bigbook quant

8/12/2019 Bigbook Quant

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Numbers:

SECTION 3Time-30 minutes

. 30 QuestionsAll numbcrs scdarcreal numbers.

FiSures: Positionof points,angJes,egioos,etc. c:rn be assumed o bc in the order sbown; and angle measurescan be assurned o bc positive,Lincs showDas straight can bc assumcd to b straiglt.Figures can be assumcd o lie in a plane unlcssotherwise ndicatcd.Figures tbat accompanyqucstions are intcnded to provide informatioa uscfut in answcring the ques-tions- Hoscver, unlessa notc atates hat a figure is drawn to scete,you should solvc thesc-problimsNOT by cstimating sizesby sight or by mcasuremcnt, but by using your lnowlcdge of matlrcmatics (seeExamplc 2 bclow).

Directions: Each of thc QuesJigns -15 consistsof two quantities, onc-in Column A aqd oo. in Column B- youare to compare hc two quantitiesand chooscA if thc quantity ia Column A is greater;B if thc quantity in Column B is greater;C if thc two quantities are equal;D if thc relationship cannot be derermined rom the information girrcn.

Note: Since here reonly our choiccs, EVER MARK (E).CommonIIl6EIiion: In a question, information conccrning onc or both of the quantities to be compa.red s centered abovethe two columns.A symbol that appears n both columnsrepresentshe samc hing in Column A as tdoes n Column B.

Column A ColumnB Samole Ans*crsExample : 2 x 6 2 + 6 ( D @ @ @ @Examples24 rcfer o A PQR"

Example2: NQ @ @ G ) ( D @(sincc equal measursscannotbe assumed,even though Plfao,dNQ appcar equal)

Example3: @ ( D @ @ @(since f is bctweenP ar'd Q)

Example4: w * z r80 @ @ ( D @ @GincePC is a straight ine)

4lGOON TO THE NEXTPAGE.

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ABcDif thequaatityn Column A isgreater;if rhequantity n Column B is greater;if the wo quantities reequal;if the relationshipannotbc dercrminedrom the nformationgiven.

ColumnB Columa A Column Bl - 3 1 - m

Column A

- 2 y + 3- - )

d : 5.$89a and @ is rhedecimalexpressionord roundcd to the nearcst houvndth.The number of dccimal 4placeswbere d and @differ

. r * 2 y > 82 x + 4 y

xn is an even nteger nd a multiple of 3.- t 8. The remainderwben nis dividedby 12

J "

2A" F4uilateral triangle PQR is formed by oiningcenters P, Q, and R of tbe circles.Each pairof circles asexactly nepoint in common.9. The perimeter oftriangle PQR The circumference fthe circlewith cenrerQ

The volume of a cylin-drical rank that hasaradiusof I meierand aheigbt of 20 meters

The volume of a cylin-dncal tank &at hasaradius of 2 mctcrs and aheightof l0 meters

Square MNPQThe perimeterofpertagoD MNOPQ

hasarca36. GO ON TO THE NEXT PAGE.30.

6,

p and g aredifferentprimnumbcrs. is the eastprimenumbergreatcrthan p, and s is thc leastprimcanmbergrater han g.r - P s - q

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ABcDif the quantity in Column A is grcatcr;if the quantity in Column B is greater;if the two quantities are equal;if the rclationship cannot be determined frsm the information givcn.

ColumnB Column Ad s + 0

Thc timerequired o)trarel * rrilesat fu-zmitesperhour

*;|'if*fi:g*r:,

Column A

Ttrc timercquired totravel d miles-at smileswr hour

AR{f is isosceles nd IRSI : *--',,r- ,The sum of the measures l2O"-of the two anglesof AR^SIthat have equal measure .

J ; \ 6 7 * g x 2 + 3

Colqmn B

O is the center of rhe circle and LAOC is ariglt angle.

Julio'ssalary Maria's new salary

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I .

12"

BDBefore Maria changed obs, her salary was24 percentqt61g hes Julio's salary. Aftcrlvlariachanged obs, her new salary was 24 pcrccnt lessthan her old salary.

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ryE$ Eacbof thcQstions 1630 has irrc uswerchoies. Forcachof thescquestions, clectbebestof theanswErlnioesgirur.

16. { r9 - l 8 - r7 - l 5 ' ) ( 20 - 19_ t8 _ 17) :.(A) - 36(B) -6(c) -4(D) I(E) 2

17" f 3x - 2 : '7,thcn 4: :(A) 3

(E) 12

Weight(pounds)

I9. Thedotson thegraphabovendicateageandy"gbt for a sample f 25studenrs.Wnit percent fthese tudents re esshan19yearsold andweighmore han I l0 pounds?(A) 36%(B) &%(c) 4%p) 48%G) s2%

20. Thegreatest umberof diagonalshatcanbe drawnfromonevertex fa regulai -sided olygons( ) 2(B) 3(c) 4(D) 5(E) 6

GO ON TO THE I.{EXTPAGE.

18.Of thcfollowingwhich scloscsto .fO f

(B) 5

( q ?(D) e

(A) 6( B ) 5 .(C) 4x(D) 3(E) 2

1 5 1 6 t 7 l 8 t 9 2 0 2 t 2 2 2 3Age years)

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Questions l-25 rcfer o thc foUowingSrephs.AVERAGEDAILY CIRCI.'I-ATIONFOR NEWSPAPERX

. 6 mE Hs mE $ o ml i r u12 zmlm1940 1950 1960 rno 1980

Year iJ

TOTAL YEARLY ADVERTISII\TGREVENUE FOR NEWSPAPERXES s o6 a oo 3 08 z o

2.

AVERAGENUMBEROF PAGESPER NEWSPAPER OR NEWSPAPERX80604020

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21. ln howmanyof theyears bownwas he averagenumberof pages ernewspapcrt lcast wiceasmuchas he averagen 1940{A) Four(B) Thrce(C) Two[D) OneG) None

22" n l95A, f theprintingcostperne*spaper as$0.05,what wouldhavebeenbe total costof print-ing the average aily circulation?(A) 532,500(B) S26.000(c) s23,500(D) 522.000(E) 52,600

23. In 1980henurnber fdollarsofadvertisingevenuewashow many imesasgreatas heaverageailycirn:lation?(A) s00(B) 200(c) r00tD) -s0{E) 20

+

Tbe percent decreasen averagedaily cirmlationfrom 1960 o 1970was approximately(A) l0%(B) 12%(q 2a%(D) 26%G) 32%Which of the following sratqnentscan bc inferredfrom the data?

I. The greatestncreasen total yearlyadvertisingrevenueoler any l&year period shownwas527millon.II. In eachofthe l0-yearperiodssho*n in whichyearly advertising evenuedecreased. veragedaily circulation also decreased.III. From 1970 o 1980heaverage umberof pagesper newspaperncreased y 10.I onlyII onlyIII only'I and IIII and iI I

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1 t

25,

(A)(B)(c)(D)(E)

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26. lf 0 < s, < l, thenwhichof thc followingcanbctruc?(A) s < -l and r > 0( B ) s < - l a n d r < - l(C) s > -l and r < -l(D) s > I and r < -l ) s > l a n d l > l

27. Onscgm.:ntWZ above,rf WY :21, XZ = 26.afr yZ istwice WX, wbatisthevalrrc f Xy?(A) 5(B) t0(c) l l(D) t6(E) It cannotbc dcterminedrom the nformationgircn.

28. To rcproducc nold photograph, photographercharges doltars o makea negative,{ aoU"r,for eac of tlre irst l0 prints,and { doiars foreachprint n excessf l0 prints. f $45 s the totalchargeo makea negativeand20prints from an oldphotograph, hat s thevalueof x ?(A) 3(B) 3.5(c) 4(D) 4.5(E)s

29.Whichof tbe ollowingsequal o j of 0.01pcrcent?(A) 0.00002s(B) 0.00025(q 0.m25(D) 0.02s(E) 0.25

" \ 1n\

30. In thc figure aborrc, achof thc four squares assides f lcngth x. If LPQR is formedby oiningthc centcrsof threcof thc squares,what is thepcrimetcrof APQR in tcrmsof x ?G) 2'O

,rf;--T- * ,2 r + JT

Ea

(B)(c)@ 1 S + 2(E) 1t + rrE

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Numbers:Figures:

Note:CommonIffiIiion:

SECTION 7Timc-30 minutes

30 QuestionsAll numbcrs used arc real numben.Position of pcints, angles, egions,etc. can bc assumed o be n tbe order shown;and angle ueasufescan be assumcd to be positiw.Lines shown as straight can be assumedo be straight.Figures can be assumed o lie in a plate unlessotherwisc ndicated.Figurcs hat accompanyquestions rE ntended o providc information useful n answering hc gues-tions. However, unlessa note states hat a figure is drawn to scale, ou should solve heseproblemsNOT by estimating sizesby sight or by measurement, ut by usingyour knowledgeof mathematics seeExample2 below).

Directions: Each of thc Questions l-15 consists f two quantities,one n Column A and one n Column B. Youire to cornpare the two qGn-iiiiEiZilEooscA if the quantity in Column A is greater;B if thc quantity in Column B is greater;C if the two quantitiesare equal;D . f tbc relationshipcannotbc determined rom the information given.

Since herearc only four choices, EVER MARK (E).In a question, information concerningone or both of the quantities o be compared s centcredabovethe two columns. A symbol that appcars n both columns representshe samc hing n Column A as tdocs n Column B.

Column A Column B SampleAnswers

Examp le : 2 x 6 2 + 6 o @ @ @ @Examples24 refer o A PPR.

Example2: PN NQ @ @ @ ( D @(sinceequalmeasures aunotbe assumed, ven bough Pl{and NQ appcarequal)

Example3: @ o @ @ @(since/{ is betwetn P and Q)

Example : l 4 r + z t80 @ @ e @ @(sincePQ is a straight ine)

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ABcD

i'k

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if the quantity n Cotrmrn A is grtater;if thcquantity n Column B is greatcr;if thc two qurntitics arc equal;if the relationshipcanaot bc detcrmined rom thc informatioa given"

ColumnAl. Tbc number f monthsin 7 years

LABC is equilateral.Line Qand line rn is parallel to side

r ) s ) 0

Column B ColumnA ,Col{mnB- , -Ttrccircuafercacc f circlc C is lga.

5. Thcdiamcterof cirdc C 9

7" Theareaofthebascof thecubct is a positive intcger..

4 t1 : j

(0.82F(0.82P (0.82)6Forall realnumbcrs a, lel a..: | - a.

((-t; ' ; ' 2'

C'OON TO TlrE NEXT PAGE"

Thenumberofdaysin 12weeks8 I9 ' 8 1l _ I' 2'l 9t

is parallel to sideA C . BC

10.60

r.tsr

3.

4.


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if tk quantity n Column A is greater;if thcquanrity n Column B is greater;if thc wo quanriticsare equal;if rhc clationship annotbc derermincdrom thc nformatioagiven.

Column A Column B ColumnA

ABcDColumn B

Team X scoredp pointsmore than ream I, andthc two teams ogetherscoreda total of l0 points.

The areasof the two shadedegionsof the circle areequai"The areaof unshaded The areaof unshadedregion .d of thecircle region I of the circle

. r * 0

13. Twice the numberofpoints team I scored

I A ( - r - l ) ( x ) ( . r + l )

The areaofThe IengthofsegmentPS

1 o - p

(x)(x{x)

APpS isa5 .The lengthofsegmen S.R

ot 2r

t ) .*y.

r . , xl r l

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Dxrecrioar: Erch of th Qrcstions1630bas ive :rrlrq^eruiccs. hr eachof tbcscqucstiongsclcct hc bcsrof thcffi&bagirrcn- t

16. fq a ccrair Sop, notcbooks hat normallyscllfor59ccaB cacbareon saleat 2 for 99cents,Howmrrh canbc sarrcdUVpurclasing l0 of thescnote-bookr at tb salcpricc?(A) $0.r5(B) 50.95 '{c) 31.10(D) il.t5 i 'G) S2.m

17. Whichof Sc following s a solutionox * x 2 : l ?(A) -l(B) 0

I(c) *L(D) i@) Nonc of the above

A

16. In tlrc figureabove, AB is e linc scgmert.Wbat ist h c v a l r r c o l ' l f zx + y

19. If thc alrage arithmcticmcan)of 5 consccutiveintcprs is 12,what s thcsurnof thc has aod grcat-cstofthc 5 intcgcrs?

r0,/.

20. What is thc pcrimcter of the rcctangh shonra above?

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(A) 24(B) 14(c) 12(D,rr( E } 1 0 .

(A) 14(B) 24(c) 28(D) 38(E) 48

(A) *(B)i(c)*co)c ) *

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Questions l-25 rcfer o thc ollowing hart.

