@L|R}6CD l0C)HCC WhL/h `CmCDiD`  R@W1  Y0@R !L` D  C D     )16CS S)  C)D1 p p 0 C9DI pCDL~CiCDiD`HAYDEN SOFTWARE( SCORE IMPROVEMENT SYSTEM FOR THE SATA. System User's GuideB. Quantitative ComparisonsC. Fractions And DecimalsD. PercentagesE. Ratios And Proportions F. GraphsG. Motion ProblemsH. Mixture ProblemsI. Business And Work Problems J. SequencesK. MiscellaneousDA. Using The QUANTITATIVE COMPARISONS AND WORD PROBLEMS MODULEB. Organization Of The System)A. Definitions, Analysis, And StrategiesB. Examples with TUTORMODEC. Examples Without TUTORMODE MAIN MENU Detail MenuPROGRAMREVIEW'M = Main Menu Q = Quit R = Restart M = Menu | = Back'R = Restart M = Menu O = Omit | = BackP = Paragraph Q = QuitPx X`H232435; 1 ;  hh@2 e1i1L;Hҍ 00) 08 109hh@ Ҡ2e1i1232435ޥ<<8=LxLLLLLLL LL: LT LL_ L L L L ! h`LL6 LLL LhLJLTLLLLLLL&LN LL ! v 5 7 h` Ltv W h`h  ` v 5 v h` v v v v Lx  v [ v h`t v 8 v [ v v h`v   7 Nh`Y sLw ! v Lr  7 A[08!sh`v h`  v 5 h` v W v  ]h` v v h` v v v v >v`h0BJKՅԩ3D ELVK:h0BHI V`hhhhhhh΢ e˅ː`˪8包˥卅̩***ΥeͥeΠˑȥ̑Ȋȩ`h h       i  w  L l wv   ` ӠŠҠϠ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ]  ] ] ] ҠӠͧϠנΠϠŠҠҺENTER YOUR NEW ANSWERϠŠҠҠĺENTER YOUR PREVIOUS ANSWER Ϡՠ٠ԠϠԿ٬ΩӠҧϠנŠӠէϠנĠӠçϠӠӧϠ ҠӠŠҠϠ ŠҠϠ ԠŠƠŠŠ  RAW SAT TIME SCORE SCORE REMAININGENTER TOTAL OF PREVIOUSLY RECORDED DATA ĠӠ ƠՠȠϠŠŠĠŠ VERBAL NUMBER CORRECT = VERBAL NUMBER INCORRECT = MATH NUMBER CORRECT = MATH NUMBER INCORRECT = ҠԠӠΠϠhPͩΩ vw'u vt$hPͩgΩ̢Pvw`   ` vHwH)8w hwhv` (wLO ˑΥPɚ` v` w` t`  |`έ͠ ɛLv LOL u k'u`     HL `8Ii8HhIi J`m 8 Ln,8`,`jnNN)P˩gȈ i(ː `@ hhh hHH` j H h`v8`)0i(mw j  fjfj(j`vw(wv`έ) & &΅ͦνi`w,I˥i(ː`ˮvʊ mvJfJf˅̢,ue˅˽e̅`PPgѩi  PR 0m `  0έͩP˩̩@Ѡ075Ȍ 2ˬȌ  e˅ːвˍȱˍL խ ` L/ =`ɛ& `!ɛέ `Lɛ ڭ...eͭeΠȩͩ`ЩP  K``P ` `ϩЩ`fff1j$$$$>`<|fl0fF0p88p``~0~ 0`@ 80 @~~`0 0```nf>ff~fff~~f<flxxlf`````~cwkccfv~~nf8pp8?ww<~~~<x`x`~<~~<0~0 ~ <>f>``|ff|<```<>ff>>ff>|``|fff8<<``lxlf8<fkc|ffffff>|f```>`<|~ffff>fff<ck>6f< x~ 0~$B00fff S`ѩ Pυ˩Ѕ 0 P `L}) ȱˍ 0ȑˍm mː` ˩ȱ)ȩˍ8` ˍ ȱˍ  `  ȭ  `ˍ̍˭`˭`P˩̢ѱϑ `P˩̩Тѱˑ`` #mm P˩ 0 P `m 8J P˩ 0 P`H232435; 1 ;  hh@2 e1i1L(Hҍ 00) 08 109hh@ Ҡ2e1i1232435ޥ<<8hl˩l̠e˅ː`hҢҩyҍ* \*`h, \`&%8%0%## # # ## #@#"!@!`! ! !0!!!!!!!!!!!!! ! !`!@!""@#`#0# # # #$@%0%8%&1,25560 NEXT I70 CLOSE #1UMMT.DUM"11 NOTE #1,A,B12 ? A,B13 CLOSE #114 STOP 30 FOR I=0 TO 12440 POINT #1,X,I50 PUT #Pg p} @ЩѠxeЅАeЅАѹkI(eЅАѹl8аѹ l(eЅАѹl@}(eЅАѹ(lPeЅАѹ7l(eЅАѹFl(eЅАѹUlЈ(eЅАѹdlЈ(eЅАA}ѹslЈ(eЅАѹlЈ@ЩѠ(eЅАшeЅАѠ lЈ eЅАйlЈWeЅАѹlЈ$eB}АѹlЈ3ЩѩͩΩMЩN͈ТEͩΩBЩV(eЅА(e͐ͅ ݠ Щ8j Ј Յ8j C}Ј8j Ј %8j Јjjjjjjj} ЩѠk8 IЈѩйk8 IЈD}Щѹj8 󩰅Ѡ!k8 ЈU  R  $%& S0 S0 &%&$8DLwE}jjjjj} bdpejk Vbde hi V0LjLQUANTITATIVECOMPARF}ISONSANDWORD PROBLEMS* "SAT" AND "SCHOLASTIC APTITUDE TEST"ARE REGISTERED TRADEMARKS OF THE COLLEGEENTRANCE EXAMINATION G} BOARD. THESEMATERIALS HAVE BEEN DEVELOPED BY ARROWINSTRUCTIONAL SYSTEMS, INC. FOR HAYDENSOFTWARE COMPANY, INC. WHICHH} BEARS SOLERESPONSIBILITY FOR THEIR CONTENTS.ATARI CONVERSIONBY ANDREW TAYLOR(!9$%.3/&47!2%3#/2%NNNNNNNNNN)-02/6%-%.4NNNN3934I}%-&/24(%NHJHJ JHJYʀJYʀJYʀYʀY$%6%,/0%$"9!22/7).3425J}#4)/.!,3934%-3 ).##/092)'(4# "9(!9$%.3/&47!2%#/ ).