheother.Inotherwords,thepointwherethe

diagonalsintersect(cross),divideseachdiagonalintotwoequalparts.

18


Rectangles1

Nameasmanyproperties,re

formulasasyouknowabouta

19

Rectangles1|Answer

Asquareisbotharhombus(equalsi(equalangles)andthereforehasalltboththeseshapes,namely:

Thediagonalsofasquarebisectea

Thediagonalsofasquarebisectit

Thediagonalsofasquareareperp

20


47/121


Rectangles2 Continued

Nameasmanyproperties,relationships,and

formulasasyouknowaboutasquare

MATH:GEOMETRY

21

Rectangles2|Answers

Asquarehasalargerareathananyotherquadrilateralwiththesameperimeter. Theareaisthewidthtimestheheight.Soinasquarethisissimply:,wheres isthelengthofoneside. The"diagonals"method.Ifyouknowthelengthsofthe

diagonals,theareaishalftheproductofthediagonals.Since

bothdiagonalsareequal,thissimplifiesto:

whered isthe

length of either diagonal

22


Circles

Pleasedefinethefollowing:

Center ?

Radius ?

Diameter ?

Circumference ?

Area ?

Chord

? Tangent ?

Secant ?

23

Circles|Answers

Center Apointinsidethecircle.Acircleareequidistantfromthecen

Radius distancebetweenthecenthecircle.Itishalfthediameter

Diameter achordpassingthroug Circumference distancearoundt

Area a region enclosed by the cir

24


48/121


Circles2

MATH:GEOMETRY

25

Whataretheformulasfor

Circumferenceofacircle?

Areaofacircle?

What istheapproximatevalueof?

Circles2|Answers26

Circumferenceequals:

Areaequals:


CoordinateGeometry

Whatistheequati

slopeofaline?

27

CoordinateGeometry

Slopeofalineequatio

28


49/121


CoordinateGeometry2

Ifalinehasanegativeslopeless

than1 whatdoesitsayaboutthe

line?

MATH:GEOMETRY

29

CoordinateGeometry2|Answers

Negativeslope meanslinemovesfromtheupper

lefthandquarant (Q2)tothebottomrighthand

quadrant(Q4)orinsimpleterms,itisadecreasing

line.

Positive

slope

means

the

opposite

(duh) Sincetheslopeislessthan1,itisaflatline(as

d ) Si l i i i

30


CoordinateGeometry

WhatslopesdoLinesA,B,andC

Positive/Negative?

Less/Greaterthan1?

C

31

CoordinateGeometry

LineA

PositiveSlope

Slopegreaterthan1

LineB Slopeisneither

32


50/121


CoordinateGeometry4

HowtofindtheXandYintercepts

ofaline?

MATH:GEOMETRY

33


Bestoptionistopluginthevaluesintothe

equationoftheline

Forexample,alineisy=mx+b TofindtheYintercept(thisiswhenthelinecrosses

theYaxisandthusXiszero)solve:y= b

34


CoordinateGeometry

IflineM withaslopeof

goest

2)andB(4,3),whatisthelengt

AB?

35

CoordinateGeometry

Theslopeinformationinthisirrelevant

TofinddistancebetweenAandBiscalculatedusingthePythagoreanTheorembydrawingatriangle

36


51/121


CoordinateGeometry6

Findtheequationofalinepassing

throughthepointsA(5,4) andB(2,6)

MATH:GEOMETRY

37


A(5,4) andB(2,6)

Tofindanequationofalinebasedontwo

points,usethisformula:

;

38


CoordinateGeometry

IflinesAandBareperpendi

other,whatistherelationshi

slopes?

A. Inverse

B. Opposite

C. Positive

D. ReciprocalE. ReciprocalandNegative

39

CoordinateGeometry

Therelationshipbetween

slopesof2perpendicular

linesisnegativereciprocal

.Inotherwords,the

twolinesareperpendicular

40


52/121


CoordinateGeometry8

Arethetwolinesbelowperpendicular?

MATH:GEOMETRY

41


Toanswer,findtheslopeofeachlineandthen

checktoseeifoneslopeisthenegativereciprocal

oftheotheroriftheirproductequalsto 1.

SlopeAB=

Slope CD

42


CoordinateGeometry

Whatisthepointofinters

linesthathavethefollow

y=3x3andy=2.3x+4?

43

CoordinateGeometry

Thekeytosolvingtheintersecti

atthepointofintersection,bot

sameXandYcoordinates.

Thus,ifYcoordinatesarethesaputthetwoequationstogether

44


53/121


CoordinateGeometry10(Hard)

Doesthecurve 16

intersecttheYaxis?

1 16

2 5

MATH:GEOMETRY

45


16 istheequationofacirclecenteredatwithradius4.

Statement(1)byitselfisinsufficient.S1saysthatthecenterofthecircleisfurtherthan4unitsawayfrom

the

origin

but

it

doesn't

specify

whether

the

circle

is

farenoughfromtheaxisnottointersectit.

Statement(2)byitselfissufficient.FromS2itfollows

46


54/121


Enumeration

Therearethreemarbles:1blue,1grayand1

green.Inhowmanywaysisitpossibletoarrange

marblesinarow?

MATH:PROBABILITY&COMBINATIONS

1

Enumeration|Answers Solution: Let'swriteoutallpossibleways

Total:6

2


Enumeration2 Therearethreemarbles:1b

green.Inhowmanywaysisi

arrangemarblesinarowifb

marbleshavetobenexttoe

MATH:PRO

3

Enumeration2|Answ Solution: Let'swriteoutallposs

arrangemarblesinarawandth

arrangementsthatsatisfyquest

4


55/121


Enumeration3

Inhowmanywayscan5dressesbe

arrangedinastoredisplay?


5

Enumeration3|Answers 1.Howmanyobjectswecanputat1stplace?5.