House ofReprescntatives

PROFILEOF CONGRESSN YEAR X(total membership:535)

ScnateHousc ofRepresentatives Sctrate

Party2 9 2 , . . D e m o c r a t i c . . . . . . . . 6 21 4 3 . . . R e p u b l i c a n . . . . . . . . . 3 84 T S .. . . . T o t a l . . . . .m n

Sex4 1 8 . . . . . . M a l e17. . " . Female

Ag e27 . " . , Younges t .7 7 . . . . . O l d e s t4 8 " . .Average (arithmetic mcan)

Religion255"". .Protestant107". . Cathol ic18 . . . Jew ish .4 . " . . . . . . . M o r m o n . . . .5 1 " . . " . O t h e r

Profession2 1 5 . . . . [ - a w y e r . . . . 6 38 l . . . . . . . B u s i n e s sx e c u t i v er B a n k e r . . . . . . . 1 54 5 . . . . . . . . . E d u c a t o r . . . . . - . . . . 51 4 . . . . . F a r m e r o r R a n c h e r . . . . . 62 2 . . . . . . . C a r e e rG o v e r n m e n tf f i c i a l . . . . . . . . 024 . . Jou rnalist r Communications xecutive .. 42 . . . . . . . . . . P h y s i c i a a . . . . . , . . . . 01 . . . . . . . . V e t e r i n a r i a n . . . . . . . . . . . . . . .0 . . . . . . . . . G e o l o g i s t . . . . . . . . . 26 . . . . . . Workeror Ski l lcd radesperson. . . . . . 02 5 . . . . O t h e r . . . . . . . . . . . 3

Ethnic Groupl 7 . . . . . . B l a c k A m e r i c an .2 . . . . . . A s i a n A m e r i c a n .4 . . . . .H ispamcAmer ican

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348054

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21. In thc Scnate, f 25 malc members were rcplaced by25 fcnalc memben, tbc ratio of male membcrs tofcmslc membcrs would bc

Approximarclywhat pcrctot of thcmembers fCongress rc lawyers?(A) 63%@) s8%tct s6%(D) s2%{E' 4e%lf 5 senators re Catholic Dcrrocrats,how manyscnators reneithcrCatholicnor Dcmocratic?

24. If all lawfcrs and all wotrtelg n the Housc of Reprc-*ntatiws votc for thc passa$ of a bill, how manyBore votcs will bc ncsdcd fs a maFrity?(A)(8){c)(D)(E)

(A) 4 o I{ B ) 3 t o l(C) 3 to2{ D ) 2 t o l( E ) l t o l

4352n0It cannotbc detsmincd from tlec nformationgrcn.

Waichof thc following caobe infcrred from theinformationgirtn in thc chart?I. More than80pcrccntof themcn #b"ogrocre mcmbers f th Hoosc of Reore*ntaliras.n. Thepercentdmesrbcrs who ara-etcgizcd asfarmcn or raqchcrss grcater or,il*=Feus ofRepresentativcshanfor theSod-,m. Tbc mcdianage n thc Scnares S};.l i'

(A) I only(B) II otrty(C) III only(D) I and II(D I and III

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23.(A) ?e(B) 74(c) 69(D) 3l(E) 2l

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26.f xy* O,+

Thenumber0.01 s howmany imesasgreatas henumber0.0001)2(A) ld(B) lo{(c) 106(D) tdG) t0r0A certaincakc recipcstates hat the cakcshouldbebakd in a pan8 inchesn diameter.f Jlrleswansto use he recipeo makea cakcof thesamedepthbut'12 ncbesn diameter, ywhat actorshouldhemultiply herecipengrcdieoa?

29. lf x > 0 and .y > 0, whichof thefollowingisequivaleuto^ ) * - *

c ' i - - rG)l , - ,( D ) 1 - I' y x yF' * - | ,

(c)

)2't.

(A) r0(B) 18(c) 45(D) e0(E)roo28"

z [It/v x '(B)

Iv x6f:

I---=

(A)

JU ,

(D)+J xThe cos in dollars, of manufacturing x refrigera-tors is 9,000 * 400x. The amount receivedwhensclling these x refrigerators is 500.r dollan Whar isthe leastatrmLrerof refrigerators that must be manu-facturedand sold so that the amount received s arleastequal to the manufacturing cost?

(^)2i@) z 1(c)i(:D) l;rer j

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FOR GENERAL TEST I ONLYAnsrcr l(cy mO Fercoatager.d Eranrlrpor Arrrrcrlng EechQrcotf,onCorncdy

'Efud P+ br |he $qp oadamios rfio look the GF Gr|oral Ted in a rcsnl hr- ,ar prid

cEEcAAIBEcDDAABABoDDEBcE

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t l12t311151C77r 8l 9n212.za216

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11 A1 2 D13 c '11 B1 5 A1 6 E1 7 E1 8 D1 9 AA B21 B2 CA B21 EA D2 6 C2 7 DN EA AS E

tL)847976CTrc6SPe5012657Is75s818363g290715871473111 917

1 C2 A3 Cr t B5 A8 B7 B8 D9 A1 0 c

1 l D1 2 D1 3 C1 4 D1 5 S1 6 81 7 E1 8 B1 9 4n c21 B2 , DA D21 E6 A% Dn c2 8 8N ES D

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8a687g)717168$78m6l604Erl826355897&5le633717051il8898769583046313661 9

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SCOREOHVEBSIO}ISOR E}IERALESTOXLYAND HE ERCEIITSELOW'Rtttcn

Trtd &llffirr fr ryHtcdla * Ecdrd I *dd *Srort Lh s.ar l*r S.|t lltoil R rSaonYrrtd o .rfirtrt A'|ttllcdScdd * 3.dd ta Set8d %sceil Llor Sco.r Edsr *an Belor

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99s9999998$97s$95939?90&l87 97E68il81797671a1fit8666

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61 0600580570il550510530s20s00

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ABcDif tbe guantity in Column A b grcaterif thc quentity in Column B is grcatcr;if tle tyo quantitics are equa\il the rcletionship cannot bc dctcrmioed from the information givcn-

ColumnA ColumnB

The perimeter of square Seter oftbe rectangleabove.The length of asideof S

is equal to the perim-

0 < a < b < c

C is a circle with radius 3The ratio of thecircumfercnce of Cto tlre.diarneterof C

x * 3

Qslumn A

z - x

CohrmnB

r f ) 03 t + 4 rr + t

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12.

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*^r$"oflic QucstiousG3o has iw answtf,choioes. ord of the qr*s&"c schq3bo5g4 oftD?enss,tt cnorcc8 rtn.

B{:sbF:;:lIgbq".i.

* - s 2lo. --l- =(A) It ((B)T-(ct s(D) 8(s) 15

17- What is0.423658oun& ro rh nearesttbousandth?(A) A.42(B) 0.423{q 0.424(D) 0.42361V10.4237

It- If 3(-r * 2) = x - 4, tben x :(A) -5(B) -3(c) I{D) 3{E) 5

I i "-: : : - ' ' r, I ' : ' : , '19. If .r2+ 2rl + y2 :9, thcn (.r * .yt' :l '

(A) 3(B).r8( q ntD).36(E) 8l

I tb ratangplarcoordinate systcnabore,if x :4.8, th y :(A) 3.0(B)r.z(c) 3.4(D) 3.6(E) 3.t

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Questions l-25 refcr to thc followingSraphsNATIONAL HEALTH EXPENDITURES OR COUNTRY X, 1975.1986( I billion 1,000,000,000)

Total National Health Expenditures(in bil l ionsof dollars)Private vs. Public NationalHealthExpendinrresas a Percentof Total National HealthExpenditures

807A6050,lt)3020t 0

(in dollan) 600500400300200100

Note: Drawn to scale.

t40r30t2ai l01009080706050403020l 0


l 00

S33$$1""\"i+i{t-"iNational Health ExpenditurePerCapita

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21. For how manyof &c years hownwas hc amountof private realthexperditures t leastdoubte lresnount of public bcalthcxpenditures?(A) Nonc(B) One(C) 11ro(D) Thrce(E) Four

?2. t shich of th years rom 1975hro,oh 19g6nastk national healthexpenditure ercaiita moscn1'r-ry oqualto half thpcrcapiiaexpenditurport9E4?r975,9nt9791980yn2

.lji&'+t." :. .&.qJane as mc&4Cma asmany*Canndienr:acCanadianrdfr*b hercolhcti6,ir. hbhof rhelolowing_CANf,{OTe bcnuiber of etamgon

If -r is thenrmttr on thcnumber inebetwca5 and 15 batb nriceas ar tioil 5 as from 15.thcn "r is

(C) ll '_,'-,'; ' '(D)l?*, "' ..n,h$'lJane's olkrdodl

{r.j

Cio ON TO THE NE)ff PAGE.

(A) s?3(B) t0

, *ui" : ' j i i : i : ' i

r - ' t i t : : . i :r#*' i ,t". ;

(A) e6(B) 80(c) 72(D) 6E(E) 54

n.(A)(B)(cl(D)(E','

{A)(B)(c)(D)(E)

q&c following which s thebestapprcximationofthc perccot ncreasen tbcnationalh;aftb expcndi_ture percapira rom l98l to t9g2?35%n%frt/ot0%5%

Oftb following which sclosesto theamounl ofpublb national heatthexpenditues,n billions ofdoilars, n 1980?

25.

(A) 25(B) 30{c) 35{D) 4s(E) 70It canbc inferred from thegraphs hat in lg77 kpoprrlationof Country X, in millions,wasclosest owhichof the following?(A) 120(B) t50(c) reo(D) 240(E) 250

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29. A distillate flows into an mpty 64-gatlondrum atspout I and out of the drum at spout 8. If &erate of flow through 'l is 2 gallons pcr hour, howmany gallonsper hour must flow out at spout .8 sothat the drum is full in exactly 96 hours?

28" In the figure above, f the areaof t}le smallersquareIregion is i ttrc areaof the larger squarc region, thenthe diagoial of tbe larger square s how many incheslonger than the diagonal of the smallersquare?

(A)i(B) ;(c)?(o)1G)3' . l . t J z - t( ' ) i

52c)

FOle farmer has two rectangular ields-The larger field- has twice the lengrhand 4 rimes he *idth of thesmallerield. f tbesmallerieldhasarea K. rhentheareaofthe larger ield sgreaterhan the areaofthesmaller i.ld L&"t *jluniT(A) 2K(B) 6K(c) 7KfD) 8X(E't t2K

@[#(E' ,/2

100


32/565

FORGENERALTEST2ONIYAnswer Key end Percentqgesr of F*arnineer Answering Each QUestion Correcdy

aa-_l

F3l-gF

'Eslirnated P+ fot the group ol erarniroas who loot he GFE GeneralTes| in a rceoi ttrE+year porin

$

F'a

t:BFFIiarfIbiti

tt

ffi: " t ' t - "

lruYTICtttt{JTY \/Srtu 3 t rddIlm? lctI|' F + I| S.r l illt P +r D2 83 E. 3 C5 l C .c . . 8 :'1. *r ..J*f -' 'l'-",$ '..-'*"'Br19 :- ;o jll i*$ i'1 3 i ' E -1{ *,,;+':.15 ..,j-'.,\- _ i r l : rl e . . Dr 7 ' ' Bt 8 . " A1 9 . Cf r ' c '

21 AZ BA E2 1 l } .6 E

I

f 7 3l 6 sl s 2l 8 al 1 el s ol, &lr ttt"8t -8 r[ir[.,GaP - 6 tl"',aE.L'' si . sl : : s i' a4Atlrl58,t62A

l l B1 2 01 3 E1 4 El s oI1 6 c1 7 c1 8 Dl e El t o B1 1 1 E1 1 2 E1 1 3 II 1 4 Al r i At1 1 6 At 7 7 Ci 1 8 B1 9 En c21 C2 . 9n c2 4 E2 5 8

9079385Av,75607fTI50st5278355 l58433861rtss860684145

{trnrfm ftrgury -7Srcds| t t 3llor tlfor$.r lE t l + mlai lilsrt. P +1 82 D3 A4 D5 B6 A7 . 8a . {9 D, 1 0 A t: 'I t c12 B'13 [ } , . :1 1 B , . r1 5 C

. . . 1 6 0 - ,. . ' 7 7 D, : . 1E C1 9 52 0 021 A2 . DN B2 4 E2 5 82 6 C2 7 4n c2 s E l' 3 0 E l

l s )1 8 2I 7 8l oI E '1 7 6l nl eJ 5 01 . 5 6t . ,f . s[ . '38l.;, Oll \ E ll z 2I| 1,1797871n2&,7352&6152I4GI

r A2 C3 B4 A5 c6 B7 B -. 8 01 9 Arlo 8, ' :: 1 1 , ' C .t t 2 D1 3 A.71 D. r 5 0 .