# BMI ERROR ;stop fo}r any err3870 LDA TIMER ;wiK}thin time limit?3880 CMP #8+13890 BCS CHK3 ; no!3900 DEC TESTCNT ;yes, dec t}est cnt3910 CHK3 DEC CURRCNTL}3920 BNE CHK2 ; test more intervals3930 LDA TESTCNT ;all intervals OK?3940 CLC }; assume all is OK395M}0 BEQ ACCEPT ;Yes, accept: PROTECTED3960 DEC RTRYCNT ;else, re-try Op3970 BNE CHK13}980 ERROR SEC ; GiveN} up!3990 ACCEPT BCC WAIT4000 LDA #$FF4001 STA $02444010 JMP $E4774020 WAIT LDA #04030 STA T}IM4040 STA TIM+140O}50 TAX4060 WAIT1 INX4070 BNE WAIT14080 INC TIM4090 BNE WAIT14100 INC TIM+14110 LDA TIM+1412}0 CMP #184130 BP}NE WAIT14140 LDA #04150 STA $02F04160 LDA #$7D4170 JSR $F6A44180 LDA #34190 STA IOCB+24200 D:AUTORUN.BAK210 STQ}A IOCB+44220PgЩѠxeЅАeЅАѹkI(eЅАѹl8аѹ l(eЅАѹl D  C D     )16CS S)  C)D1 p p  S}0 C9DI pCDL~CiCDiD` DD˙` d J)L ! T}D L(( LL()  L| L( S LH 0p n   U} CY?  q  L L  ` ) V} `A! d߰")-݆ "  $G@LLL&0") $G% W}H0 3S8`G ȱG ȱG   Gȭ Gȭ GG}GHiH8(()) G$H% `(0 X})8` d)L ݆ & LGȘ ݆LL d  ! LL d)N>Q  HH) Y}  hyhyB q L> Lm JJ  Ln*` dB%' Z}8  H H` 1 { LL   !L     Hh SY?  q  1L [}  !? S   q 1 L   Ll  Lg E`L   !L)  q 1L \}) `L0AM݊L݉ ML  N݆LLLNLMLHG!@ ]}1F GȱGLLEEȩÑEȑEEȑE Ed E7EȩE  q ^} L !,0,0SGɛ L 1 !L EHEh W G gLLSROTCES EERF _} G) *Gȩ GȽG GȌd q q G`  8   0G  `D `}CEDC0X:Ȣ Y ȱC* ? 0.. , 0%n ?A[ 0 : L`L  `, 0`Y a}`piH n0)բY? 08`0  b}  0$L GGȽG L `8L`L c}8`  05G)݁,G)ȱGȱGHh0})Hh` B! 8`8iiiLE` d}E8FEh( l0`ɃLL L8^~jj8jHi hEEEiEȱEiE` dTE e} H8EEȱEEȩEh J E8   . m  i`LI!)E1FR f}1LJ舩9GIH`LJJ`HGHh l` g} S gL   8 rii `дCDCG W  h}C  Lq` X٨`DOS SYS IIIIIIIIIIIIIIIC`0 ߩ0}}00 i} HE |||DDOS DOSDOS SYS } j} }j k}b7PRNTS SYSB>DUMMT DUMB?AUTORUN SYSCRDOS SYS l} 0`BDELV !B m}`LVUQ   ]   TU J ]L!T  #      TU  n} L ? .  t`GBJ V~DEHI B V0dV o}QDEHI VF9 ,0 ,0 s0hhL  L` H hDHEh p}DEL8HI   0 HI,0 0  9 .G VLO q},0 L4*IJ`llD1:AUTORUN.SYSNEED MEM.SAV TO LOAD THIS FILE.D1:MEM.SAV J y08 B|DEHI r} V0 0`B;DELV䌚 !B y`@ʆ v s? F0Ξ05: [ BDEHI s} VY8 B V  @  /DE `E:D1:DUP.SYSERROR-SAVING USER MEMORY ON DISKTYPE Y TO t}STILL RUN DOS B;DE J V (` 9 V⪍ ઍ  - u}LLu DEHILV 9 .l 9 .l  `` s$B VBH v}I|DE V BLV nB,DE J V* \*` B V BLVDEHI BLVL w}1u H232435; 1 ;  hh@2 e1i1LHҍ 00) 08 109hh@ Ҡ2e x}1i1232435ޥ<<8 }7Ȍ!E`Ȍș`[ȌHșhL`LOAD "D:QUANT.BAS"RUNhz} DR a   x X) L S` i`{}7Ȍ!E`Ȍș`[ȌHșhL`LOAD "D:QUANT.BAS"RUNh[##MNDNFXABBLBSCDEFMPRRESCANF1F2F3FLINTTLTXDSSCSKTMCPPMERWRSRTSRSSWCP}}XYYLNXXOORRRVRHRIPCAQQFMMFTMTVDVDVRC~} }@@@ !"#$%}&'()*+,-./01234}56789:;<=>?@ABCD}EFGHIJKLMNOPQRS}QUANTITATIVE COMPARISONS, A0"F:@, A(, @A"@+F:@,&A(,AB7t+F:B7t},&A(, ss;@p,;@,;@@,;@,;@,;@,;@,;@,;@,;@}, ss;@,;@,;@,;@,;@',;@,;@,;@,;@,;@,GG;}@,;@,;@p,;@p,;@p,;@,669@<@,9@E<@,9@,6-?}:AQ,) +@@)AV@ Q0@@ @70@@Q0@@ }@"F:@, A(" @%A"@+F:@,&A(,AB7t+F:B7t,&A(, A"P }A!0!T 6-?:,6-!6-?:A a,+ A J?:A!Q#8<,"68<,-# @u@'}8<,"6-?:A d,' @uB"8<, Au" @uD- 6-% A #7<,4~S- @hG 6-&}K  @N @ @PP 6-% A R "6-$T7<,4~ A Z " $n, 6}. A"6-?:A!E,, @x 4~RA AP 4~RC A 7<,4~Q6-?:,$ 0~S}D Ap$6-?:A d,6-$6-"8<,%68<,- @ 0~SB A`! 6-"}8<,%!68<,-38<,%6-6-?:,) Ay3 @ Au @/ 6-6-?:,6-8<,)}")"%/6- 6- 6-% A " 46-?:A ,"6.~SP! 4~SP A ! Ay 0~SG} A0 A(-@$6-?:<<<<,( (-@$6-?:<<<<,( /6-?:<<<<,%6}-?:<<<<,/ Ay56-+A:7<%,,,$'56-A:7@<@%,,G%6-+A:7@<@%,,,$'G6-+A:7}@<@%,,,$';6-A:7@<@%,,;6-A:7@<@%,,$ A 6-$'6-$'}A%6-+A:7@"<@"%,,,$'A6-A:7@%<@%%,,6-?:<<<<<<<<,$ 0~SH A@)6}-?::8<,,467B:,%@,.'*6-?:<@ ,4 A?6.7<,6-?:<@!,?6.SELECT THE CORRECT ANSWER} A A0" $4)4EEA A  4*" A 0O A  6- "6-} "6-?:<, A ) 6-?:,68<,-8<,%)68<,- @ 2)3 A  "6- } 6- "6-?:<, A 68<,-@:,0 0 A: 68<,- 68<,-8<,%D26-?:<@ ,}26.CORRECT, THE ANSWER IS IA67B:,%@,.-67B:,%@,.'7 AA APN 68<,- 68<,-8<,}%X-6-?:<@ ,-6.THE CORRECT ANSWERY167B:,%@,. IS '167B:,%@,.Z-67B:,%@,.'# }A- APb#+2Q)3,*0*0# Av 6- 0Q A A" AP A } 0 A 6-6-?:,$ 6-&"6-?:,$ @4 A 4~SB)4~SD.6-?:A d,46-}7<,0~Q A`%6-A:7<+B:,&,%,,%6-8<, " AV AX+68<,-8<,& 8<, }+68<,- 6-&6-7<,0~R A  "6-?:, @  6- A  0 A}'6-?:A d,6-"$6-'$ A 5 6-?:,-@E"--68<,-1 5 ,-@-}$68<,-( , 0 6-6-6-6-!6-'6--6-0$ 4)4~ET6-* "6-?:,$4 6-?:,} @>AdAUR"F:Ad,"AU" AP\6.>:?:A!,,$;'?:A!<<@$ AG6-?:,V}6-?:A!E,K6-?:<@$,#6-?:<<<,)6.3 A<6-?:,K6-?:A!E,6-?:A!E,$G6-?:<,)}6.NUMBER CORRECT = =67B:,,.