2.Howmanyobjectswecanputat2ndplace?4andsoon:3,2,1

Therefore,thetotalnumberofarrangementsofndifferentobjectsinarowis

1 2 2 1 !

6


Enumeration4(Ultra IfN isapositiveinteger,wha

of1!+2!+.N!?

Nisdivisibleby4

isanoddinteger

MATH:PRO

7

Enumeration4|Answ Thisisaveryhardquestionthatre

traditionalapproach(assomeoftGMATquestionsoftendo)

Analyzingfactorials,youwillnoticfactorialswillhave3asthelastdigwith5!,eachsumendswithazero6!=720,andsoon.)

8


56/121


Combinations1

Whatisthenumberofpossiblearrangementsof

objectskfromacollectionofdistinctobjectsn?


9

Combinations1|Answers Acombinationisanunordered collectionofkobjects

takenfromasetofndistinctobjects.Thenumberofwayshowwecanchoosekobjectsoutofndistinctobjectsisdenotedas:

Totalnumberofarrangementsofn distinctobjectsisn!

10


Combinations2 Whatisthenumberofpossible

objectskinacertainorderfrom

distinctobjectsn?

MATH:PRO

11

Combinations2|Answ Apermutationisanordered col

takenfromasetofndistinctob

ofwayshowwecanchoosekob

distinct

objects

is

denoted

as:

1.Thetotalnumberofarrangem

objects is n!

12


57/121


Combinations3 Whatisthedifferencebetween

combinationsandpermutations?

Whentousewhichformula?


13

Combinations3|Answers Permutationsformula

!

!isusedwhen

sequenceofchoicematters(meaningagroupABCisdifferentfromBACorCBA).Classicexampleis

choosing

nominees

for

3

specific

positions

from

a

poolof10candidates!

14


Combinations4

Ifsixbusinesspartnersareh

aroundtable,howmanysea

arrangementsarepossible?

MATH:PRO

15

Combinations4|Answ Thedifferencebetweenplacem

thatinacircleisfollowing:ifwe

oneposition,wewillgetdiffere

a

row

but

the

same

relative

arracircle.So,forthenumberofcirc

of n objects instead of n! we ha

16


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Combinations5 Ifthereare5chairsinaroomandBoband

RachelwanttositsothatBobisalwaysleftof

Rachel,inhowmanywaysthisseating

arrangementbeachieved?


17

Combinations5|Answers NotethatleftofRachel,doesnotmean

immediatelynexttoRachel,justleftofher.

Thisconditioniscalledsymmetrybecauseit

eliminateshalfofthepossibilities(RachelcansitonlyleftorrightofBob).

18


Combinations6(Ultra Inhowmanydifferentwaysc

peoplebedividedinto4team

each?

90

105

168

4202520

MATH:PRO

19

Combinations6|Answ Thesolutiontothisproblemisthe

combinations.Firstwegetoneteanumberofwaystodothiswouldbcombinationis2outof6or

,an

fourcombinationsmultiplied,wetotalnumberbythenumberofwachosen since we are not intereste

20


59/121


Probability1

Whatistheprobabilitythatan

eventn willoccur?

Whatistheprobabilitythatan

eventn willnot occur?


21

Probability1|Answers Theprobabilitythatanevenn willtakeplaceis

whereN isthetotalnumberofpossible

occurrences

The probability that an even n will not occur is the

22


Probability2 Whatistheprobabilityofgettin

flippingacoin?

Whatistheprobabilityofgettin

die?

MATH:PRO

23

Probability2|Answe TheprobabilityofgettingTailsw

is

or50%sincethereare2tota

onlyoneoutcomeeachtimethe

The probability of getting a 4 wh

24


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Probability3

Abucketcontains10greenand90white

marbles.IfAdamrandomlychoosesamarble,

whatistheprobabilitythatitwillbegreen?


25

Probability3|Answers Thenumberofgreenmarbles:n=10

Thenumberofallmarbles:N=10+90=100

Probability:

10%

There

is

one

important

concept

in

problems

with

marbles/cards/balls.Whenthefirstmarbleisremovedfrom a jar and not replaced the probability for the

26


Probability4 Ifthereisacoinandadie

probabilityofgettinghea

afteroneflipandonetos

MATH:PRO

27

Probability4|Answe Tossingacoinandrollingadiea

events (occurrenceofoneeven

influenceoccurrenceofotherev

independenteventstheprobab

ofallprobabilitiesofindepende

28


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Probability5

Ifthereisa20%chanceofrainonanaverage

day,whatistheprobabilitythatitwillrainon

thefirstdayandwillbesunnyonthesecond?


29

Probability5|Answers Theprobabilityofrainis0.2;thereforeprobability

ofsunshineisq=1 0.2=0.8.Thisyieldsthatthe

probabilityofrainonthefirstdayandsunshineon

theseconddayis:

P=0.2*0.8=0.16

N h ki i h i i i

30


Probability6 Therearetwosetsofcardsw

{1,3,6,7,8}and{3,5,2}.IfRob

randomlyonecardfromthe

cardfromthesecondset,wh

probabilityofgettingtwood

MATH:PRO

31

Probability6|Answe Thereisatotalof5cardsinthe

themareodd:{1,3,7}.Therefo

ofgettingoddcardoutofthefir

Thereare3cardsinthesecond

areodd:{3,5}.Therefore,thep

32


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Probability7

IfJessicarollsadie,whatisthe

probabilityofgettingatleasta"3"?


33

Probability7|Answers Twoeventsaremutuallyexclusiveiftheycannot

occuratthesametime.Fornmutuallyexclusiveeventstheprobabilityisthesumofallprobabilitiesofevents:

P(AorB)=P(A)+P(B) Thereare4outcomesthatsatisfyourcondition(to

34


Probability8 Thereare8employeesinclud

Rachel.If2employeesareto

chosentoformacommittee,

probabilitythatthecommitte

BobandRachel?