1 6 Er 7 c1 8 A1 9 8a 821 Cz z BA D21 AE C2 6 Cz 7 EA Aa og r c

e,&)TIs79n,e6t28tv8l4'ar3E'30a.ss7l33n8lwlna5A5en35a

- r A2 03 A4 C5 E6 87 08 C9 B1 0 E

1 t D7 2 01 3 E't1 D1 5 C1 8 81 7 B1 8 E l1 9 An 82't A2 , CA B2 4 CX E2 6 ' D2 7 8z A B2 9 43 0 831 A3 e cs t A3 0 03 5 03 6 C3 7 C3 8 A

7995887556g742a2ETEEa663A3527n72785248I797347324759948t8082t o4236732627m

2 03 A4 E5 C6 E7 B8 E9 Bt o c

11 01 2 D1 3 E1 4 E1 5 A1 8 81 7 Er 8 c1 9 Dn A21 A2 , ON A2 4 E2 5 82 6 C2 A A2 9 03 0 c31 EQ . O3 0 8u 83 5 A3 6 D3 7 E3 8 A

7670577263555a8083E67C.5251*t26253{T?,153692a7959673559682a.6334g73837312726

IUI


33/565

SCOREOTIVERSTOI{SORGEI{ERAI EST OIILYTXO HE EBGE}ITSELOW'R|tScn

Y.ttrl orn't}Strt i farryticrtE hf I Sc|tdt * Ssrtd %Scrr erbr Scorc lrtor Scfi g t r &r$oitYarbrl 0mdifrirr t8rltlicalScehd .L S8|lrd % Sc.lqt 9lScon Stlsr Scoc Sdsr Scnn ialr72-767170

696E6756656il

61 l50 1

l ' ,1 5 8l s 7| - -t :l r "l s 41 5 352( t50{94E47tl64544434 14B

I

7507407307A7107ql6m57056065064063061 06005$5805705605505rt0n30(x5105004S470460458u0430

99aoaa

&7Sn099qA9796959193Qtans

9696c)o1I8EE7t(E3EI

E00800790780n07507107307'.'z9710

87e&82m7873aa6966

9999Y597Vf94929189b l

6360

504743402734

800 96

800 oo700 79 800690 n 800680 75 790570 73 7m560 71 750650 63 710E40 67 720630 65 710620 62 700600 58 590

39{1736? tv335tJ I392928m25?1232221ml o181 71 6I 41 ?t a1 11 0:o76

G5

430 34420 31410 28400 25390 23380 ?0370 18360 t5350 13350 13340 11 180330 9 170324 E 1603i0 7 44 0310 7 13 0300 5 420290 1 410260 3 q00?80 3 38027A 2 370

590 56 670 84580 53 660 81570 51 650 8B550 49 630 75550 46 520 73540 44 610 705?C 39 500 675 0 37 584 62500 34 570 594S 32 550 5330 540 50n 520 4525 510 12?1 500 3319 480 3317 179 3016 150 2614 1rt0 7311 1m 19t0 4r0 17

2ffi?s25023 0u0?002002J920020r?c02AC231

fl30?? nJ ' g3m280?40220

2 1 020c?c[2C0?00

3903S3S0310??n32t)300290280?60250240?l o? 1 020c

aI111111'II

86

31111

1 4t lI7bf,?J21'l'lI1

' P e r c e n l K ot i n t b e l o u t he s c a l e d score i s b e s e d on f h e per l o . r ance o i g -54 , 9 -o5e\ ?h i nees sho l o o k t he c e n e r a tTest belwteo Octobr 1, I 987, rod Seplember 30, I 990. This percei l beiow Inior r rai ion i used ior score reporrsdurrng the I 99 1 9? test, nt year .

r08


34/565

Numbers:

SECTION2Time-30 minutes

30 QuestionsAll numberssed rc ealnumbcrs.Position f points, ngles,egions, tc.can bc assumedo bc n thcordershown; nd anglemcasurescanbeassurnedo bc positive.Lines hown sstraight anbc ssumedo bestraight.Figures anbeassumedo tie n a prane nresstherwiscndicated.

Figurcs:

Figures hat accompany uestionsare ntended o provide information useful n answering he ques-tions. However,Jrnless note states hat a figure is drawn to scale,you should solve hcse-probtimsNoT by e^stimatingizesby sight or by measi.rrement,ut by using your knowledgeof mathernatics seeExample2 below).Directions: Eachof thc Questions -15 consistsof two quantitics,one n Column A and one in Column B. youare to comparc he two quantiticsand choosc

A if thc quantity in Column A is greatcr;B if the quantity in Column B is greatcr;C if the two quantiticsare cqual;D if the relationship ca'not bc dctcrmined from the information given.Note: Since herearc only four choices,NEVER MARI( (E).CommonG6Jiillfon: In a question' nformation conccrningone or both of the guantities o be compared s centeredabovetbe two columns.A symbol that appeirs in both columns eprcscnts he same tring in Column A as tdoes n ColumnB.


i. _

KE;

;'.,tt

Example : 2 x 6 2 + 6 o @ @ @ @Exampfes 4 refer o A ppR.

Examplc 2: NQ @ @ @ ( D @(sinceequal measures annotbc assumed,cven though Py'Vand NQ appcsr equal)

Examplc3: @ { D @ @ @(sincc { is betweenP andQ)

Examplc4: w * z It0 @ @ ( D @ @(sincePQ isa straight ine)


l 1 5


35/565

ABcDif tbe quantity in Cotumn A is greater;if the quantity in Column B is reater;if the two quantitiesare equal;if therclarionship annotbedetermined

Column A

+ 0.9

r *t

Figure INote: Drawn

5. The area oftheshadedregion shownin Hgure I

Column B

9(r.0+ 0.09)

Figure2to scale.

Thc area of theshaded egion shownin Figure 2

(i e Uonu, f$450plusv a9 percentncrease

from the information given

Column A

rn annualsalary

sP, Q , R , S . T, andcircle as shown.

The length of arc peR

The total number oflitersof water in xtanks,eachcontaining20 liters of water.and 2r tanks, eachcontaining35 liters ofwater

ColurnnB

A bonus t$500plusan 8.5percentncreasein annual alan'

U are pointson the

The lengthof arc S?"L/0The total nurnberofliters of'water in xtanks,eachcontaining25 iten of water.and 2x tanks, eachcontaining30 itersofwater

r : 3 0R : 5 9

_ 7 x 49 N x 9

Let_the drop" ofa squarebe definedas thepenmeterof the squareminus the engthof oneslce.The drop of a squarewith area25 20

.ry.

R 22

)2 i . i * l

8 .

9 .

C'OON TO THE NEXT PAGE.

l r 6


36/565

if the quantity in Cotumn A is greater;if the quantity in Columri B is grearcr;if the two quantitiesare equal;if the relationshipcannotbc determined rom the information given"

ColumnB ColumnAolumnA

r c * x : 9 0y * z : 9 010. Theperimerer f R.SIU l0l l . ( r - 2 F (x + 2)2

(8X16X32X64)2x*v12. The avemge arithmetic 9mean)of x and y

ABCD

ColumnB( a + b f = 4 9a b 1 2

x : l - yx 2 + z x y + y z x + y

CO ON TO THE NEXT PAGE.

R I U (6x + 4)'

lr7


37/565

Dnctio:s:. Each of theQucstions1630 has ivt answer hoices. orcachof thescqucstions,sclect he bestof tbe:rnsscrcDorceslven.16. In a ertain class,f tbcreare 35menand 63womenthcn hc ratio of mento women s

IL - - - - - L -19.Thc figurcaboves a rectangular olidwithAB : 10,8C : 10, aad CD : 3. What s thetotal surfaceareaof tbe figure?

n . 6 x 2 - l S x - 2 1(A) 3(2r + 7)(x - t)(B) 3(2x - 7)(x + l)(C) 3(2r - l)(x + 7)@) -9x2 - 2l@) -9x - 2t


D

C) *{B)( q ;i") ;@ ) l (A) 320(B) 300(g 2n(D) 160

{E) 2317. StretsL, M, and nf are straight and leve andthcy intersect to-forrn.a triangle. If streets L andiU intcrscct at a 40oangle and if street ,l/ is perpen-dicular to strcet M, at q-hat acurc angle do streetst and nf intersec0{A) 30"{B) 35'{c) 40'{D} 45'(E) 50:,

,8 ('- i)1' *)'{A}p ) i{ q i{")c ) *

t i 8


38/565

Questions 2 -25 refer ro the following gfaphs.

t940r950r9601970I|98 5r986

II 950| 9601970t980l 9851986

FARMING IN COUNTRy X: 1940TO t986FarmPopularim in millions)

1 2 3 4Average armSize in acres)

Note:All graphsdraw-no scale.21. Country X's farm population n t9g6wasaDDroxi-mately how many million? To. he.nearest0 percent, hedccfinen farn popu-lation n Country ,y betwcen 950 nd t960 corc-rnted whatperccnr f tbc t950 arm poputation?2 .55.57.59. 0r0.022. Tlaedecrease,n millions, n thenumberof farmsfrom 1950o 1970wasapproximalely

(A) t.6{B) 2,0{c) 2. 6(D) 3.0{E) 3. 6

(A)(B)(c)(D)(E)

(A) t0%(B) 30%(c) fi%(D) 6%(E) t50%

t5 20Numberof Farms(in millions)

"*tE&:FFIfL7-*nBF:It::iict lat.-tI&,tlt

l l 9 C'OON TO THE NEXT PACE"


39/565

24" In Country X, the average and sizc a 1940 wasapproximately what fraction of thc average arm sizein 1986?25. In -1986, o*ql X hadapproximarelyowmanymillionacres f farmland?

(A) I,100(B) 400(C) l,t0tD) l l(E) 3


(A)i( " )3( q ;t " )3(E)i

r20


40/565

?E.*,:ra'l

a26. lf n. s theaveragearithmeticmean) f the hreenumbers,9, and ft, what s thcvaiuc f & intermsof n ?(A) 3n - 15( B ) n - 5( O n - 1 5(o)t+,o., n * 15\- , 3

27" Whichof the ollowingCANNOT becxpressedsthesumof tbesquares f rwo ntegers?(A) t3(B) l7(c) 2l{D) 2e(E) 34

28. lf AB : .B.Yand XC = CD in thc figurc above,what is s in terms of p and r ?(A) 180 2(p + r)(B) p + r -X)(C) 2(p + r)( D ) p + r(E)ry2

29. Mary has3 dollan morc thanBi[ has,btrt Sdollanlcss haa Jaachas. f Mary has x dotiars,bow---manydollan do Janeand Bill hareattogithrf

30. If. f -isan ntegerdivisiblcby 6 but norby 4, thnwhitihof th following CA}{I{OT be al iitcgcfl

( A ) 2 x - 8( B ) 2 x - s(C)2x -2(D) 2.r + 2(E) 2r-+ e

, , ' r i(B)3( e t( D ) *@ #

t2r


41/565

Numbers:FiEures:

SECTION 6, Trrne-30 minutes, 30 Questions

All numberi used are reat numbers.Position of points, angles, regions, etc. can bc assumed o bc in thc order shown; and angle measurcscan bc assumed o bt positive.Lines shown as sraight can be assumcd o bc straig}t.Figures can bc assurned o lie in a plane unlcssotherwisc ndicated.Figurcs hat accompanyquestionsare ntcnded o provide nforr4ationuscful n answering he ques-tions. However, unlessa note states hat a figure s drawn to scale, ou should solve heseproblemsNOT by estimatingsizesby sight or by measurement, ut by usingyour knowledge of rnathematics sccExarnple2 bclow).

Sincc hercareonly four cho ices,NEVER MARK (E )

D i rec t ions : acho f theQues t ions t - l 5cons is t so f twoquan t i t i es ,one inCo lumnAandone inCo lumnB.Youare to compare the two qiEiffiii'iEThooseA if the quantity in Column A is grcatcr;B if the quantity in Column B is greater;C if the two quantitiesare equal;D if the relationshipcannot be determined rom the nformation givcn.

Note:CommoaInformation: In a qucstion, nformation concerningone or both of the quantities o bc compared s centered bovcthe two columns. A symbol that appears n both columns represcnts he same thing in C-olumnA as itdoes n Column B.

Column A ColumnB Sample AnswcnExample l in$ 2 x 6 2 + 6 ( D @ @ @ @Examples?4 rcfer to A PQR.