=:8<,,G AM6-?:<@,/6.NUMBER INCORRECT = C67B:,,.=:8<,,M }AM6-?:<@,/6.NUMBER UNANSWERED = C67B:,,.=:8<,,M A6-?:A R,$R" 6.Q"67B:,}%@,.=:,\2 "(?:A!Q:@0,26.C:6.DB6.EJ6.FG 6.M6.P6.R=6.ӠŠҠϠG6.~SC6. } W6-A!'6-A!0'6-A!B3-A!3?-A!6K6-A!HW6-A!T76-?:A!!,@%-6"}Here the emphasis is on reasoning. Theproblems are to be done quickly& withlittle computation. You are given twoquantitie}s& with information on eitheror both. You have to decide which isthe larger quantity. The factsconcerning the quantities a}re centeredabove both columns.~RAEach question consists of twoquantities& one in Column A and one inColumn B. You are to} compare the twoquantities and choose the correctanswerA if the quantity in A is greater;B if the quantity in B is great}er;C if the two quantities are equal;D if the relationship cannot bedetermined from the information given.~RANotes~1. }In certain questions& informationconcerning one or both of thequantities to be compared is centered.2. In a given questio}n& a symbol thatappears in both columns represents thesame thing in Column A as it does inColumn B.3. Letters k& n& and }a stand for realnumbers.~RAThere are four choices here not five.The scoring formula is changed to~Number Correct - 1/3 }Number Wrong = RawScoreEach problem you answer incorrectly hasa penalty of -1/3& as opposed to -1/4.These problems seem }easier to do& butbe careful of guessing since thepenalty is greater.~ET~ETCopyright ARROW INSTRUCTIONAL SYSTEMS` } July 1983s is on reasoning. Theproblems are to be done quickly& withlittle computation. You are given twoquantitieEach of the questions in this sectionconsist of two quantities& one inColumn A and one in Column B. You areto compare the} two quantities andchoose the correct answerA if the quantity in A is greater;B if the quantity in B is greater;C if the} two quantities are equal;D if the relationship cannot bedetermined from the information given.~RANotes~1. In certain q}uestions& informationconcerning one or both of thequantities to be compared is centered.2. In a given question& a symbol }thatappears in both columns represents thesame thing in Column A as it does inColumn B.3. Letters such as k& n& and a st}andfor real numbers.~RA~Q` COLUMN A COLUMN B1. 5T - 20 = 30` T 10~RC}C1. (c) Solve for T& then make thecomparison~` 5T - 20 = 30` 5T = 50` T = 10Since 10 = 10 th}e answer is (c).~RA~Q` COLUMN A COLUMN B` 4 yd& 2 ft& 4 in2. ---------------- 15 in` 4}~RCA2. (a) convert everything to inchesthen divide.` 4 yd& 2 ft& 4 in` ----------------` 4` 1 yd }= 3 ft` 4 yd = 12 ft` 1 ft = 12 in` 2 ft = 24 in` 12 ft = 144 in` 144 in + 24 in + 4 in` ----------------}-----` 4~RA` 172 in` ------ = 43 in` 443 in is greater than 15 inNote~ A good student will look a}t thetwo columns before he does theconversion. It is obvious that 4ydsdivided by 4 is greater than 15 inmaking COLUMN A g}reater than COLUMN B.Remember do not do the computationsunless absolutely necessary.~RA~Q` COLUMN A COLUMN} B` 28 13. -- = -` y 2` y 57~RCB3. (b) Use Geom}etry property~ crossmultiply then solve for y.` 28 1` -- = -` y 2` y = 5656 is less than 57 theref}ore (b)~RA~Q` COLUMN A COLUMN B` __` / 14. / -- 25%` \/ 16~RCC` } __ _` / 1 \/14. (c) Rewrite~ / -- as -@@` \/ 16 \/16}then divide~` 1` - = .25 = 25% so (c) is correct.` 4~RA~Q~SB~SP077056077111132111077056~SH1511B C~S}H0711A~SF` COLUMN A COLUMN B` 2 2 25. (AB) + (BC) (AC)~RCC5. (c) }According to PythagoreanTheorem~` 2 2 2(AB) + (BC) = (AC) . Therefore thetwo sides are equal.