MATH:PRO

35

Probability8|Answe Combinatorialapproach: Thetotalnumberofpossiblecomm

ThenumberofpossiblecommitteeandRachelis1

P

=

Probabilityapproach: Th b bilit f h i B b R

36


63/121


Probability8 Part2 Thereare8employeesincludingBoband

Rachel.If2employeesaretoberandomly

chosentoformacommittee,whatisthe

probabilitythatthecommitteeincludesboth

BobandRachel?


37

Probability8 Part2|Answers ReverseCombinatorialApproach: Insteadofcountingprobabilityofoccurrenceofcertain

event,sometimesitisbettertocalculatetheprobabilityoftheoppositeandthenuseformulap=1 q.

Thetotalnumberofpossiblecommitteesis=28

Thenumberofpossiblecommitteethatdoesnot includesbothBobandRachelis:m

2

where, is

the number of committees formed from 6 remaining

38


Probability8 Part3 Thereare8employeesinclud

Rachel.If2employeesareto

chosentoformacommittee,

probabilitythatthecommitte

BobandRachel?

MATH:PRO

39

Probability8 Part3 Reverseprobabilityapproach:Wecanchooseanyfirstperson.

Then,ifwehaveRachelorBobas

can

choose

any

other

person

outpeople.

If we have neither Rachel nor Bob

40


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Probability9 JuliaandBrainplayagameinwhichJulia

takesaballandifitisgreen,shewins.Ifthe

firstballisnotgreen,shetakesthesecond

ball(withoutreplacingfirst)andshewinsif

thetwoballsarewhiteorifthefirstballis

grayandthesecondballiswhite.Whatisthe

probability

of

Julia

winning

if

the

jar

contains

1gray,2whiteand4greenballs?


41

Probability9|Answers Sometimes,at700+levelyoumayseecomplex

probabilityproblemsthatincludeconditionsor

restrictions.Forsuchproblemsitcouldbehelpful

todrawaprobabilitytreethatincludeallpossible

outcomesandtheirprobabilities.

N I i b i

42

d d h k


65/121


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66/121


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VERBAL STRATEGIES


68/121

ContentsofFlashCards BasicStrategiesandPrinciplesofSente

Correction,CriticalReasoning,andReaComprehensionwithafewexamples

Illustrationoferrorsandrightanswercthroughexamples

2


69/121

CriticalReasoning

Contents

MainPoint/MustBeTrue

Weaken

Strengthen

Assumption

R l h P d

2


BasicDeconstruction

Step1:Readthequestionstemandcateg

Step2:Readthestimulusandidentifythconclusion

Step3:Trytofocusontheconclusionandthatmightberight

Step4:Useprocessofeliminationtorule

choices.

Don't

try

to

make

them

fit!

Step5:Makesureanswerchoicemakess

3

MainpartsofaCRque

Conclusion

4


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MainpartsofaCRquestion

Conclusion:Thisisthefinalargumentthatthe

authormakes.

Premise:Theseareevidentiarystatementsthat

supporttheconclusion

Assumption:

These

are

unstated

premises,

on

whichtheconclusionandsometimesthepremise

reston.

5

VERBAL

Premise&Conclusion

PREMISE CONCLUSION

Supportstheconclusion Answersthe

questionofWhy?

Hasatoneoffinality andconveysthefinal

messageofwhattheauthorissaying

Because Thus

Since Therefore

6


TypeI AscertainCon

Thesearequestionswhereweas

stimulusistrue andtrytofindan

aresupportedbytheconclusion

PossibleQuestionTypes:

1. Inference

2. MainPoint

3. MustbeTrue

7

TypeII Strengthen&

Thesearequestionswhereweas

givenanswerchoicesaretrue an

bestonethatwillsupportthest


8


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TypeIII WeakenandHurt

Thisisbasicallytheoppositeoftheabovetypeand

aimstodisprovetheconclusionofthestimulus.

Hencewetaketheanswerchoicetobetrue here

aswell.


1. Strengthen2. Assumption

9

VERBAL

MostCommonMistakeTypes

OppositeAnswers

Doestheoppositeofwhattheanswerchoiceis

supposedtodo

Peoplepickthembecausetheymightgetconfused

aboutthequestiontype

10


OutofScope/IrrelevantAnswers

Talksaboutsomethingcomplete

discussionathand.

Peopletendtopickthesewhent

unsureofwhattheyresupposed

ToneMismatchAnswers

Answersthatdontagreewithth Mightbetoostrongortooweak

stimulus

MostCommonMistak11

MainPoint/MustBeT

Whichofthefollowingrepresentsthemain

Whichofthefollowingcanbeinferre

CorrectAnswerChoices

Canthisanswerchoicebeprovenorvalithe stimulus? Is this answer choice true t

12


72/121


Tobeconsideredforthisyearsmeritscholarshipaward,studentsneedto

haveperfectattendanceanda4.0GPA.Alexistheonlypersonintheclass

whohasa4.0buthehashad5absences.

Theclaimsabove,iftrue,moststronglysupportwhichofthefollowing

conclusions?

A. Nostudentatthisschoolhasperfectattendancefortheyear

B. Somestudentsatthisschoolwhodidnothavea4.0alsodidnothave

perfectattendance

C. Alexistheonlystudentwhocouldbeconsideredfortheaward

D. Nostudentatthisschoolqualifiesfortheawardthisyear

E. Manystudentshaveachievedperfectattendancebutnever4.0GPAs.

A B C D E

13

VERBAL

A:Exaggeration.

B:Possible,butnotnecessary

C:Thestimulusclearlysaysthatyouneedboth

perfect

attendance

and

4.0

GPA.

D:Thisistrue.IfAlexistheonlyonewhohasa

A B C D E

14


Weaken

Whichofthefollowing,iftrue,callsintoquargument?