Example_ :

. ' ' \\"

NQ @ @ o j " o 6 . |jF(sinceequal measuFesaanot "rbe assumcd,even though PIttand ffQappcar equal)

Example 3: @ ( t @ @ ( D(sincc lf is bctwecn P and Q)

Example 4: w * z tE0 @ @ o @ @(sinccPp isa straigbtinc)

140GO ON TO THENEXTPACE


42/565

ABCD

if the quantiry n Column A is greater;if the quanrity n Column B is lrcater;if the two quantiticsare equal;if the relationshipcannot be determincd rom the informationgivcn.ColumnA ColumnB

2 x + 3 y : 3 x * 2 y

The circle with centei .6 has radius r.E D : +

a

The areaof AEBD The area of the shadedrcgonx y * 0

x : lx

ColumnA

Ttrcareaof a circulatregionwith circum-ferencc6d

Thc original scllingpriceol the ltemL- .tlf=Vz :)

ColumnB> y > 0

0Thc circumfercm ofa circular regionwitharea16r

( x ( 4y : 5

$120x --$ lg


x4931

0.7vA.discount of z()percentof the original se[ing priceot an rtemreduces he pri to $72.

x - yvJ2l +Jts

r4l


43/565

ABcDif tbe quantiry in Column A'is greater;if the quantiry in Column B is greater;if the two quantitiesare equaif the relationshipcannot be determinedfrom the information given.

Column B Column Aolumn A

X : ZRT

Im ,X costs fwioe as much as item Z. and itemmsts $3 more tban balf dtecost of itsn Z.l l. The cost of itcm X The cost of itsm Y

For all integers x and y, lct x * y be defined asfollows"x * y = - l r + y i

3* ( * 4 ) 3 - 4

Column B

1 7 x l l x 4 8

p 2 + m 2


A rectangular textbook pagemeasuresE] inchesbyLI I inches.The page s partitioned into reciangularspaces"h + inctr yI in"n.

14. The number of suchspaceson the textbook page

R.S

n 2

12.

t42


44/565

'i

r-&Dircctions: Eachof theQucstions1630 has iveanswer hoices.For eachof theseqrstions, sclcct be bestof ttrcansweich-oicesven.16. If 2Jr * y :8 and 3x : 6, then y : It. Mario boughtcqualnumbcrs f 2-centard 3-ccatstamp6.f the totalcostof thesr2mpswas$ .00,

whatwas he totatnumbcrof stamps ought?A) 2(B) 4(c) 6(D) 8(E) r2(A) 25(B) 34(c) 40(D) 46(E) s0

NumberofI-awnMowersMonday 752TLesdayWednesday / ) fThursday 7yFriday

17. Thc table above showsthe number of lawn mowersproduccdby Company l, each workday last weekexcept Friday. If Company Z produced an average(arithmctic mean) of 750 lawn mowers per day foithe workweek, how many lawn mowersdid itproducc on Fridaf(A) 736(B) 73e(c) 742(D) 750(E) 758

300,c a 6

19. In squarePQR.Sabove,"ApfS basapcrimcar 'of 30.What s the areaof quare peRS?

lf r > 0, rhen ,/U2Srt :(A) 0.0513(B) 0.0514(C) 0.05rj(D) 0.512(E) 0.511


-s

(A) 30(B) 50(c) 60(D) 7s(E) r00m.a

143


45/565

Qstions 2l-25 rcfer o.tb folh'siegdata.PRODUCTIONOF PHOTOGRAPHIC EQUIPMENT AND SUPPLIES

World Production9tttl96g(valuc n rnillisnsof dollars)

C-ountry1965

koentVahr ofTotalt966

FercentValrc ofTotal1967

PcrentValue of Total1968

ftrccntVaftc ofTotal1969

FercentVahp of TotalUnited Stat6 -- 2,2963503v)24796

957650

9.59.89.87.02.12.72.1t.4

2,t31 67.5371 8.9363 E. 72?4 6.595 2. 3104 2. 580 t.972 1.7

3,1 94 l t3702831061078976

6E.49.08 . 16.22.32.32.0t .7

3,5S54fi439299120l l 5r0582

68.48.88.65.82. 42. 32 . 1r . 6

3,770 67.A550 9.85r0 9 . r3t0 5.5t40 2.5130 2.3I r 5 2 . 195 t.7

'4YgWestGermany--Unitcd KingdomFrancc- - - - - - - - -Bclgiumr s , - - - - - - - - 'Othercountrics

Total -- 3,560 100.0 4,190 100.0 4,5t0 t00.0 r00.0,15 5,6m tm.o

r9('5Total: 2"296 illto{t

UNTTEDTATES RODUCTIONr97l

Total: $3,980Miltion

Ivbtim-PL"nrrEEa$pnentStiII-PiculeEquipcrcrx

MctirJo-Pbfx?EqoiFentSriu-PicarcEquiprui

Pr4arcd Pho*ocbmizlsMicrofilrnftuip'r*r

Pboodpmicels

ScrsitizedCoods53% SensitizedGoods4? %

OffiCopien

25 %

t4 GO ON TO THE NEXT PAGE.


46/565

6*

2 t . In 1969bevalucof photographic quipment ndluppl*s produced utside he UnitcdStateswashowmanymilliondollan?5501,950

5,6207,470ll,2&22. Wbat wasLhevahr, in miilions of dollars,of thcmotion-picrurecquipmcntprodrcd inrlrc UnitcaStatcsn l97l "l

23. In llXS whict country,s otal.production f photo.gaphic equipment"1-o ,rpptiis *" oorJt in valtreto rhccombincdproductidi of *oti-on_piiur" *omicrofilrncquipmentn tle Unitci St,I i" ,usame ear?(A) Iraty(B) France(C) UnitedKincdom@) WestGcrminv(E) Japan

l.n tl65 tlrcvalucof scnsitizcd oodsproducodnthUnitd tatcs as"pry:*frltAi 1r,", L,ll*3f ofphotogr;pnrcqupmcntnd rpprics(A)(B)tci(D)(E)

(A) tE4(B) t88(g le3(D) tee(E) 203

producedn thevorld?

25.From )68o 1969,hevalue fphotocraohic:quiprnT andsupplicsrodrnj by i;;Inqrascd by ap,prorimatcly wbat peroenit6) n%(B) t8%(C) l|c/o@) 120/u(E) l0%


(A) @%(B) 50%(c) 4s%(D) 40'/o(E) 35%

i;t-rFi-

2, Lg i5 / 357"

I45


47/565

,a\'- 1 o

The figure aborrc is formed by two owrtapgingsquancq each having sidesof 6 centimetsrs in leng6.If P and Q are the midpoiots of the intcrsecringsideg what is tbe ars" in square centimctcrq of thshaded region?

For which of the following scts of numbrs is tb.prodwt of the three numbers less than'each mrberof thc set?/ i , ? , iF. - ; , - t , 1'/u, -). , ,

I onlyII onlyIII onlyI andIIIII and tII

If x is au odd negative integer and y is an evenpositive intcgr, then ry must bc which of thefollowing?(A) Odd and positivc(B) Odd and negative(C) Even and positive(D) Even and negative(E) It cautot be determined rom the informationgven.

Which of the following expresseshe areaof theshaded region in the figure above?) 1(A) l:;r-

- 2 - r - , , 2(B ) .+, 2 _ y 'x 2 + x y

A

x 2 - x y4

29.

(A)(B)(c)(D)(E)

30.

(c)(D)(E)

n.

(A) T2(B) 63(c) 60(D) 54(E) 4s

28. If x aad y arc numbers oa tb number linc abovc,which of the following statcurcsrtsmust be true?

I oatyItr onlyI aad r onlyI ard Itr onlyI, II, and II

x y < 0x * y < 0x - y < 0I .II .IT.

(A)(B)(c)(D)(E)

t46


48/565

ATAITNCATBILITYVSecfon 1 Sactionlhlar A.5nt P f&r$ar Anrrrr I P+f r s1 2 c1 3 81 4 El s E1 6 E| ' 7 01 8 cl e oI r 0 AI1 1 1 CI t 2 Bl r 3 sl 1 4 El t s BI r s E1 1 7 Al r E El r e E ll 2 o D I1 2 1 S Iz E l? 3 o l2 1 B l2 5 A l

7683693234< t955272605f5.137386654a215 l604ti35626r1 9

1 0 1 9 02 A I A S3 o l s s1 e 1 5 65 A l s s6 C 1 6 37 . C l e r8 I l z s9 C l t sr 0 o l 8 tl t c 1 8 31 2 E 1 4 1t 3 D l s 31 4 O l z 4l s E l r a1 6 D l m1 7 e l 1 l1 8 D l 5 2 ll e c l 7 3 l2 0 A 1 6 8 l2 t B l s s l2 2 C l s o l2 3 A l 7 2 l2 4 A l 6 4 l2 5 E t 3 8 l

FORGENERALTEST3 ONLYAnswer Key and Percentoges* of ExamineesAnswering Each euestion Correctlv

'Esttrnated P+ for t'.'egroupot erarnineswho rook r'e GR Genrar e=l in a ,eced thre-y"a *n*.

r A2 A3 84 Aq ^6 87 on n9 A1 0 I' n o

1 2 CJ ? t1 5 A1 6 Ct t E1 8 D1 9 A2 0 3n cn s2 4 8? 5 A2 6 A28 .ln l3 0 =

90908080&566152595.41IE38?,83g)6250667990767145494715.l:'z.

2 C3 B4 D5 A6 87 A8 09 C'r0 0

l l 0 '1 2 C'r3 I'ra C1 5 A1 6 B1 7 Cl E C1 0 EM E2 r Bzr. oz j C21 A2 5 A6 02 7 8n oA D3 0 A

748071776665575t474 lma908?na62c)857557tllt46645462?l

maz5645424986917552444332?8n82o t546889617047s5fon818r

37271 8

1 A

< nA N7 AQ N9 Er v t r

l l B1 ? E1 ? a

1 5 D1 6 St l 61 t il q a2 0 02 2 8n c21 C2 3 A2 6 A2 7 82 8 C2 9 C3 0 A31 CJ Z b? ? n3 4 C? ( c3 6 A3 7 A3 8 8

915545E9070491{t331n315367650F587nu66408587797854JZ1a2422

DEInAoEn

IoABE5AUAEoADtrBAtr

1345b7I

1 01 11 21 3, t rr 61 7l 81 920?' ,< J24l )?6272829303 1JZsua l

+ 5)(2x + 3)

I At {;xl 4

{ . t + 3 ) ( 2 r + 5 )x > 0

GOONTOTHENEXTPAGE

202.


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ABcDif the quantity in Column A is greater;if the quantity in Column B is greater;if the two quantitiesare equal;if the relationship cannot bc determined from the information cir/en.

Column B ColurnnAThc largestcircular tabletop that can tJgcut from accrtain squarepieccof wood has a circumference ofl05z irches.The lengthof a sideof thc piccc of woodbeforc tbc tabletop iscut from it

Column A

The numbcr of differ-ent positivedivisorsof 12

3x2- 3y2x - yx - 1 ' * 0

Column B

3(x - y)9.

1 6 n : l o r ll0t

Maria's wceklynet salaryof $i85 is 65 percentof herwekly grosssalary.Maria's weeklygrosssalary

: / x l x p* a

S . i a * i a n C c , f : ii e t t r m i n e dGOONTO THE NEXTPAGE.

l05a

The number of differ-ent positive divisorsof 50

3 x 3 x nnp\p

. s Tw\"\_-- \\ \SR URSTU is a parallelogram.x y*rf

I .

12.

I

r.t:t:

243


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Directions: Eacb of thc Questions1630 has five answer choices.For eachof thesequestions.select he best of theansweritoiccs given.

16" If 8x - 3y = 24 and -y : 0, tbstr(A) 3 (B) 4 (C) s (D) 6

I 7. If the sum of 3, 7 and x is I 8, then the average(arithmeticmean)of 3, 7, and r is(A) 6 (B) 7 (C) 8 (D) e (E) l0

18" f n : 3, what s the value f 2n + l?(A) e (B) 13 (C) l7 (D) 33 (E) 65

20. Three ln6iyi{rrals contributed $800each oward thepurchase f a computer. If theybought he com-puter on sale or S1,950plus l0 percent ales ax,how much mone:)'should be refunded o each ndi-vidual?(A) $6 5(B) $8 5(c) $r50(D) $l9s(E) $255


r :tE) 8

l 9 In thefigureabove.x =(A) 30 (B) 35 (C) 60 (D) 75 (E) r50

2U


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Questions l-25 refer o the ollo*ing graphs.

2A008060

IIIII

{ i ty EE T F

NATIONAL HEALTH EXPENDITURES: 960TO 1978l t t t t t i l t t l- TotalHeairhExpenditures--- PrivateHealrhExpenditures"'; PublicHealth Expenditures

Note: Drawn to sale.

TOTAL NATIONAL HEALTH E.XPENDITURESAS A PERCENTOF GROSSNATIONAL PRODUCT

Note: Drawn to scale.

1)I

sss"\8ge69"o96se$"$-$SI$$S."S

CO ON TO THE NEXT PACE.