~RA~SD~Q}` COLUMN A COLUMN B` _______` / 1 1 1 16. / -- + -- - + -` \/ }16 49 4 7~RCB6. (b) Ans. According to the law ofsquare roots you must add inside thesquare root before you} take the squareroot.` L.C.D. = 3.0625` _______` / 1 1 1 1` / -- + -- - + -` \/ } 16 49 4 7` _______` /49 + 16 7 4` / ------- -- + --` \/ 16 x 49 }28 28` ___` / 65 11` / --- --` \/ 784 28~RA` __` } \/65` ----` 28` 8+ 11` -- is less than --` 28 28Therefor}e (b) is correct.~RA~Q` COLUMN A COLUMN B7. 280% of 12 34~RCB7. (b) Ans. Follow percentage} rules andreduce.` % is` --- = --` 100 of` 280 y` --- = --` 100 12` 100y = 3360` y =} 33.6 is less than 34Therefore (b) is correct.~RA~Q~SB~SP085056077111132111085056~SH1511B C~SH0712A~SF` }COLUMN A COLUMN B8. (BC) (AC)~RCD8. (d) Ans. Since it is not given that}s.` 3/8 C = 12` C = 12 x 8/3` C = 32 gal. Ans.~RA~Q15. Mr. Jordan owns 3/5 of the stock ofa corpor%?}ation. He sells 2/5 of hisshares for $16&800. What is the totalvalue of the corporation's stock?(a) $170&000 (b) $80&000%@} (c) $60&000(d) $70&000 (e) $160&000~RCD15. (d) $70&000 Ans.` Let y = value of the stock2/5 x 3/5y = $16&800` %A} 6/25y = 16&800` y = $70&000 Ans.~RA~Q16. A tank 1/4 full requires 10 gallonsto make it 7/8 full. What is the%B}capacity of the tank in gallons?(a) 20 (b) 10 (c) 16 (d) 15 (e) 13~RCC16. (c) 16 Ans.` Let C = capacity in ga%C}llonsgallons in tank originally +gallons added = gallons in tank at end` (1/4)C + 10 = 7/8 C~RAMultiply both sides of %D}the equation by8& the LCD& to eliminate thedenominators.` C 7` 8- + 10 = 8-C` 4 8` 2%E}C + 80 = 7C` 80 = 5C` 16 = C Ans.~ET~ET C 7` 8- + 10 = 8-C` 4 8` 2$?~Q` 3 5 71. Combine~ - - -- + --` 4 12 20(a) 1 31/60 (b) 41 (c) 41/60 (d) 91(e) 100)G}~RCC~Q2. Combine into a single fraction~` m 2m 3m` - + -- - --` 2 5 10(a) 6m (b) 3m/5 (c) 6m/5 (d) )H}0(e) 1~RCB~Q` (1.2)(.1)3. Simplify~ ---------` 2` (6)(a) 1/300 (b) 1)I}/100 (c) 1/30(d) 1/3 (e) 1/3000~RCA~Q` 1` 20 - 10 x -` 24. )J}Evaluate~ -----------` 2(a) 17.5 (b) 7.5 (c) 5 (d) 2.5(e) 1.0~RCB~Q` 1 1` )K} - + -` a b5. Simplify~ -----` 2(a) (a + b)/2 (b) 1/(a + b)(c) 2/(a + b) (d) (a + b)L})/2ab (e) 1~RCD~Q6. A snapshot measures 1 7/8} x 2}. Itis to be enlarged so that the longerdimension will be 4}. What w)M}ill be thelength of the shorter dimension?(a) 3 7/8} (b) 3 3/4} (c) 2}(d) 2 3/4} (e) 15/16}~RCB~Q7. If a man trave)N}ls K miles an hour forL hours and T miles an hour for Mhours& what is his average rate inmiles per hour for the entire dis)O}tancetraveled?` Total DistanceNote~ Average Rate = --------------` Total Time()P}a) (KL + TM)/(L + M)(b) (KL + TM)/2(c) KL + TM(d) (K + T)/2(e) KT~RCA~Q8. A locksmith finds a 1/2} cylindricallock to)Q}o small for the opening. Thenext larger size will fit. Which of thefollowing sizes should he use?(a) 3/4} (b) 9/16} (c))R} 5/8}(d) 17/32} (e) 3/5}~RCD~Q9. Reduce 216/540 to lowest terms.(a) 1/2 (b) 2/5 (c) 1/4 (d) 5(e) 1/8~RCB~Q10.)S} 5/8 - 1/4 =(a) 1 (b) 2 (c) 3/8 (d) 1/8(e) 1/2~RCC~Q11. 3/4 x 4/15 =(a) 1/2 (b) 1/8 (c) 1/3 (d) 1/5(e) 1/4~)T}RCD~Q12. (a/b) x (x/y) =(a) ax/by (b) ab/xy (c) a+b(d) ay/xy (e) ab~RCA~Q` 5/18 + 2/913. Simplify~ -)U}---------` 6/36(a) 3 (b) 7 (c) 6 (d) 18 (e) 9~RCA~Q` 2` a a 2 114. -- / - x - - - =)V}` 20 5 a 2(a) 1 (b) 2 (c) 1/2 (d) 0 (e) 1/4~RCD~ET~ET0(a) 1 31/60 (b) 41 (c) 41/60 (d) 91(e) 100(J}Percent} means divided by 100. Thus52% means 52/100 = .52 or 52 parts outof 100. A percent is a ratio& that is afraction-X} whose denominator is always100.Note~ A percent may be called a rate -that is& so many per hundred.