Whichofthefollowingmostseriouslyunde


Doesthisanswerchoicebreakdowncaualternatecause,showthatthecauseeffexistentorreversed?

Answerchoiceshouldbreakdownstructutakentobetrue)

Couldbeinrelationtoagrossgeneralizatorincorrecthypothesisfromfacts.

15

16


73/121


Thereare350brandsofcellphonesinthemarkettoday.However,ourstore

onlystocksthetop10brands.Inordertoincreaseoursales,weplanto

increasethesizeofourinventorytothetop50brands.

Whichofthefollowing,iftrue,pointsoutamajorflawintheplanabove?

A. Thecapabilitiesofthetopfivecellphonesarealmostthesame,withno

brandhavingconsistentsuperiorityinallrespects.

B. Thetop8brandsaccountforalmostallthecellphonessold

C. Asusersgetmoresophisticated,theywanttotryoutthelesserknown

brandswhichmightoffersomeothervaluetothem.

D. Lesspopularbrandsprovidelittleprofittothestorebecausetheyhaveto

bediscountedtobesold

E. Theleadingbrandsarenowlosingsalestolesspopularbrandsthatoffer

similarfeaturesforalowercost

A B C D E

17

VERBAL

A:Irrelevant.Doesthisaffectprofitmarginsforthestoreiftheyweretoincreaseinventory?No

B:Thismeansthatthestorealreadyhasthebrandsthatsellthemost.Increasinginventorywillhave

littleeffectonprofitmargins.CorrectAnswer.

C: This almost strengthens the argument.

A B C D E

18


Strengthen

Whichofthefollowing,iftrue,strengthensth

Whichofthefollowing,iftrue,wouldmostsigscientistshypothesis


Doesthisanswerchoicereinforcetheconcluvalidateanassumptionorruleoutadiscrepacausality?

Answerchoiceshouldstrengthenstructureof

tobetrue) Needstodirectlystrengthenconclusionbybr

validatingreasonsorassumptionsorfindingmdirectstrengthening,moveon!Donttrytom

19

20


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Recently,severalcompanieshavewithdrawntheiradsfromMagazineA,becausethe

editorialboardofthemagazinehaddecidedtochangetheimagethatthemagazine

portraysfromoneoffamilyvaluestooneconcernedmorewithsexandviolence.Surely

thisindicatesthatthedecisionmakersinadvertisingagenciesdostillhaveasenseofmoral

proprietythatoccasionallydrivestheiractions.

Whichofthefollowing,iftrue,wouldstrengthenthisconclusion?

A)Theadvertisersregularlyreviewtheplacementoftheiradvertisements.

B)Itisarareeventforseveraladvertiserstowithdrawalltheiradvertisements

simultaneouslyfromapublication.

C)Theadvertisers,whenquestioned,admittedthattheirclientswouldloserevenueasa

result

of

the

advertisements

being

withdrawn.D)Theadvertisersallplacednewadvertisementswithotherpublicationsthatemphasised

familyvalues.

E)AsurveyofthereadershipofMagazineXsuggestedthatthemajorityofthereadership

thinkthatthestandardofthemagazine'scontentshadfailedsinceitstransformation.

QuestionfromGMATClub(95810)

A B C D E

21

VERBAL

A:Thisisirrelevanttothequestionofmoralpropriety.

B:Thisdoesntnecessarilypointtomoralproprietydirectly.Dontmakeunnecessary

connections!

C: Once again, no correlation to what were talking

A B C D E

22


Assumption

Theauthorassumeswhichofthefollow

Theargumentcannotbetrueunlesswhstatementsareassum


Supporter:Linksunrelatedelementsinthlogicalgaps

Defender:Eliminatesthealternativesand

weaken

the

conclusion.

AssumptionNegationTechnique:Narrowanswerchoicesandthennegatethem tverb(suchthatthemeaningofthesentennegatedchoiceweakenstheconclusion,t

23

24


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Intheory,itspossiblethatbacteriadevelopedonMarsearlyinitshistoryandsomewerecarriedtoEarthbyameteorite. However,strainsofbacteriafromdifferent

planetswouldprobablyhavesubstantialdifferencesinproteinstructurethatwould

persistovertime,andnotwobacterialstrainsonEartharedifferentenoughtohave

arisenondifferentplanets.So,evenifbacteriadidarriveonEarthfromMars,they

musthavediedout.

Theargumentismostvulnerabletowhichofthefollowingcriticisms?

A.ItfailstoestablishwhetherbacteriaactuallydevelopedonMars.

B.ItfailstoestablishhowlikelyitisthatMartianbacteriaweretransportedtoEarth.

C.Itfailstoconsiderwhetherthereweremeansotherthanmeteorites bywhich

MartianbacteriacouldhavebeencarriedtoEarth.

D.ItfailstoconsiderwhetherallbacterianowonEarthcouldhavearisenfrom

transportedMartianbacteria.

E.Itfailstoconsiderwhethertherecouldhavebeenstrainsofbacteriathat

originatedonEarthandlaterdiedout.


A B C D E

25

VERBAL

A:ThisisirrelevanttotheargumentthatstatesthatevenifbacteriacamefromMars,theymusthavediedout.

B:OutofScope!

C:Again,thisdoesnttalkaboutbacteriastrainsdyingout

A B C D E

26


ResolvetheParadox

Whichofthefollowing,iftrue,helpsexpla

Whichofthefollowing,iftrue,helpsexdiscrepancyintheargu


ActiveResolution:Donttrytodisprovetgiven.

Doestheanswerchoiceaddressthefact

MUST

conform

to

the

stimulus TheanswershouldaddressBOTHsidesof

resolveit.Itshouldntstrengthenthepara

27

28


76/121


77/121


78/121


79/121


ArecentsurveyofallautoaccidentvictimsinDoleCountyfoundthat,oftheseverelyinjured

driversandfrontseatpassengers,80percentwerenotwearingseatbeltsatthetimeoftheir

accidents.Thisindicatesthat,bywearingseatbelts,driversandfrontseatpassengerscangreatly

reducetheirriskofbeingseverelyinjurediftheyareinanautoaccident.