S.*"sTfs"ds"$s*

205


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21. In llX9 approximately what was the amount of pri- 24. For the year in which public health expendituresvate health expe.nditures? were closest o $40 billioru total health expenditureswere approximately what percentof tbc gross(A) $25billion (B) $30 billion (O $45billion national product?6r>) $50biltion (E) $70 billion (A) l0%(B) e%22. For rhe yearsshown, what was the first year in " (C) EYowhich the amouot of public health expenditures (D) 7%was at leastS3O illion? (E) 6o/o(A) 1960 25. Approximatetywhat was he amount of the gross(B) 1962 national product in l96E?(c) r964(D) 1968(E) 1970 (A) Sfin biil'ion(B) $750 illion(O S800 illion23. ln 1976 pproximatelywhatwas he ratio of the (D) $950billionamountof privatehealthexpenditurcso the (E) h cannotbe dcterminedrom the nformationamountof publichealthexpenditures? given.( A ) 3 ; l( B ) 2 : l( C ) 3 : 2( D ) 2 : 3( E ) : 3

GOONTO THE NEXTPACE.

zffi


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26. lf x and y arc ntcgersand x > y > 0, howmany integersare there between,but not includ-ing, x and y?

27. For which of thc following expressionswould thcvalue be lcss f 350 were replaced by A7 ?r. 2.500 350III" ^;JX ,

Iil "l + t' 350

(A) None (B) II only (O III only(D) I and III (E) II and IiI

28. If the circumference f circle P is 15.714and thecircumference f circle Q is 6.28. then the diametcrofcircle P minus the diamcter ofcircle e isapproximalelyequal to(A) r.5(B) 3.0(c) 5.5(D) e.0tE) e.4

29. According to the numbcr linc aborrc, which of thefollowing points has a coordinate most ncarly cqualt o P x v 2( A ) l ( B ) 8 ( g c ( D ) D ( E ) E

30. A rctangular rug covcrs half of q rectangular floorthat is 9 fect widc ad 12 fcct long. If tbc dimcnsionsof thc rug are in thc samc ratb as tbosc of the floor,how maay fect long is tbe rug?

Figurcdrawnto scalc.

a - b = ? Y \ 7

( A ) x - r( B ) , r+ y( C ) x - r -( D ) x + y -{ E ) x - r +

Note:

G ) ?(q 2.,n(A) 6

tD 6.,n{o 4,fr

^ q/i - , " ,l f l LII

/ 1' -n 9 lr ' --: _ F,r t' Lc ' tl a i ^ _ _-1-

I

' l . \ l ' )C = - v , 1 -

tEEi:

zVI


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Numben:

/SECTION 6 VTime-30 minutes

30 QuestionsAll numbers uscd are real numbers.Positionof points,angles, egions, tc.can bc assumed o be n the order shown;and anglemeasurescan be assumd to be positive.Lines shownas straightcan bc assumed o bc straight.Figurescan bc assumedo [e in a planeunlessotherwisc ndicated.Figures hat accompany uestions re ntended o provide information useful n ans*ering the ques-tions. However, nless note states hat a figure is drawn to scale,you should solve hescproblemsNOT by estimating izes y sight or by measurement, ut by usingyour knowledgeof mathematics seeExample2 bclow).

Figures:

Directions: Eachof the Questions-15 consists f two quantities, ne n Column A and one n ColumnB. Yo uare o compare he two quantit iesnd chooscA if the quantity n Column A is greater;B if thc qu8Dtity n Column B is greater;C if the two quantities re equal;D if the relationship annot be determined rom the information given.

Since hercareonlv four choices, EVER MARK (E).In a question,nformationconcerningone or both of the quantities o be compared s centercdabovethe two columns.A symbol hat appears n both columnsreprescntshe same hing in Column A as tdoes n ColumnB.

Colurnn A Column B SampleAnswers

Note:CommonGi6iffiiion:

Example . 2 x 6 2 + 6 ( D @ @ @ ( DExamples 4 reter o A PpR.

Frample 2: NQ @ @ @ ( D @(sinceequalnrasures cannotbe assumed, ven hough Pdand /VQ apparequal)

Example3: @ O @ @ @(since [ is betweenP and Q)

Examplc4: w + z r80 @ G ) ( D @ @(since p isa straightine)

220GOONTOTHENEXTPACE.


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ABcDif the quantity in Column A is greater;if the quantity in Column B is greater;if the two quantities are equal;if the relationship cannot be determined from the information given.

Column B Column AolumnA(3)'2" The heightof rhe higherboard minus the heightof the lowerboard

y - x

P4. The perimeterofsquare PORS

5. A number between5 and l0

There are wo diving boards at a certain pool. Thcheight of the lower board is 3 meters. The height ofthe higherboard is I meter greater than twice theheight of the lower board.

ColumnB3 l4 - j

y < z < xy < w

x : 3y : - |

4.5 meters

sThe perimeter of theshaded rectangularregionA number between8 and 14

9. The number of min-utes n 3.15hours

x + y

The numberof min-utes n 3 hours l5minutes

J , xy2

t l: , y : 5 ,z : 3 0

30

GOON TO THENEXTPAGE

221


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ColumnA Column B

Fields X and Y are to be enclosedwith fencins

t

given.ColumnA ColumnB

_r'.and : arepositive ntegers,and z > x > 7'

ABCDif the quantity in Column A is greater;if the guantity in Column B is greater;if tbe two quantitiesare equal;if the relationship cannot be determined rom the informalion

l ' ' lL Il--+rom--l-T-II470mII

and Rf : 5.l0,r

l ,I t .

that costs$24per meterI L The costof th efencingneededto enclose '

The cost of thefencing neededto enclose )'

The remainderwhenz is dividedby .r The remainderwhenz is divided bv y

GO ON TO THE NEXT PAGE

n > 0dl--L-lll--n l--l-k " t)t

The crrclehascenter OThecircumference fthe circle

90t 2

t l

Fa70 m---1

222


76/565

c :L9l:Et

Directions: Eachof the Questions1630 has five answerchoices.For cachof thescquestions, clect he bcstof thcansweiifioices givcn.16. A certain machincfills a bag with 7 ouncesofpotato chips n 3.5seconds. t this ratehow manyseconds dl it takc the macbine o fill a bag withl5 ouncesofpotato chips?

(A) 6.5 (B) 7.0 (q 7.5(D) 8.0 (E) l l .5

17. On a number linc, the disunce bctwcn hc nropoints with coordinates - 5 and I is how much lessthan the distancebetwecn he two points with coor-dinates2znLd14'(A) 6 (B) E (C) t0 (D) t2 (E) 16

In the figure abovs, f x = 4y, then y :(A) 30 (B) 16 (g 37.5 (D) 40 (E) 50

19. f45 perccnt f z is 405,what s 35pcrcent f n ?(Ai 6l(B) &(9 ta(D) 250(E) 315

In tlrc trianglc abovg r =(A) 65 (B) 40 (C) 35 {D) 25 (E) l0

GO ON TO THE NEXT PAGE.tE.

(r + l0)' 2r '

223


77/565

Questions2l-25 refcr to the following graph.

FAMILY T'S EXPENDITURES S A PERCENTOFITS GROSSANNUAL INCOME'J J

3027242 l

; t 8d 1 5

t /

96J

0-o*j*o':l::w t"s*"1r""'

* In 1981. 00%In 1984. 00%= 550.000= M5.000

Note:Drawn o scale

GOON TO THE NEXT PAGE

.*"'".tsx;::.-.::""""*

4 1 ,LL A


78/565

l t.iIBEFa:a'

2l. In 1984or how manyof theseven ategoriesistedwereerpendituresgreatcr han 9 perceniof Fam_ily X's grossannual ncorne?(A) T*'o (B) Three {C) Four(D) Five (E) Six

22. In 1983Family X useda rotal of 49 prcntof itsgrossannual ncome for fwo of the categories isted.What was he total amountof Family i's incomeused or thosesamecategoriesn tggi ?(A) St6.200(B) S 7. i50(C) Sl9.r00(D) S2t.0s0(E) 521..t00

23. From i9t_t o 1984he ncreasen Family ,y-smiscellaneousxpenses asmost nearly which ofthe ollor^np ?{A) 53.0t10(B) S3._


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26. Of thc following, which is greatest?

(D)# G)ffiIf x, 1', and z are consecutive ositive ntegers,with x < y


80/565

EEftFOR GENERAL TF,ST5 ONLY

Ansrser 'nl P"tt$g:1otjt"-in"." A*ing Eacheuee$,onorrectty

GFIEGeneral Test in a rrcent Freeyea, Oraod.

F

i

:

1

o7I

t 0

EbAAADA

BDAEDB

EB

B

,l34)o78910

12t a

AbBA

A

B

o

9187788488. 777964

1651 6 3I 57452a878085&|qa&


81/565

SCORECON\TERSIONS OR GENERALTF,ST ONLYAND TEE PERCENTSBELOW'

.pcrcdt sing bctow thc $etd sr6 bsrd d th" prrtqBsrca of thr 84,a,96O enminos [|lo t6k tho Gncral T6t berteen october'l' i984'

rnd Sspt$5d 30, 1987

trr SaoraScalcalSco?.t aod Pcrcgntr Ecloi'f r I f f f i i f r . t t J t

ta'r .5r t ar .lr tctr .If lfl sro.rScalsd Scorca and Parcaotr 8'low'y.rtd A bsEdvr t AtdYred I

S.rt lalgr Sott lrhr Scott l.br7976

72T170@686f66658463626l60558555554Ns?< t5044E:.a17

ir. 45a54431241

m?907t0n07607507307n7107m05?0e60650.6.0Eto6e06t 0mg,5mg056055054053052051 05m(t{0474160

99s9999999897s96G94929189EE8685&i

s8@800790760

Is9897$

8280t a7513

/ w7507307m

s9168uv

716E656360

6A0 18660 71650 12630 67620 65610 62580 5E580 55570 s3560 51

800&msu

ss9999

555249.5

800790760710

9S$97o795

&3$37s3432313029a27625?1z32.21a191E1 71614't 312l l'1087

G5

4{n45014430444104104S3903EO374fl360g340340330w3103fl

1543403734

540530s20( 1 n5004904804045044

{6434138s31a t

2573?1191 71 6141 11 067

5

110

73C 94710 92690 E9680 88660 &4| u i l630 7E6 1 0 7 4600 71580 66

31312A6212181 E1 61411121097

4304&410400390370360.s3.{0.g

ru5505305205004in4704g440120400390.fl340

w5848

3734alv

mN270260zfi?4mm2102t0

12

31 0300INm24m210m200mN200200

1 81 61 :

I65

2

,I0000

1'I0n

320

270260

m210m?00

200Nffi2@200 0

d

unn

228


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Numbcrs:

5rL i lu} JT-rme-30 mrnutes

30 QuestionsAll numbersused re realnumbers.Positionof points,angles, egions. tc.can bc assumedo be n the ordershown;and anglemeasurescan be assumedo be posit ive.Linesshownas straight an be assumedo be straight.Figurescan bc assumedo lie in a planeunlessothcrwisendicated.Figure-s-thatccompanv uestions re ntended o prorrdc nformationuscful n answcring he qucs-tions. Howcver.unless note_slateshat a figure s drarrn o scale, ou should solve hese-problemsNOT by estimating izes 1'sightor bv rneasurcment,ut by'using our knowledge f matirematicsse eExample2 below).

FiSures:

Dircctions, Eachof the Questions-15 consists f trro quanriries"nc n ColumnA and one n Column B. youare to compare hc two quantities nd chooseA i f theauanl i t n ColumnA is greater ;B i f t hequa i : r i i 1n Co lumnB rss :e le r :C i f the woquant i t ies reequal;D if the relarionship annorbe der:rrnjnedrom rhc nformationgiven.

Notc: Since here reonly our choices,iEVER M..1,RKE).Commoniii6friiion, h a question, nformationconcerningone or boih of thc quantities o bc compared s ccnteredebovethe two columns.A symbol hat appean n born columns epresentshe sime ling in ColumnA as tdocs n ColumnB.

CoiumnA ColumnB SampleAns*tn

i.,l :'8,.

t] '+: iIa-

r:TitiF.aiiz:*$F'7t .tig'

Example : 2 x 6 2 + 6 r D @ @ @ @Exarnples4 refero L peR.

Examole : N8 @ @ @ ( D @(sincecqual measures annotbc assumed, ven bough Plfand NQ appearequal)

Example : @ ( D @ @ @(since { is between andQ)

Example : * - * z rt0 @ @ ( D @ @(sinccPQ isa straightinc)

GO ON TO THE NEXTPAGE.

1 4 1


83/565

ABcDColumn A1.76 100

ColumnB0.176 r0

2. x + y

22

y + zOne bacterial cell of a cerrain type is placed nt petri dish. Cclls of this type divide onceeveryday.

| 3. The total numbcr ofbacterial cells in thcdish at the end of4 days f no cellsdie

s + f = : + ft3.

3 , 4a - 3. 3{51 4(4)4{5)- 2 1 r 1 2- l ( y ( I

6.