` % is` -Y} % use --- = --` 100 ofFill in known values. Solve theresulting proportion by crossmultiplying and dividing.~R-Z}A` % 6Example~ --- = --` 100 24` x 6` --- = --` 100 24` 24x -[}= 600` x = 25% Ans.~RA` 2 1/3 140Example~ ----- = ---` 100 x` 2 1/3x = 14000` -\} 7` x = 14000/ -` 3` x = 6000 Ans.~RAThe following is -]}a method to solve mostpercent problems.` % decrease amt. decrease` ---------- = -------------` 100 o-^}rignal` % increase amt. increase` ---------- = -------------` 100 orignal` % discount amt. disc-_}ount` ---------- = -------------` 100 orignal~RAExample~` 2` x .36y` -`}--- = -----` 2` 100 1y` x = 36% Ans.~RAExample~` % decrease amt. decrease` ----a}------- = -------------` 100 orignal` 20 120&000 - x` --- = -----------` 100-b} x` 20x = 12&000&000 - 100x` 120x = 12&000&000` x = 100&000 Ans.~RANote~ In conver-c}ting from fractions topercents and decimals& bear in mindthat per cent means }divided by 100}.Thus& when you convert to p-d}ercent(words or symbols) you must multiplythe original number by 100 so as not tochange the original value.Correspondingl-e}y& when you convert frompercent to a decimal& you must dividethe original number by 100 for the samereason.~RAExamples~-f}1. 0.0294 = 0.0294 x 100 = 2.94%2. 0.13% = .13/100 = 0.00133. 1 1/2% = 1.5/100 = 0.0154. 2.78 = 2.78 x 10-g}0 = 278%5. 3/4 = .75 x 100 = 75%6. .35 = .35 x 100 = 35%~RAExample~ If the length of each side ofa squar-q}_b7PRNTS SYSB>Q0 B?AUTORUN SYSB'RDOS SYSByAUTORUN BAKBH|QUANT BASB BAA B!BBB B$CAA B3CBB BFCCC BWDAA B {DBB BDCC BEAA B ECC B"AA BAB BBCC BEBB "#AA e is decreased 20%& what is thepercent decrease in area?` Let y = side of large square` 4` -y = side of -r}small square` 5` 2` original area = y~RA` 2` -s} 4y 4y 16ynew area = -- x -- = ----` 5 5 25` 2 2` -t} 2 16y 9ydecrease = y - ---- = ---` 25 25` % decrease in area = 9/25 x 100` -u} = 36% Ans.~RANote~ You should memorize thefollowing~10% = 1/10 20% = 1/530% = 3/10 -v} 40% = 2/550% = 1/2 60% = 3/570% = 7/10 80% = 4/590% = 9/10 100% = 1~RA33 1/3% = 1/3 -w}66 2/3% = 2/325% = 1/4 75% = 3/412 1/2% = 1/8 37 1/2% = 3/862 1/2% = 5/8 87 1/2% = 7/816 2-x}/3% = 1/6 83 1/3% = 5/6~RAExample~ The population of a city isnow 120&000. If the census shows a 20%increase over t-y}he previous census& whatwas the previous population?Let100% = previous population120% = present population = 120&000` -z}1% = 120&000/120 = 1000100% = 100&000 Ans.~ET~ET0 = .52 or 52 parts outof 100. A percent is a ratio& that is afraction,5~Q1. Write .3% as a decimal.(a) .003 (b) .3 (c) .03 (d) 3(e) .0003~RCA1. (a) .003 Ans.` .3` = ---1|}` 100` = .003 Ans.Note~ rewrite .3% as .3/100~RA~Q2. Write 4.5% as a fraction.(a) 4/1000 (b) 45/10001}} (c) 5/100(d) 45/100 (e) 45/10~RCB2. (b) 45/1000 Ans.` 4.5% = 45/1000` = 4.5/100` = 45/1000 Ans.1~}~RA~Q3. 40% of 80 =(a) 20 (b) 60 (c) 32 (d) 30 (e) 2~RCC3. (c) 32 Ans.` % is` --- = --` 100 of` 1} 40 y` --- = --` 100 80` 3200 = 100y` 32 = y Ans.~RA~Q4. 120% of 20 =(a) 24 (b) 20 (c) 60 (d) 421} (e) 90~RCA4. (a) 24 Ans.` % is` --- = --` 100 of` 120 y` --- = --` 100 20` 2400 = 100y1}` 24 = y Ans.~RA~Q5. What percent of 70 is 25? (to thenearest percent)(a) 30 (b) 35 (c) 38 (d) 26 (e) 36~RCE1}5. (e) 36 Ans.` % is` --- = --` 100 of` y 25` --- = --` 100 70` 70y = 2500` y = 35 1}5/7%` y = 36% Ans.~RA~Q6. What percent of 15 is 45?(a) 3000% (b) 30% (c) 3500%(d) 300% (e) 600%~RCD6. (d) 31}00% Ans.` % is` --- = --` 100 of` y 45` --- = --` 100 15` 15y = 4500` y = 300% Ans.1}~RA~Q7. 14 is 170% of what number?(a) 8 4/17 (b) 8 1/10 (c) 9 4/14(d) 8 (e) 0~RCA7. (a) 8 4/17 Ans.