Theconclusionaboveisnotproperlydrawnunlesswhichofthefollowingistrue?

A. Ofallthedriversandfrontseatpassengersinthesurvey,morethan20percentwerewearingseat

beltsatthetimeoftheiraccidents.

B. Considerablymorethan20percentofdriversandfrontseatpassengersinDoleCountyalways

wearseatbeltswhentravellingbycar.

C. Moredriversandfrontseatpassengersinthesurveythanrearseatpassengerswereveryseverely

injured.

D. Morethanhalfofthedriversandfrontseatpassengersinthesurveywerenotwearingseatbelts

atthetimeoftheiraccidents.

E. MostoftheautoaccidentsreportedtopoliceinDoleCountydonotinvolveanyseriousinjury.


A B C D E

41

VERBAL

A:Thisisatrickyquestion.Ouraimistoproveacorrelation. Letssay100peoplewereseverelyinjuredand100werenot.Outofthe100severelyinjured,80didntwearseatbelts.

Probabilityofapersonnotwearingseatbelttogetinjured=

Probability

of

a

person

wearing

seat

belt

to

get

injured

=

B: Doesnt establish the correlation between whats being said. Hence

A B C D E

42

ReadingCompreh

Contents

GlobalQuestions

MainPoint/PrimaryPurpose

PassageOrganization

AuthorsPerspective/PassageT

Local Questions

44


80/121


FourQuestionsforRC

Readfromgeneraltospecificatthreelevels.Changeyourreadingstrategy,notyourreadingspeed.Answerthefollowingquestions.

Why?MainPointofthepassage.

How?Structureofthepassage Introduction,ExampleandCounterExample.Andsoon.

What?Whatisbeingsaid?(MainPointofIndividualParagraphs)

WhatTone?Makesureanswerchoicemakessense!

45

VERBAL

CONTINUATIONOFOLDIDEAS INTRODUC TION O FNEWIDEAS

Continues elaboratingonanideathats

alreadybeenpresented

Introduces anothernewidea, perhaps

tocontrastsomethingpresented.

Furthermore However

For Instance But

Newvs.ExistingIdeas46


CommonIndicators

VeryCommonQuestionType

Primarygoalofreadingpassage

point!

Main PointorStrong

47

VeryCommonDistraction

Dont focus on the difficulty of t

DifficultWords,Phrases

CommonIndicators48


81/121


CommonIndicators

Paycloseattention!

Dontmemorize!

Verycommonquestionindicator.Makeamental

noteofwherethelistoccurs,soyoucanreturnto

it,ifnecessary.

ListofThings/Enumerations

49

VERBAL

Ifauthoritiesarementioned,thinkabouthowandwhythisauthoritativeremarkisnecessary.

Mightrepresentconflictingviewpointsorideas.

Reference withAuthority

CommonIndicators50


Matchthecorrectdateswithth

mentioned

Perhaps,makeanoteofthedat

handversionoftheeventonyo

DatesandNum

CommonIndicators51

CommonIndicators

Ideasthatarementionedmore

passage.

HiddenReferen

52


82/121


CommonIndicators

Ifseveralviewpointsarepresentedinthepassage,

makenoteofeachpointandwhossayingit/why

itsbeingsaid.

Understandingofthesecounterexamplesorviews

areveryimportant!Theywillbeindicatedby

wordssuchasHoweverorIncontrast

Contrasting Views

53

VERBAL

Commonwhenthepassageisofscientificnature

Makeanoteofthedefinitionandexpecttobe

ti d b t d t di f th

Definitions

CommonIndicators54


Type

Global L

BasicQuestionTypes55

QuestionTypes

MainPoint/PrimaryPurpose

Global BroadQu

56


83/121


BroadQuestions

RepresentsCoreIdeas

Willaskaboutthebroadermeaningofthe

passage,andwhatitseekstoconvey.

MainPoint/Primary Purpose

57

VERBAL

Thiswillaskaboutthestructureofapassage

Forinstance,thestructuremightbesomething

Passage Organization

BroadQuestions58


BroadQuestions

Thesequestionsaskyoutoreflecperspective

Understandwhattheauthoristrywhereheorshestandswithresp

presented.

Istheauthoraggressive?OristheWhatisthetoneofthemessagec

AuthorsPerspective/To

59

QuestionTypes

SpecificReference

Function

Local SpecificQuestion

60


84/121


LocalQuestions

Willrefertoaspecificlineorparagraphinthe

passageandaskforaquestionrelatingtothat.

Mightinvolvecrossreferencingwithother

relevant

information

presented

elsewhere

in

the

passage

SpecificReference

61

VERBAL

LocalQuestions

Questionsaboutwhatapieceofthepassage

either

a

paragraph,

a

line

or

even

a

word

is

trying

toaccomplishwithrespecttothebroaderscope

Function

62


LocalQuestions

SimilartoCriticalReasoningQu

sametype.

Therequiredanswerwilleither

conclusiveviewpointpresente

i.e.themainpoint

Assumetheanswerchoicesgiv

Strengthen/We

63

LocalQuestions

Again,similartoCriticalReasoninsametype

Willasktoidentifyanaction,amo

Parallel Reaso

64


85/121


RCinaNutshell

Therightmentality:ThepassageWILLbe

intentionallyconfusing.Getusedtoit!

Awarenessofcontent:Thepassagesmightbe

fromhumanities,socialsciencesorsciences.

Dontgetboggeddownbyonekindorget

excitedaboutanother

ReadingPattern:GeneraltoSpecific

65

VERBAL

RCinaNutshell

Understandquestiontypes: GlobalorLocal

Pre

phrase:

Frame

a

rough

answer

before

you

pickanswerchoices!