242

if tbe guantity in Column A is greater;if thc quantity in Column B is greater;if the two quantitiesare equal;if thc rclationshipcannot be detcrmined rom the information given.

ColumnA

The engthof RI

Column B

Twice the lengthof R.S

S I

^v l,RSTV is a square.

r = 2s =( r - 3 5 ) r ( r 3s )5

An aviator in Mexico flev 300kilometersin a straight ine due easr rom point P topoint Q and then 400 kilometers n a straightline due north ro point R.9. The shortest istancefrom point P to

point R550 kilometcrs

I0. The numberof pr i rnenumbersbetween 0and 20The numberof primenumbersbctween30and 40



84/565

AsCDColumn A Column B

x ) o (I L Thc numberof The numbcr of sccondsminutes n x * 100 in 6O(x + l0O) minuterhoun

+.,62.

t 3 . (R,5)2 1542 (RT)2

,13

if the quantity in Column A is grcatcr;if the quantity in Column B is grcatcr;if tbe two quantitiesare equal;if the relationship cannot bc dcrcrmincd rom thc information given.

ColumnA ColumnBt/ f r=4 and y2=6

t4.15. Thc length of thediagonel of a squarewith cach side oflcngth 2

Thc hcigbt of atrianglc with cachside of lengtb 3

CO ON TO THE NEXTPAGE"

ib:Ft1L

liE

i

a

t.a*It-


85/565

Directio{rs:.Eachof thc Qucstions 6-30 has ive anssfcrchoiccs.For eachof thcsequestions,sclect he bcstof thcanswerchorces lven.

r c . x | =(A) * (B) I

17. l f k = 15, hen(A ) 156(B) 23(c) -23(D) -204(E) -360

t 9 . If x equals25 percentof a number, thrn125pcrcentof the number s(A)# (B)f (c) r.25x(D) ax (E) 5xlf the cost of a long{istance phone call sc cents or the fint minuteana t, cenrsoreachadditionalminute, whar s the cosL nccnts,of a lO-minutecall of this type?(e)i . (B) c I +,(D)7c (s)?.

(c, 3 (D) 6(* - 2)180- = k

( E ) 6 *

GO ON TO THE NEXT PAGE18. In thc igure bove,hearcaof square64.Whar s hearca f AeRT?

(A) 48 (B) 32 (C) 24 (D) 16PQR^S s

(E) 8

244


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PERCENT ONTRIBUTED O PROFITSBY EACH OF THE6 DIVISIONS, THRU U, OF COMPANYY FOR t9?9Ar. iD tgEO

: .t .Irt

t:ti :

?

F'

Quest ions l-25 refer o the ol lowing raphs.

,,on,.'?13.*.oooln 1980 hatwas heaveragef theamountscontributedo profits yDivisionL andDivision7"?(A) S .000,000(B) Sr,500,0o0(c) $3.000,000(D) 54,500.000(E) 56,500,000DivisionR contr ibutedowmuchesso heprof i ts f CompanyY in 1980han n I979(A) 5600,000(B) $300,000{c) $t80,ooo{D) $120,000{E) $too,oooln 1979hegreatestontr-ibutiono profits yoneof thes ixdivisrons aswhatpercent f theleast ontr ibut ion?(A) t jEc (B) 90c; tc) 100%(D) 900ra (E) 1.000%

l-

E.,tlltil{:7

2 l

22.

23 .

t980Profits= t30,000,m0 . . '24. lf the six divisionsare ranked eachycaraccording o thcir dollar contributions oprofits, from grcatestcontribution to lowest,how many divisionsranked lower in 1980 hanin 1979

(A) None(B) One(C) Two(D) Three(E) Four25. How many of the divisions contributed moredollars o profits n 1980 han n I979 ?

. (A) On e(B) Tw o(C) Three(D) Four(E) Five

GO ON TO THE NEXTPAGE"

245


87/565

26. In a certainspartmentbuildingexactly j ofthe apartmentshave wo bcdroomsand exactlyIf of the two-bedroom apartmentsarc frontapartments.Which of the oltowingcould be th etotal numberof apartmentsn the building?tA) 42{B} 50{c ) 5 l(D ) 56(E ) 57\l hich of the following could be the arca of anisascelesrianglewith pcrimeter E and one sideof length8 ?(A ) 6{ B ) t 2( c ) t4t D ) l 6{E ) rEWhena certainnumber s dividedby 7, th eremainder s 0. If the remainders not 0 whenthe number s dividedbv 14. hen fr-eemaindermustbe{A ) | ( t s ) 2 . (C ) 4 (D ) 6 (E ) 7,,*

2 9 . f x ) 0 a n d 2 x - t = 2 ; i ,

(c) |(D) v'7(E) jT+ t

then x =

(A)t r;(B)Y

27"

28.

p0/1 f the radiusof a circle s decreasedy 30 per-- cent,by whatpercent i l l heareaof thecircular egionbedecreased?(Aj t1Va(B) a97a(C St%o(D\ 6AVc(E) 907c

244


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SECTIONTim-30 minures30QuestionsNumbers: All numberssed re ealnumbcrs.FiSures: Position f points,angles,egions,tc.crn bc assumcdo be n theordershown; ndanglcmG1,ure3canbc assumedo bc positive.Lines hown ssrraight anbcassumedo besrraight.Figurcs anbc assumedo ric n a plancunressrherwiscndicated.

FigureshataccomPanyuestionsre ntendcdo providenformationuscful n answeringhequcs-tions'However, nlcss notcstateshata ligure sdrawrio scalc, 6u should olvehesc roblemsNor by estimating izes y sightor by mcaiuremcnt,ut by using "urr""*r.dge of mathcmaticssecExample below).Dryctions: Each f rht Qu.*tPnt l -ll. consistsf twoquantitics,ne n column A and one n columnB.youarc to comparehe wo qua-iiilElffihoosc

I i tle quantiry n ColumnA isgreater;I if the quantiry n ColumnB is reatcr;C if thc two quantitics rcequel;D if thc rclationshipannot cdcterminedrom he nforrnation i'en.Note:CommonIffiEiliion:

Column A ColumnB Samole nsrcrs

t.:T:*:.r1::atF':::

Since hcreare only four choices, EYER MARK (E).In a question, nformationconccrning oDcor both of thc quantities o bc compared s centercd bovcthe two columns.A svmbol that appeirs n borh columns;.;;;;;;-;c same hing n Column A as tdoes n Column B.

I

ialt:a-t

,.ltsFFEa:

Erample l: 2 x 6 2 + 6 o @ @ @ ( DExamples4 rcfero A peR.

Example2: NQ @ @ @ l D @(sinceequalmcasuresennotbc assumed,even hough pl{and NQ appearequat)

Examplc3: @ ( D @ @ @(sincc Y s bctwecrP andQ)

Example4: w + z rE0 @ @ ( D @ ( D(sincePp isa straighrinc)

2nGO ONTOTHENEXTPACE.


89/565

ABcDColumn A

l . 2(t03) 5( t02) 7Column B

2577 n * x = 2 3n = 3

2.

l o r s l o t t0 ( x ( l

4. x - y y - x6)fl. number f bondsL/ tbat werepurchascdfor 12,500

6. The$olume of asphere hat ha sradius4a, D, and c are consecutive dd integers,notnecessarilyn that order.

a - b b - c

The number of bondsthat were purchardfor $3.500The volume of asphere hat hasdiameterE

248

if the quantity in Column A is greater;if the quantity in Column B is greatcr;if the two quantitiesare equal;if the relationship canoot bc determined rom the information given.

Column A

E.

ColumnB

The lengthof PR is 12.Tbe lengrh of pS 8

x = - l x lx * 0

The altitudeof a certain riangularsail s2 metcrs reater n length han ts base. heareaof thc face of the sail s 24 squaremeters.

9.

10. Thc lcnglhof the baseof the sail 4 meters

GO O] ' iTO THE NEXT PAGE


90/565

ABcD

l t .ColumnA

(-t)7? (-2)aColumn B

t0t32.

Y l 2L = -z 5

R S = $ T = T U = UR =RT

t 3 ." r = i t *

x, y, end z ere positive aumbers.X Z

u9

if thc quantity in Column A is greatcr;if thc quantity in Column B is greatcr;if thc two quntitics are equal;if the rclationship cannot bc dctcrmined from thc information given.

Column A14. Tbc arca of a circularrcgion yith diametcr x

'*{ti

_ c' geg_gThearea ofa squereregion with diagonalof lcngth r

On Juty I tbc ratio of mcn ro r'omcn n Club Xwas9 to AL During thc monrh,2 addirionalmen aad2 edditioiel womenoincdtbc club,and no members roppcdout.15. Tbc ratioof mcn o +' wornDn Club X at

thecnd of July

CO ON TO THENEXTPAGE.


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Directions: Eacb of the Qucstioar 1630 has fivc answerchoices.For each of thesequestions,sclegt hc bcst of theanswercnotcsgrven.

16..lf x = 3 is onesolution o thcequationx 2 * r x - 2 0 = 4 , t h e n7 =(A) -8(B) -5(c) -3(D) 5(E) 8If the valueof a ccrtain fraaion is equal o 0.4and the dcnominator of tbe fraction is 15, henthe numcrator of the fraction is(A) 6(B) 8(c) e(Di r2(E) 37.s

19. What was the original priceof an itcm if a dis-count of20 pcrccntreduced hc priccto ll00 ?(A) $8 0(B ) $120 i(c) st2s(D ) $150(E) $250

20. The numbcrofconncctions C that can bcmade through a s*'itchboard o which I tele-phonesare connecleds givenby tbe formular= -7IrlI ,., - -T-. now many morc coillestronsare possiblewith 30 telephoneshan yith X)telcphones?(A) 435 (B) 245 (C) t9 0(D) 45 (E) l0

CO ON TO THE }TEXTPAGE.It" ln thc figure8bove, he ratio of x toto 2. What is the valueof y ?(A) r0r (B) 72 (C)36 (D) 3

y i s 3(E) 2

250


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Qusstions2 -25referro the following graph.

Total

1917-1978EXTBOOK NVENTORYFOR SCHOOLSX ANDBY YEAR OF PURCHASESchool XInvcntory: 1,500

School IT otal 1971 1978Invenrory: 2,000

l2Vo

t2% 2 t %

Notc: Al l books werepurchascd ew on July I of eachyear

t 3%

EVoVo

(25) Which of the following staremenrsan bev inferred rom the graph?

(asa pcrccntof thc 1977-197t nvenrorv)

\21) Whar pcrcent f School I/ 's 1977-197g- tcxtbook nventorywasboughr n 1975(A) e%(B) t2%(c) 2t%(D) 33%(E) It cannotbe determined rom the nforma-tion given.

22. ln School X how many of thc inventoricdtextbookswerepurchasedprior to 1976?(A) 100 (B) 120 (C) 1lf0(D) t ,34O (E) 1,3E0

23. How manyof the inventoricd extbookswcrcpurchased y the two rhools combincdduringthe years1974,1975. nd 1976(A) 495(B) e4otc) t,020{D) t,435{E) 2,800

24. lf SchoolX purchascd00 cxtbooksn t97landall of theseextbooks itherwere ountednthe nventory r hadbcendiscardedeforeheinventory,whatpercent f thescextbooks adbeendiscarded?(A) t$Vo(B) ZWo(C) 50Vo(D) 89%0(E) t00Vo

I. School X hasa smailerenrollment hanSchool I/ .' I I . If the ageof a book is thenumbcrofyearssince purchase, hcn the average(arithmetic mean)agcof a book in theSchool I/ inventory is less han that ofa book in the School X inventorv.llL According ro the invenlory,Sclobt Xand School Y purchascdhe samcnumber of textbooks n 1976.

(A) None (B) | onty (C) II only(D) I and l (E) I I and I I

251 GO ON TO THE NEXT PAGE,


93/565

26. V t ofthcnumbcr f womcnattendingcertain anccs equal o I thenumber f mcnattending, hat ractionof thoscattending rcwomen?(A)31rl?( q +(D)i( D *

In thc figurc above, O is tbc center of the circle.lf A,E= 10, what is thc area of the circlc?rff:.(A)-"10r (B) 20r (C) 25r

(D) 50r (E) l00r

How manyof the positiventegerscss han25arc2lcss han an ntcgermultiple f 4 ?(A) Two(B) Three(C) Four(D) Five(E) Si xl f 7x - 4y= - l and 5x * 3y = 52, henx - y =(A) -4(B) -3(c) 3(D) 4(E) 5The floor of a company's storage oom hasanareaof 20,000square eet. f thc floor is in theshapcof 8 sqriare, pproximatclyhow many ee tlong s eachside?(A) r40 (B) 450 (C) 50 0(D) r,000 (E) 5,000

30,

27.