` % is1}` --- = --` 100 of` 170 14` --- = --` 100 y` 170y = 1400` y = 8 4/17% Ans.~ET~ETCopyright 1}ARROW INSTRUCTIONAL SYSTEMS` July 1983c) .03 (d) 3(e) .0003~RCA1. (a) .003 Ans.` .3` = ---03~Q1. Write .6% as a decimal.(a) .006 (b) 6 (c) .6 (d) .06(e) .0006~RCA~Q2. Write 6.7% as a fraction.(a) 67/100 5} (b) 6.7/100 (c) .6(d) .06 (e) 67/1000~RCE~Q3. Write 3/5% as a decimal.(a) 6 (b) .006 (c) 600 (d) .06(e) .6~RC5}B~Q4. Find 70% of 120.(a) 83 (b) 81 (c) 100 (d) 84(e) 120~RCD~Q5. What is 160% of 30?(a) 70 (b) 80 (c) 48 (d5}) 50 (e) 60~RCC~Q6. What percent of 80 is 35?(a) 42% (b) 30% (c) 16% (d) 20%(e) 44%~RCE~Q7. What percent of 3 i5}s 78?(a) 500% (b) 750% (c) 2600%(d) 2500% (e) 1500%~RCC~Q8. $8.00 is 25% of what?(a) $32.00 (b) $12.00 (c) $72.5}00(d) $22.00 (e) $0~RCA~Q9. 18 is 150% of what number?(a) 100 (b) 10 (c) 15 (d) 12(e) 150~RCD~ET~ETCopyright5} ARROW INSTRUCTIONAL SYSTEMS` July 19836 (d) .06(e) .0006~RCA~Q2. Write 6.7% as a fraction.(a) 67/100 46A RATIO is another name for a divisionproblem.The RATIO of A to B means A/B or Adivided by B or A~B (read A to B).Exam9}ple~ 2ft.~3yd.` = 2ft.~9ft.` = 2~9 Ans.Note~ In RATIO proplems always comparelike measurements~RAA PRO9}PORTION is an equation of 2 equalratios. To solve a proportion crossmultiply and divide.Example~` x 8` - = --9}` 5 10` 10x = 40 cross multiply` x = 4 divide both sides by 10~RAThere are two types of proportions~DIR9}ECT proportions and INDIRECTproportions.DIRECT PROPORTIONS - as the firstquantity increases the secondincreases& or as t9}he first quantitydecreases the second decreases.Specific Cases~ Changing feet to miles£s to ounces& inches on a map 9}tomiles& cost of food - the more you haveof the first item the more you have ofthe second.~RAExample~ If a articles cost9} b cents&how many articles can you buy for$1.00?Note~ Unknown articles = y& $1.00 = 100cents.` DIRECT PROPORTI9}ON` articles cents` a b` - = ---` y 100` 9} by = 100a` y = 100/b articles~RAINVERSE PROPORTIONS - as the firstquantity increases the seconddecrease9}s& or as the first decreasesthe second increases. They vary inopposing direction.Specific Cases~ More people spendingtim9}e on a job - less time the jobtakes& the more pulleys - the lesseffort to raise a load& the more fuelefficient the car - t9}he less gas ituses.~RAExample~ If a supply of food will lastb boys& d days& then how long will itlast n boys?Note~ y =9} unknown boys. One fractionwill need to be INVERTED.`INVERSE PROPORTION`boys (not =) days boys days` b 9} d b y` - not = - use~ - = -` n y n d` n9}y = bd` y = bd/n` y = bd/n days Ans.~RAExample~ If n pads can be bought for$5& 9}how many pads can be bought for ddollars?y = the unknown pads` DIRECT PROPORTION` pads $` 9} n 5` - = -` y d` 5y = nd` dn` x = -- pads Ans.9}` 5~RAExample~ On a certain map& two townsare 2.5 inches apart. If the actualdistance is 20 miles& how m9}any incheson the map represent 1 mile of actualdistance.~RAy = unknown inches` DIRECT PROPORTION` map 9}(in) actual (miles)` 2.5 20` --- = --` y 1` 20y = 2.5` 9} 25` y = ---` 200` y = 1/8 mile Ans.~RAExample~ A sum of $600 is to be divide9}dinto 3 parts in the ratio 3~5~7. Findthe largest part.y = the common multiplier&` 3y = smallest part` 5y = seco9}nd part` 7y = largest partTherefore` 3y + 5y + 7y = 600` 15y = 600` y = 40` 7y = 7(40) = 9}$280 Ans.~RAExample~ A pulley having a 9} diameteris being driven at 1000 rpm. It isdesired to belt it to another pulley9}which is to run at 600 rpm. Find thediameter of the second pulley.` INVERSE PROPORTION` diameter (in.) rpm` 9} 9 600` - = ----` y 1000` 600y = 9000` y9} = 15 in. Ans.