66

SentenceCorre

Contents

SubjectVerbAgreement

VerbTenseErrors

NounAgreement

Pronouns

M difi

68


86/121


DeconstructingSC

Step1:Readthequestionstemandthinkofpossibleerrorsinthesentence,subjectverbagreement,tensemismatchetc.

Step2:Readtheanswerchoiceandsplititintotwogroupsbasedonoverallstructure.

Step3:Oneofthegroupswillcontainanerror.Eliminatethegroupandresplitthenextgroup.

Step4:Useprocessofeliminationtoruleoutwronganswerchoices.Don'ttrytomakethemfit!

Step5:Makesuretheanswerchoicemakessense!

69

VERBAL

Grammar ThesentencehastoadheretotherulesofgrammarfollowedbyStandardEnglish.

Meaning The sentence has to have a relevant

WhatsTested?

ThreeQuestionTypesYouWillSee

70


Spelling TheGMATwillnotteknowledgeofspellings

Punctuation Addingacommaandsimilarthingswillnotbete

however,

are

tested.

Capitalization TheGMATdoeyourknowledgeofcapitalizatio

Andwhatsnot?

ThreeQuestionTypesYo

71

Thisdealswiththeissueofplur

Singularsubjectsmustusesing

ErrorsTested

SubjectVerbAgre

72


87/121


Removetheadditionalinformationandreadthe

sentencewithoutthem.

BarelyseventeenandleadingtheFrencharmywearing

amansarmor,JoanofArc,anilliteratepeasantgirl

fromtheFrenchcountryside,brokethesevenmonth

oldseizeofOrleansinninedays.

Readingthesentencewithoutthatpartwehave:

BarelyseventeenandleadingtheFrencharmywearing

amansarmor,JoanofArc,brokethesevenmonthold

seizeofOrleansinninedays.

Trap1: Phrasesbetweensubject andverb73

VERBAL

Ifthereareexpletives,thencheckforsubjectverb

agreement,byrearrangingthesentence.

Somecommonexpletives:

There Here

Trap2: SubjectFollows Verb74


Ifthereismorethanonenounor

pronouninasentence,thenthesu

agreementMUSTbeconsistent!!

TwoExceptions:

Conjunctions(OR,NOR) AlwaysSI

UsageofEACHorEVERY AlwaysS

Trap3: MultipleNounsorProno75

Pronounslikeall,any,more,most

andsoon.

Pluralityisbasedonwhattheinde

referringto!(Thisistheanteceden Exceptions:

Trap4: Indefinite Pronouns76


88/121


Tense

Past

Present

Future

Forms

Simple

Perfect

Progressive

PerfectProgressive

ErrorsTested

VerbTense77

VERBAL

IncorrectVerbTense

ShiftinVerbTense

VerbTense SubTypes

ErrorsTested78


Thenumberofnounsmustbecotheyarereferencing.

Incorrect: MattandDavebelievedworkintheirengineeringclasswitheirdreamofbecomingagreate

Correct:MattandDavebelievedtintheirengineeringclasswillhelpdreamofbecominggreatenginee

ErrorsTested

Noun Agreem

79

PronounAntecedentDisagreem

Incorrect Use of Relative Prono

UseofPronou

ErrorsTested80


89/121


ThepronounMUSTrefertoitsantecedent.

Thepronounantecedentrelationshipshouldbeconsistentthroughoutthesentence.

Incorrect: Eachofthewomenselectedforthe

scholarshipwereaskedtosubmitanapplication.

Correct: Eachofthewomenselectedforthescholarshipwasaskedtosubmitanapplication.

PronounErrorSubTypes

PronounAntecedentDisagreement

81

VERBAL

Thishappenswhenthereisadditionalinformationbetweenthepronounandantecedentmakingiteasytolosetrackoftherelationshipbetweenpronouns

andtheirantecedents.

Distancebtw.pronoun&antecedentTrap 1:82


Theseareverygeneralpronounboth,everyandsoon.

Incorrect:Manyofthestudentslearnthathisorherexamwas

Correct:Incorrect:Manyofthesurprisedtolearnthattheirexagraded.

Indefinite PronounsTrap 2:83

AntecedentsthatSOUNDSplur

singularorviceversa.

Trap 3: Misleading Antecedents84


90/121


Theyrelategroupsofwordstoanounorpronoun

which,whom,whomsoever,whereandwhy.

Twotrapsofincorrectusage:

IncorrectPronounChoiceforPeopleandThings

Differencebetweenwhoandwhom

PronounErrorSubTypes

Incorrectuseofrelativepronouns

85

VERBAL

WhoandWhomwillalwaysrelatetopeople.

Thedoctorthat performedthesurgerywashonored

shouldbewho

Trap 1: PronounChoice86


Verysimpletrick!

Makethefollowingsubstitutions: He Who

Him Whom

Thesubstitutionthatmakessensew

thecorrectwordinthatcontext.

Sometimesitmightbenecessarytosentenceforittomakesense.

Trap 2: Whovs.Whom?87

Misplacementofadjectives(desc

serene)

and

adverbs

(describe

ve

Modifiers

ErrorsTested88


91/121


ErrorsinCountNouns(canbecounted trees,bottles,billions).Quantifiersaremany,both,few,several,acoupleandsoon.

ErrorsinNonCountNouns(cannotbecountedwater,liquid).Quantifiersaremuch,alittle,abitandsoon.

Somemodifierslikeall,andsomecanbeusedforboth.

Trap1:89

Quantifiers

VERBAL

Misplacedmodifiersaremodifiersthatareplacedinthewrongpositiononasentence.

Incorrect:Shortonmoney,thecarwasthebestoneTanyacouldfind.