252


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,,7-GGrtr:rt**

FORGENERAI,TEST6 ONLI'AnswerKey and Percentages'of ExamineesAnsweringEachouesrion correcuy

Slcl ion5

123567I9

1 01 1

1 51 61 7l o1-o202 1

z)

Slsuon

R o r i .l rt r , t u )A , 9 . t i ru : 4s s . l l 5

lt r t AF &1 i 7ID 8 5 8c ; l sA - a i r ^in l a - IA c a , 1 )a a ' r aI 5 ' 1 i 1 4n q t I 1 a > b

{ 2Gfoot bddcr lcaningagainsta vcrtical erll wirhtbc bascof th laddcr l0 fcct from thc yall is rulbd2 fectfartbcr out from th wall, caucing n" top "fhc ladder o drop r foct. - - --

#F l l eF

7'l


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m"R$ff.a*oo* to* hasiveanswerhoices'oreach f theseuesrions,etecthebesr fl 6 If th" olT raxon aDappliancc ried ar $300 sbetween5 pcrccntand8percent,hen hcost (price

plussalesax) of thcappliance ouldbe(A) $3t0(B) $312(c) $314.(D) S3tE(E) 1325Wx + (3x + 5.r)J (3x * 5x) :

lt{fi of thefollowing s rheprdrcr of rwo posi_u\c mtcgcfi whoscstm is3 ?

If an integerl, is subtractd f.;1" inteser .r andthe result s(A) equalro x(B) Iess han 0(C) less han x(D) greaterthan 0(E) greaterrhan x

20.A circle with radius 2 is inrersecredby a line arpoints R and T. The maximumpossib,leisianceb e t w e e n R a n d l i s17.

(A) 4x(B) tx(O lOx(D) I2rG) nx

(A) 0(B) I(c) 2(D) 3( E ) 4 &

(A)(B)(c)(D)(E)

Ia

:44nI t .


78


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Qucstions2l-25 refer to tbc followinggraph3 I . - i r ,l - . ;

INCOMEAND EXPENDITURESF AN INTERNATIONAL EIVICEAGET{CY..-,i5.,191Incomc Expenditurcs .r;i- ;, "r-

Individuals0.9.h

Corporations ExPenditures'1.9% Transmitted toTotal : $60million

Otlrcr Ageocies4.3%Note: Drawn to scale.

Total = $6Omillion

GO ON TO THE NE}ff PAGE.

iIEB:Iai

United StatcsGovernment26.6%

GovernmentsOther than theUnited States

SpecialFund-raisingProjects28.0% ContriburcdCommoditicslg.50h

79


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21"

22

Approximately how much of the agencT's n@mewas providod by contributed commodities?(A) Sl2 millisa{B) $14million{C} $15million(D) $17mil l ion(E) $19mrUi,onOf the foIowing; the category that had expenditurcsmost nearly equal to tk average arithmctic mean)expenditures pcr category was(A) refugee housing(B) emergencyworkers(C) postdisaster assistance(D) new investments@) commoditiesIncomc from which of the following souroeswasmost nearly equal to $2.9 million?(A) Unitd Stalcs government(B) Freigbt rcimbursernert(C) Investment(D) IndividualsfE) Corporations

, l(39Io yeal {, i of thc ascrrcy'sefugee ousing xpen-ditures,I of its cmergcncyworters expenairures,I) 1of its commodities expcndirurts, and i of its post-disaster assistanceexpenditures werc directly relatedto one earthquake. The total ofthese expenditureswas approximately how many miilions of dollan?(A) s(B) 1(c) e(D) l l(E) l3

25. Of the follo*ing, which is the closcstapproxima-tion to the percent of freight expendituresNOTcovered by freight reimbursemcnt income?l20h28Yo350h390h723h

GO ON TO THE }IEXT PAGE.

(A)(B)(c)(D)(E)

23.

80


118/565

t+r*

26. n thcfigurabove,ifx : ll0 and : lg,tbcn z :

t 027. What is theareaof thc triangular egionabove?

28. A wid* rcivcd { of hct htisband,sestrtc,andeach f ba rh*r; rceilld I ** brhoe. Ifthc widowsd onc of br sm rcceiwda t6l of$60,000rm thc 6tatc, what *as th amouatofthecstatc?(A) Seq000(B) S96,000,(g $16,m0(D) Sl35;m,,'. lG) stag6s

, t . -29. If tl4: 0, whichof the foflowingmuc.|'&Lf

( A ) r : 2 a n d y : 3( B ) : 2 e d y * 3( C ) _ r : 0 a d y : Q@ ) x : - 2 a d : 3( E ) x : - 2 a n dy * 3

30. f x =0.88E,/: .r ,638t, and z:(O.gggf,thenwhichof thc following is true?( A ) r < y < z( B ) x < z < y( O y < x < z@ ) y < z < x( E ) z c x < y

(A) l0(B) 40(c) 50(D) 60(E")ru

(A) 24(B) 30(c) 40(D) 48(E) 60

8 l


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SECTION3Trme-30 minutes

25 QuestionsDrcctionsi Eachqucstionor groupof questionss basedon a pessagcr setof conditions. n answcring omeof thequestions,t rnay bc useful o drav a rougb cEagam.For eachquestion, elcct he bestanswer hoicegiven.Qucstions l{A circus Eunager urust divide eglrt circus acts-F, L,M, O, & I X, znd Z-into two groups of four actseach,onc group scheduledto paform, one act at a time,in ring I and tbe other group'scteduled to perfor4 alsoonc a,t at a time, in ring 2. All acts ake equqlly long toperform, and every act that takesplace in one of therings must bc scheduled or exactly tbc sane time slotas an act tbat takes place in tbe other ring. fiie schedulemust also conform to the follorving conditions:

Act F must take place in one of the rings at thesametime that act M takesplace in the otherring.Act L must take place in onc of the rings at thesame time that act O takes placc in the otherring.Act R must take placc in tbe samc ring as act F.Act T must take place in the same ring as act O.Act X must be the secordact that tokesplace nring 2.l. Which of the following witbout regard to the orderin which thy will bc pcrformd coutd be the groupof acts to be schcduted or performance in ring I ?

If act T performs in ring l, which of the followingacts must perform in ring 2 ?

3. If act R must perforrn in one of tle rings at thesamc irne that act T performs in tbe other ring,which of tbe following must be the secondact inn n g l ?

4. If theorder, from first to last, ofcircus acts n ring 2is O, )i, t M, which of the following is al accept-ableorder ofacts in ring l, also from first to last?

If act F must pcrform bcfween acl X and act Rin ring 2, which of the following must be rhe first actin ring I ?

If act T must take place n ring I immediatelyafteract F and immediately before act R. which actmustbe the third act in ring 2 ?

(A) F, I" M, and T(B) F, I. O, ard R{C) L, M, O, and T(D) M, O, I and Z(E) O, R, I and Z

(A) F(B} L{c) M(D) R(E' z

(A) F(B) L(C) M(D)o(E) Z

( A ) n R , L , Z(B) L, Z, F, R(c) L, z, R, FP ) 2 , L , R R(E) Z, R, L, F

(A) L(B) M(c)o(D) TF ) z

(A)(B) M(c)o(D) T@ ) z


82


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Numbcrs:Time-30 *inut",

30 Questionsdll urrnlsJi uscdare rcal numbcnPosition of points"anglcs, rcgions,etc. c8n bc sssumed o bc in tbc ordcr shown; and angle measurescan be assumed o bc positirc.Lincs ghowa as straigbt can be essumcd to be straigbt.Figurcr can bc assumcd to lic in a planc unless otherwisc indlntcd.Figures hat accompanyquestionsare intended to providc information useful in answering the ques-tions. Howevcr, unlc*s a Dotestates hat a frgurc is drawn to scale,you should solve these problernsNOT by cstimating sizesby siglt or by measurement,but by using your knowledge of mathematics(seeExample2 bctow). r

Figurer:

Directions: Each of thc Qucstions -15 consistsof two quantities,one n Column A and one n Column B. Youarc to conpare tbc two {G-nriGi?hooscA if tbe quantity in Column A is grcater;B if tbe quantity in Column B is greater;C if tbe two quantities are equal;D if tbe rclationship cannot be determinedfrom tbe information given.

Since hereareonly four choiccs,NEVER MARK (E).In a question,nformation cooccrningone or both of thequantitieso be compared s centered bovethe two columns.A symbot hrt appcars n both columns cprescntshe same hing in Column A as tdoes n Column B.

ColumnA ColumnB SampleAnswen

Note:Conmon--t,-I i lor lnatron:

"r-lgegb 2 x 5 2 + o @ @ @ @Examples 4 refer o A PpR.

Elgsils-a NQ @ @ @ ( D @(sinceequal measuresannotbe assumed, ven bough Pand /fQ appearequal)

Example3: @ ( t @ @ @(sinccN is between andQ)

Exanple 4: w + z lE0 @ @ ( D @ @(sincePQ is a straightine)

GOON TO THE NEXTPAGE.

94


121/565

tifdKry.E,*aIFt-?:

F ?..

t

4 21 - 5

ABcD

4 4s - 1ColumnA

2. T\e averagarithmtic.mean)of87,95,and1303. Tbc timethat t tatccJim to drive300milesat a speedof 52milcspcrhour

6. The engthofchord PQ

ColumnB

Tbeararage aritbdb.mean) f88,95,atd129The ime hat t tak6Lila to drive240mitesat a speod f 40milcsperhour

The cngthofchord XI

ColnmaA.

f = l a " n a

r - 5 # V + j -i-:,iitf;l.:. , '1,-ar'.,.9t t. , r80

{- t6

t -05Ms. Rogers bought an elqctric rangc on the instalt-mcnt plan. The cash pricc of the range was $4O0.The amount shc paid was$120 down andl2 monthly paymentsof $28 eact.

5. The amount shepaid for $56thc electric range in cxccssofthe casbprice

Circlewith centerO

6 is -r perccntof 24.y is 25percent f96.

2 x * y < 3x > 2

C'o ON TO THE NE)ff PAGE.

a > 0

95


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ABcDif tbe guantity in Column A b grcaterif thc quentity in Column B is grcatcr;if tle tyo quantitics are equa\il the rcletionship cannot bc dctcrmioed from the information givcn-

ColumnA ColumnB

The perimeter of square Seter oftbe rectangleabove.The length of asideof S

is equal to the perim-

0 < a < b < c

C is a circle with radius 3The ratio of thecircumfercnce of Cto tlre.diarneterof C

x * 3

Qslumn A

z - x

CohrmnB

r f ) 03 t + 4 rr + t

GO ON TO THE NEXT PAGE,

12.

| -1. .

aa

95


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*^r$"oflic QucstiousG3o has iw answtf,choioes. ord of the qr*s&"c schq3bo5g4 oftD?enss,tt cnorcc8 rtn.

B{:sbF:;:lIgbq".i.

* - s 2lo. --l- =(A) It ((B)T-(ct s(D) 8(s) 15

17- What is0.423658oun& ro rh nearesttbousandth?(A) A.42(B) 0.423{q 0.424(D) 0.42361V10.4237

It- If 3(-r * 2) = x - 4, tben x :(A) -5(B) -3(c) I{D) 3{E) 5

I i "-: : : - ' ' r, I ' : ' : , '19. If .r2+ 2rl + y2 :9, thcn (.r * .yt' :l '

(A) 3(B).r8( q ntD).36(E) 8l

I tb ratangplarcoordinate systcnabore,if x :4.8, th y :(A) 3.0(B)r.z(c) 3.4(D) 3.6(E) 3.t

GO OT{ TO TTTENEff PACE.

n


124/565


125/565

21. For how manyof &c years hownwas hc amountof private realthexperditures t leastdoubte lresnount of public bcalthcxpenditures?(A) Nonc(B) One(C) 11ro(D) Thrce(E) Four

?2. t shich of th years rom 1975hro,oh 19g6nastk national healthexpenditure ercaiita moscn1'r-ry oqualto half thpcrcapiiaexpenditurport9E4?r975,9nt9791980yn2

.lji&'+t." :. .&.qJane as mc&4Cma asmany*Canndienr:acCanadianrdfr*b hercolhcti6,ir. hbhof rhelolowing_CANf,{OTe bcnuiber of etamgon

If -r is thenrmttr on thcnumber inebetwca5 and 15 batb nriceas ar tioil 5 as from 15.thcn "r is

(C) ll '_,'-,'; ' '(D)l?*, "' ..n,h$'lJane's olkrdodl

{r.j

Cio ON TO THE NE)ff PAGE.

(A) s?3(B) t0

, *ui" : ' j i i : i : ' i

r - ' t i t : : . i :r#*' i ,t". ;

(A) e6(B) 80(c) 72(D) 6E(E) 54

n.(A)(B)(cl(D)(E','

{A)(B)(c)(D)(E)

q&c following which s thebestapprcximationofthc perccot ncreasen tbcnationalh;aftb expcndi_ture percapira rom l98l to t9g2?35%n%frt/ot0%5%

Oftb following which sclosesto theamounl ofpublb national heatthexpenditues,n billions ofdoilars, n 1980?