~RAExample~ If 10 men take 6 hours to do acertain job& how long would it take 12men to do the same jo9}b?y = unknown hours` INVERSE PROPORTION` men hours` 10 y` -- = -` 9} 12 6` 12y = 60` y = 5 hr. Ans.~ET~ET Adivided by B or A~B (read A to B).Exam8R~Q1. Find the ratio between 4 inches and1 yard?(a) 1/9 (b) 1/3 (c) 1/4 (d) 1/12(e) 1/5~RCA~Q2. A train travels 6=}/5 miles in 3minutes. How many miles will it travelin half an hour?(a) 6 (b) 11 (c) 15 (d) 12 (e) 10~RCD~Q3. Find =}the value of y if 4~3=y~9(a) 7 (b) 108 (c) 10 (d) 12 (e) 11~RCD~Q4. How many miles are there between 2cities if the=} distance is representedby a 1.9 inch line on a map having ascale of 1/5 inches to 14 miles?(a) 153 (b) 103 (c) 143 (d=}) 123(e) 133~RCE~Q5. How many cents will s books cost ify books cost b dollars?(a) sby/100 (b) 100sb/y (c) 100by/s=}(d) 100sy/y (e) bs - 100/y~RCB~Q6. If apples cost 3 for 60 cents& findthe cost of 2 2/3 dozen apples.(a) $64 (b) 640=} cents (c) 64 cents(d) 4 cents (e) 6.4 cents~RCB~Q7. If 12 tractors are needed to plow afield in 2 hours& how many tr=}actors areneeded to plow the field in one hour?(a) 24 (b) 12 (c) 18 (d) 9 (e) 14~RCA~Q8. A car that gets 14 miles p=}er gallonof gasoline can travel 290 miles on afull tank. If the same car got 28 milesper gallon& how many miles could itt=}ravel on a full tank?(a) 420 (b) 390 (c) 900 (d) 700(e) 580~RCE~Q9. If it takes 12 minutes to walk 3/4mile& how ma=}ny minutes will it take towalk the rest of the mile?(a) 3 (b) 2 (c) 4 (d) 5 (e) 1~RCC~Q10. If 9 inches of snow fall=} in 3hours& how much snow will fall in thenext 120 minutes at the same rate?(a) 0 (b) 4 (c) 7 (d) 6 (e) 5~RCD~ET~E=}TCopyright ARROW INSTRUCTIONAL SYSTEMS` July 1983/3 (c) 1/4 (d) 1/12(e) 1/5~RCA~Q2. A train travels 6<BWelcome to the MATH MODULE of theHAYDEN SCORE IMPROVEMENT SYSTEM FORTHE SAT& one of three modules designedto help you raiA}se your SAT scores.This Quantitative Comparisons And WordProblems Section is an effective toolto begin your preparation foA}r theMathematical section of the ScholasticAptitude Tests. The system is easy tooperate so that you can concentrate onitA}s content. All of the informationyou need to answer questions appearson the screen& as do instructions formoving from oneA} part of the program toanother. More detailed informationfollows in the User's Guide.~RAThe Quantitative Comparisons and A}WordProblems section provides reviewmaterial on the types of problemstypically in the Mathematical sectionof the SAT exclA}usive of Algebra andGeometry& which are included asseparate Sections in this Math Module.Quantitative comparisonproblems-A}-problems that emphasizereasoning skills used to determinewhich of two quantities islarger--improve skills in algebra andA}geometry as well as in other areas ofmathematics.~RAThis section includes ten parts inaddition to the User's Guide~` QuA}antitative Comparisons` Fractions and Decimals` Percentages` Ratios and Proportions` Graphs` Motion Problems` Mixture PA}orblems` Business and Work Problems` Sequences` Miscellaneous~RAThis Section contains a two-sided diskwhich has a ProgrA}am Disk side and aReview disk side. Always load theProgram Disk side first. Instructionson the screen will prompt you toA}insert the other side at theappropriate time.~RAMENUSThe MAIN MENU lets you move easilyfrom one section of the programA} toanother. Simply press the keycorresponding to the letter next tothe section you wish to see.