Correct:

Short

on

money,

Tanya

knew

that

the

car

was

the

bestoneshecouldfind.

Trap2:90

Placement


Misplacedmodifierswithrelati

thatorwhich)

Incorrect:Accordingtotherepo

confiscatedthathavenotbeenr

university.

Correct:Accordingtothereport,notbeenregisteredwiththeuni

confiscated.

Trap2:91

Placement

Incorrectuseofcomparativede

Illogical Comparisons

Comparison

ErrorsTested92


92/121


Whentherearetwoobjectsbeingcompared,youhave

touseacomparativeword.Whenmorethantwo

objectsarecompared,youhavetouseasuperlative

word.

Incorrect:Thoughthereportersfeltthatinjuryplayedapart

inTennesseeslosstoMinnesota,Tennesseescoachsaid

thatMinnesotahadthebest teamthatnight.

Correct:Thoughthereportersfeltthatinjuryplayedapart

inTennesseeslosstoMinnesota,Tennesseescoachsaid

thatMinnesotahadthebetterteamthatnight.

ComparisonSubType

Degree ofComparison

93

VERBAL

Onlysimilarobjectscanbecompared.Youcannot

compareahumantoadog.

Incorrect: ThoughtherecentLaysfoodpoisoning

incident has caused some buyers to question its quality

ComparisonSubType

Illogical Comparison

94


ParallelVerbsandVerbFormErrors

ParallelNounErrors

ParallelPrepositionsandArticles

ParallelConjunctions

ParallelComparisons

Parallelism

ErrorsTested95

Nounsarenaturallyparallel.Butwtheformwithaningattheend

confusedforverbs.

ParallelismSubType

VerbErrors

96


93/121


Whenasentencehastwoormoresimilarparts

linkedbyaconjunction,eachparthastobeofthe

sameverbform.

Incorrect: Thenewexampatternrequiresstudentsto

entertheirstudentIDsandsigningtheirnamesonthe

roster.

Correct: Thenewexampatternrequiresstudentsto

entertheirstudentIDsandsigntheirnamesonthe

roster.

NounErrors

ParallelismSubType97

VERBAL

Aprepositionandanarticlemusteitherbeusedbyallpartsofasentenceorbyjustthefirstpart.

Incorrect: Bydoingeachassignment,turningin

Prepositional/Article Errors



Theconjunctionsusedmustbepara

Someexamples:

Incorrect: Therestaurantnotonlyhirealso expandeditsseatingcapacity.

Correct: Therestaurantnotonlyhiredexpandeditsseatingcapacity.

ParallelConjunc

Neither nor Eit

Notonly butalso Bo

Whether or A


ParallelComparis

Whencomparisons areleftunpar

amount toanerroraswell.

Incorrect: In thebook,theauthor

fo nd editing pict res m ch more



94/121


Usageoffragmentsordependentclauseson

eithersideofasemicolon

Incorrect:Theguineapigisnotatruepig;rather,a

rodentthatbelongstotheCaviidae family.

Correct: Theguineapigisnotatruepig,butratherarodentthatbelongstotheCaviidae family.

Correct: Theguineapigisnotatruepig;itsarodent

thatbelongstotheCaviidae family.

SemiColons

ErrorsTested101

VERBAL

TheGMATwillpreferusageofthemostconcisesentencespossible.

Incorrect: Hedecidedtonotpurchasethecarduetothefactthat itwastooexpensive.

WordinessandRedundancy

ErrorsTested102


Very,verycommonerrortested

Aphrasethatiscommonlyacce

eventhoughitsgrammatically

Anidiomerrorwillmisrepresen

Idiomsareprovidedwithright

inthecardsthatfollow.

Idioms

ErrorsTested103

Amongvs.Betwee

Among:

Used when more than two items a

Example: He was the best among t

ErrorsTested Idiom104


95/121


Bothvs.Each

Both:

Used to point out similarities.

Example: Both of them were good at swimming.

Each:

Used to point out differences/dissimilarities. (Alwayssingular)

Example: Each girl had her own niche.

ErrorsTested IdiomRules105

VERBAL

Twicevs.Double

Twice:

Twice/Thrice etc. are used for comparison Example: The Toyota was twice as fast as the Honda.



EachOthervs.OneAn

Each Other:

Used to compare two things.

Example: They loved each other de

One another:

Used to compare more than two th

Example: The three brothers loved


Ifvs.Whether

If:

Primarily used only in If else sent

Example: If this is true, the market wb k t



96/121


Likevs.SuchAs

Like:

Used when indicating similarities between things.

Example: Like John, Amy was a violinist too.

Such as:

Used to list examples.

Example: There are different kinds of tigers such as theBengal Tigers, white tigers and so on.


VERBAL

AbilityTo

Correct:Dolphinshavetheabilitytoemitlowfrequencywhistles

Incorrect:Dolphinshavetheabilityofemittinglow

frequencywhistles.

ErrorsTested Idioms110


Agreeupon/to Correct: Weagreeduponthedateo

Incorrect:Weagreedtothedateof

Correct:Weagreedtoshareourroo

Incorrect:Weagreeduponsharingo

Allowfor

Correct: Onemustalwaysallowforwhilecalculatingaxialloads.

Incorrect:Onemustalwaysallowtoerrorwhilecalculatingaxialloads.


Appealto

Correct:Iappealedtohissenseo

Incorrect:Iappealedforhissense

Are in danger of



97/121


Asanadolescent

Correct: Asanadolescent,hesufferedfromattention

disorder

Incorrect:Whileinadolescence,hesufferedfrom

attentiondisorder.

Asgoodas

Correct:Itsasgoodasnew.


VERBAL

Associatewith

Correct:Iassociatespringwithflowers.

Incorrect:IalwaysassociatewatertoNiagarafalls.