25.

(A) 25(B) 30{c) 35{D) 4s(E) 70It canbc inferred from thegraphs hat in lg77 kpoprrlationof Country X, in millions,wasclosest owhichof the following?(A) 120(B) t50(c) reo(D) 240(E) 250

99


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29. A distillate flows into an mpty 64-gatlondrum atspout I and out of the drum at spout 8. If &erate of flow through 'l is 2 gallons pcr hour, howmany gallonsper hour must flow out at spout .8 sothat the drum is full in exactly 96 hours?

28" In the figure above, f the areaof t}le smallersquareIregion is i ttrc areaof the larger squarc region, thenthe diagoial of tbe larger square s how many incheslonger than the diagonal of the smallersquare?

(A)i(B) ;(c)?(o)1G)3' . l . t J z - t( ' ) i

52c)

FOle farmer has two rectangular ields-The larger field- has twice the lengrhand 4 rimes he *idth of thesmallerield. f tbesmallerieldhasarea K. rhentheareaofthe larger ield sgreaterhan the areaofthesmaller i.ld L&"t *jluniT(A) 2K(B) 6K(c) 7KfD) 8X(E't t2K

@[#(E' ,/2

100


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FORGENERALTEST2ONIYAnswer Key end Percentqgesr of F*arnineer Answering Each QUestion Correcdy

aa-_l

F3l-gF

'Eslirnated P+ fot the group ol erarniroas who loot he GFE GeneralTes| in a rceoi ttrE+year porin

$

F'a

t:BFFIiarfIbiti

tt

ffi: " t ' t - "

lruYTICtttt{JTY \/Srtu 3 t rddIlm? lctI|' F + I| S.r l illt P +r D2 83 E. 3 C5 l C .c . . 8 :'1. *r ..J*f -' 'l'-",$ '..-'*"'Br19 :- ;o jll i*$ i'1 3 i ' E -1{ *,,;+':.15 ..,j-'.,\- _ i r l : rl e . . Dr 7 ' ' Bt 8 . " A1 9 . Cf r ' c '

21 AZ BA E2 1 l } .6 E

I

f 7 3l 6 sl s 2l 8 al 1 el s ol, &lr ttt"8t -8 r[ir[.,GaP - 6 tl"',aE.L'' si . sl : : s i' a4Atlrl58,t62A

l l B1 2 01 3 E1 4 El s oI1 6 c1 7 c1 8 Dl e El t o B1 1 1 E1 1 2 E1 1 3 II 1 4 Al r i At1 1 6 At 7 7 Ci 1 8 B1 9 En c21 C2 . 9n c2 4 E2 5 8

9079385Av,75607fTI50st5278355 l58433861rtss860684145

{trnrfm ftrgury -7Srcds| t t 3llor tlfor$.r lE t l + mlai lilsrt. P +1 82 D3 A4 D5 B6 A7 . 8a . {9 D, 1 0 A t: 'I t c12 B'13 [ } , . :1 1 B , . r1 5 C

. . . 1 6 0 - ,. . ' 7 7 D, : . 1E C1 9 52 0 021 A2 . DN B2 4 E2 5 82 6 C2 7 4n c2 s E l' 3 0 E l

l s )1 8 2I 7 8l oI E '1 7 6l nl eJ 5 01 . 5 6t . ,f . s[ . '38l.;, Oll \ E ll z 2I| 1,1797871n2&,7352&6152I4GI

r A2 C3 B4 A5 c6 B7 B -. 8 01 9 Arlo 8, ' :: 1 1 , ' C .t t 2 D1 3 A.71 D. r 5 0 .

1 6 Er 7 c1 8 A1 9 8a 821 Cz z BA D21 AE C2 6 Cz 7 EA Aa og r c

e,&)TIs79n,e6t28tv8l4'ar3E'30a.ss7l33n8lwlna5A5en35a

- r A2 03 A4 C5 E6 87 08 C9 B1 0 E

1 t D7 2 01 3 E't1 D1 5 C1 8 81 7 B1 8 E l1 9 An 82't A2 , CA B2 4 CX E2 6 ' D2 7 8z A B2 9 43 0 831 A3 e cs t A3 0 03 5 03 6 C3 7 C3 8 A

7995887556g742a2ETEEa663A3527n72785248I797347324759948t8082t o4236732627m

2 03 A4 E5 C6 E7 B8 E9 Bt o c

11 01 2 D1 3 E1 4 E1 5 A1 8 81 7 Er 8 c1 9 Dn A21 A2 , ON A2 4 E2 5 82 6 C2 A A2 9 03 0 c31 EQ . O3 0 8u 83 5 A3 6 D3 7 E3 8 A

7670577263555a8083E67C.5251*t26253{T?,153692a7959673559682a.6334g73837312726

IUI


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SCOREOTIVERSTOI{SORGEI{ERAI EST OIILYTXO HE EBGE}ITSELOW'R|tScn

Y.ttrl orn't}Strt i farryticrtE hf I Sc|tdt * Ssrtd %Scrr erbr Scorc lrtor Scfi g t r &r$oitYarbrl 0mdifrirr t8rltlicalScehd .L S8|lrd % Sc.lqt 9lScon Stlsr Scoc Sdsr Scnn ialr72-767170

696E6756656il

61 l50 1

l ' ,1 5 8l s 7| - -t :l r "l s 41 5 352( t50{94E47tl64544434 14B

I

7507407307A7107ql6m57056065064063061 06005$5805705605505rt0n30(x5105004S470460458u0430

99aoaa

&7Sn099qA9796959193Qtans

9696c)o1I8EE7t(E3EI

E00800790780n07507107307'.'z9710

87e&82m7873aa6966

9999Y597Vf94929189b l

6360

504743402734

800 96

800 oo700 79 800690 n 800680 75 790570 73 7m560 71 750650 63 710E40 67 720630 65 710620 62 700600 58 590

39{1736? tv335tJ I392928m25?1232221ml o181 71 6I 41 ?t a1 11 0:o76

G5

430 34420 31410 28400 25390 23380 ?0370 18360 t5350 13350 13340 11 180330 9 170324 E 1603i0 7 44 0310 7 13 0300 5 420290 1 410260 3 q00?80 3 38027A 2 370

590 56 670 84580 53 660 81570 51 650 8B550 49 630 75550 46 520 73540 44 610 705?C 39 500 675 0 37 584 62500 34 570 594S 32 550 5330 540 50n 520 4525 510 12?1 500 3319 480 3317 179 3016 150 2614 1rt0 7311 1m 19t0 4r0 17

2ffi?s25023 0u0?002002J920020r?c02AC231

fl30?? nJ ' g3m280?40220

2 1 020c?c[2C0?00

3903S3S0310??n32t)300290280?60250240?l o? 1 020c

aI111111'II

86

31111

1 4t lI7bf,?J21'l'lI1

' P e r c e n l K ot i n t b e l o u t he s c a l e d score i s b e s e d on f h e per l o . r ance o i g -54 , 9 -o5e\ ?h i nees sho l o o k t he c e n e r a tTest belwteo Octobr 1, I 987, rod Seplember 30, I 990. This percei l beiow Inior r rai ion i used ior score reporrsdurrng the I 99 1 9? test, nt year .

r08


129/565

Numbers:

SECTION2Time-30 minutes

30 QuestionsAll numberssed rc ealnumbcrs.Position f points, ngles,egions, tc.can bc assumedo bc n thcordershown; nd anglemcasurescanbeassurnedo bc positive.Lines hown sstraight anbc ssumedo bestraight.Figures anbeassumedo tie n a prane nresstherwiscndicated.

Figurcs:

Figures hat accompany uestionsare ntended o provide information useful n answering he ques-tions. However,Jrnless note states hat a figure is drawn to scale,you should solve hcse-probtimsNoT by e^stimatingizesby sight or by measi.rrement,ut by using your knowledgeof mathernatics seeExample2 below).Directions: Eachof thc Questions -15 consistsof two quantitics,one n Column A and one in Column B. youare to comparc he two quantiticsand choosc

A if thc quantity in Column A is greatcr;B if the quantity in Column B is greatcr;C if the two quantiticsare cqual;D if the relationship ca'not bc dctcrmined from the information given.Note: Since herearc only four choices,NEVER MARI( (E).CommonG6Jiillfon: In a question' nformation conccrningone or both of the guantities o be compared s centeredabovetbe two columns.A symbol that appeirs in both columns eprcscnts he same tring in Column A as tdoes n ColumnB.


i. _

KE;

;'.,tt

Example : 2 x 6 2 + 6 o @ @ @ @Exampfes 4 refer o A ppR.

Examplc 2: NQ @ @ @ ( D @(sinceequal measures annotbc assumed,cven though Py'Vand NQ appcsr equal)

Examplc3: @ { D @ @ @(sincc { is betweenP andQ)

Examplc4: w * z It0 @ @ ( D @ @(sincePQ isa straight ine)


l 1 5


130/565

ABcDif tbe quantity in Cotumn A is greater;if the quantity in Column B is reater;if the two quantitiesare equal;if therclarionship annotbedetermined

Column A

+ 0.9

r *t

Figure INote: Drawn

5. The area oftheshadedregion shownin Hgure I

Column B

9(r.0+ 0.09)

Figure2to scale.

Thc area of theshaded egion shownin Figure 2

(i e Uonu, f$450plusv a9 percentncrease

from the information given

Column A

rn annualsalary

sP, Q , R , S . T, andcircle as shown.

The length of arc peR

The total number oflitersof water in xtanks,eachcontaining20 liters of water.and 2r tanks, eachcontaining35 liters ofwater

ColurnnB

A bonus t$500plusan 8.5percentncreasein annual alan'

U are pointson the

The lengthof arc S?"L/0The total nurnberofliters of'water in xtanks,eachcontaining25 iten of water.and 2x tanks, eachcontaining30 itersofwater

r : 3 0R : 5 9

_ 7 x 49 N x 9

Let_the drop" ofa squarebe definedas thepenmeterof the squareminus the engthof oneslce.The drop of a squarewith area25 20

.ry.

R 22

)2 i . i * l

8 .

9 .


l r 6


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if the quantity in Cotumn A is greater;if the quantity in Columri B is grearcr;if the two quantitiesare equal;if the relationshipcannotbc determined rom the information given"

ColumnB ColumnAolumnA

r c * x : 9 0y * z : 9 010. Theperimerer f R.SIU l0l l . ( r - 2 F (x + 2)2

(8X16X32X64)2x*v12. The avemge arithmetic 9mean)of x and y

ABCD

ColumnB( a + b f = 4 9a b 1 2

x : l - yx 2 + z x y + y z x + y


R I U (6x + 4)'

lr7


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Dnctio:s:. Each of theQucstions1630 has ivt answer hoices. orcachof thescqucstions,sclect he bestof tbe:rnsscrcDorceslven.16. In a ertain class,f tbcreare 35menand 63womenthcn hc ratio of mento women s

IL - - - - - L -19.Thc figurcaboves a rectangular olidwithAB : 10,8C : 10, aad CD : 3. What s thetotal surfaceareaof tbe figure?

n . 6 x 2 - l S x - 2 1(A) 3(2r + 7)(x - t)(B) 3(2x - 7)(x + l)(C) 3(2r - l)(x + 7)@) -9x2 - 2l@) -9x - 2t


D

C) *{B)( q ;i") ;@ ) l (A) 320(B) 300(g 2n(D) 160

{E) 2317. StretsL, M, and nf are straight and leve andthcy intersect to-forrn.a triangle. If streets L andiU intcrscct at a 40oangle and if street ,l/ is perpen-dicular to strcet M, at q-hat acurc angle do streetst and nf intersec0{A) 30"{B) 35'{c) 40'{D} 45'(E) 50:,

,8 ('- i)1' *)'{A}p ) i{ q i{")c ) *

t i 8


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134/565

24" In Country X, the average and sizc a 1940 wasapproximately what fraction of thc average arm sizein 1986?25. In -1986, o*ql X hadapproximarelyowmanymillionacres f farmland?

(A) I,100(B) 400(C) l,t0tD) l l(E) 3


(A)i( " )3( q ;t " )3(E)i

r20


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a26. lf n. s theaveragearithmeticmean) f the hreenumbers,9, and ft, what s thcvaiuc f & intermsof n ?(A) 3n - 15( B ) n - 5( O n - 1 5(o)t+,o., n * 15\- , 3

27" Whichof the ollowingCANNOT becxpressedsthesumof tbesquares f rwo ntegers?(A) t3(B) l7(c) 2l{D) 2e(E) 34

28. lf AB : .B.Yand XC = CD in thc figur

bigbook quant

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