Attend to



Attributeto

Correct:Iattributemysuccessto

Incorrect:Iattributemysuccessw

Baseon

Correct:Thedecisionwasmadeb

criteria. Incorrect:Thedecisionwasmade

criteria.


Begintoseedaylight

Correct:Afterworkingontheprofinallybeginningtoseedaylight.

Incorrect:Afterworkingonthepr

finallybeginningtoviewthedayl



98/121


Carefor/about

Correct:Idontcaremuchforsweets

Correct:Icareaboutheralot.

Claimto/Claimthat

Correct:Ineverclaimedtopossessremarkablesingingtalent.

Incorrect:Ineverclaimedthatpossessremarkablesingingtalent.

Correct:IneverclaimedthatIpossessedremarkabletalent.


VERBAL

Cometoadeadend

Correct:Hecametoadeadendafterresearchingtopics.

Incorrect: Hecamebyadeadendafterresearchingtopics.

Compareto/with Correct:Inevercomparedmyselftoher.



Consider(as)

Correct:Idontconsiderhimase

Incorrect:Idontconsiderhimwi

contender

Conformto

Correct:Youmustconformtothe Incorrect:Youmustconformwith


Contrastto/with

Correct:Incontrasttothepreviousrep

Incorrect:Incontrastwiththepreviousbetter.

Correct:Theredbackgroundcontrastsflowers



99/121


Creditfor/to/with

Correct:Youshouldtakecreditforwhatyoudid.

Incorrect:Youshouldtakecredittowhatyoudid.

Correct:Icreditmysuccesstomyhardwork.

Incorrect:Icreditmysuccessformyhardwork.

Correct:Heiscreditedwiththediscoveryofpenicillin.

Incorrect:Heiscreditedfor/tothediscoveryofpenicillin.


VERBAL

Debateabout

Correct:Therewasaragingdebateaboutstandards.

Incorrect:Therewasaragingdebateforstandards.

Decide on



Declared

Correct:Theteacherdeclaredall

Incorrect:Theteacherdeclareda

Defineas

Correct:Lightisdefinedasradiati

Incorrect:Lightisdefinedforradi


Delightedto

Correct:Iamdelightedtoaccept

Incorrect:Iamdelightedforacce

Different from



100/121


Distinguishbetween/from

Correct:Ihadtodistinguishbetweengoodandbad.

Incorrect:Ihadtodistinguishfromgoodandbad.

Correct:Ihadtodistinguishgoodfrombad.

Incorrect:Ihadtodistinguishgoodwithbad.

Drawaline

Correct:Wehadtodrawalinesomewhere.

Incorrect:Wehadtodrawthelinebefore.


VERBAL

Drawattentionto

Correct:Ihatetodrawattentiontothefactthatthequalityoffoodhasgonedown.

Incorrect:Ihatetodrawattentionforthefactthatthe

qualityoffoodhasgonedown.



Drawto

Correct:Hewasdrawntoherfrom

mether.

Incorrect:Hewasdrawnforherf

mether.

Easier

said

than

done Correct:Itsalwayseasiersaidtha

Incorrect:Itsalwayseasiersaidt


Electas/to

Correct:Hewaselectedtooffice.

Incorrect:Hewaselectedtoofficer.

Correct:Hewaselectedasanoffice Incorrect: He was elected as office.



101/121


Indicatethat

Correct:Studiesindicatethatstressisacommoncauseofheartattacks.

Incorrect:Studiesindicateaboutstressbeingacommoncauseofheartattacks.

Inorderto

Correct:

She

began

studying

in

order

to

get

a

good

grade

intheclass.

Incorrect:Shebeganstudyinginorderthatshegotagoodgradeintheclass.


VERBAL

Justas,so

Correct:JustasTyrawasconsideredforthescholarship,sowasMia.

Incorrect:JustasTyrawasconsideredforthescholarship,

Miaasalsoconsidered.



Left,rightandcenter

Correct:Shewasshootingemailstop

center.

Incorrect:Shewas,leftrightandcent

Knownto

Correct:Evenasastudent,Rickwask

differently.

Incorrect:Evenasastudent,Rickwas

dothingsdifferently.


Ameansto

Correct:Sheonlyvieweditasame

Incorrect:Forsomepeople,moneymeansfor/ofanend.



102/121


Morethanever

Correct:IregretnotgoingtoEurope,nowmorethanever.

Incorrect:IregretnotgoingtoEurope,nowmorethannever.

Nativeof/to

Correct:SheisanativeofVienna.

Incorrect:SheisanativetoVienna.

Correct:TheBengalTigerisnativetoIndia.

Incorrect:TheBengalTigerisnativeofIndia.


VERBAL

Prohibitfrom

Correct:Onlywhenweprohibitpeoplefrombuyingdrinksforminors,willwereducetheproblemofunderagedrinking.

Incorrect:

Only

when

we

prohibit

people

to

buy

drinks

for

minors,willwereducetheproblemofunderagedrinking.



Reluctantto

Correct:Shewasreluctanttotake

Incorrect:Shewasreluctantabouthugetask.

Requireof

Correct:Itisrequiredofallcandida

daily.

Incorrect:Itisrequiredfromallcanheredaily.


Seemto

Correct:Heseemedtobehidingsom

Incorrect:Heseemedashewashidin

pocket.



103/121


Idioms

Whichsentenceisidiomaticallycorrect?A. WillFerrell'scameoscenesaresofunnyas

anythinghe'severdone.

B. WillFerrell'scameoscenesareasfunnythat


C. WillFerrell'scameoscenesareasfunnyas


137

VERBAL

Idioms

Correctanswer:

A. WillFerrell'scameoscenesaresofunnyas


B. WillFerrell'scameoscenesareasfunnythat


138


Idioms

WhichsentenceisidiomaticallycoA. Themarkethasconfidencetha

back leveragetoincreaseprof

B. Themarkethasconfidencein

addback leveragetoincrease

C. Themarkethasconfidencein

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