~RASelecting an option fA}rom the Main Menudisplays a DETAIL MENU which offersyou the following options~A. Definitions& Analysis and` StrategiesA}B. Examples With TutormodeC. Examples Without Tutormode~RADEFINITIONS& ANALYSIS AND STRATEGIESshould be reviewed before gA}oing on tothe examples. It provides usefulstrategies for tackling the kinds ofquestions the subject covers. First&backgroA}und information on eachquestion type is presented& thenmethods for answering these questions&including valuable tricks andA} shortcuts& are demonstrated.~RAEXAMPLES WITH TUTORMODE is the core ofthe Hayden System. This option givesyou a detaileA}d& step-by-stepexplanation of how to arrive at thecorrect answer. By reviewing andpracticing& you develop more efficientA}problem-solving techniques.~RAEXAMPLES WITHOUT TUTORMODE providesquick drill and practice in areaswhere yoe are already sA}trong so thatyou can improve speed and accuracy. Ifyou answer incorrectly& you are shownthe correct answer& but no detaileA}dexplanation is provided. At the endof the section& the computer talliesthe number of questions answeredcorrectly and inA}correctly& providingan indication of how well you havemastered the material.~RAFUNCTION KEYSA function key is a key whiA}ch has aspecific effect on the program'soperation each time it is pressed.Whenever a menu is on your screen thefollowingA} function keys areoperational~` M (Main Menu)` Q (Quit)Pressing }M} always brings you back tothe MAIN MENU. PresA}sing }Q} causes thecomputer to ask if you really want toquit. If you answer }Y}& you end theprogram. If you answer }N}& yoA}ucontinue where you left off.~RAWhile text is on the screen pressing}R} restarts the section (erasing anyprevious answerA}s that you may haveentered)& pressing }M} takes you tothe last menu displayed and pressing}Q} enables you to quit.~RATheA} left-arrow key lets you pagebackwards through the text one screenat a time until the first screen ofthe section is reacheA}d. When aquestion appears on the screen& yourprevious answer& if any& is shown. Youcan replace that answer by enteringanoA}ther one& or you can leave youranswer undisturbed by pressing theleft-arrow again.~RAPressing the letter }O} leaves thecA}urrent question temporarilyunanswered and displays the nextquestion. At the end of the sectionyou have a chance to review A}all theunanswered questions.~ET~ETand displays the nextquestion. At the end of the sectionyou have a chance to review @'The HAYDEN SCORE IMPROVEMENT SYSTEMFOR THE SAT is organized into threemodules. It includes both simulatedSAT exams and coE}mplete reviews of theareas typically covered by the Verbaland Mathematical sections of the SAT.In addition to this Math MoE}dule& thefollowing modules are available:~RAThe PRACTICE TESTS MODULE includes anAnalysis of the SAT& a Pre-Test andtwo E}Practice Tests.The ANALYSIS OF THE SAT gives youinsight into the workings of theactual exam -- its organization andscoriE}ng& plus test-taking strategiesand tips for raising your scores.~RAThe PRE-TEST is adiagnostic/prescriptive tool fordeteE}rmining your strengths andweaknesses in the areas covered by theMathematical and Verbal sections ofthe SAT. It is a two-hoE}ur testconsisting of a mix of Math and Verbalquestions similar to that on an actualSAT. After you complete the test yourcE}omputer will provide scores in eachof sixteen subjects which contributeto your Math and Verbal scores. Thisprofile of yourE} performance indicateswhich additional modules in the HaydenSystem will be useful in yourpreparation.~RAThe PRACTICE TESE}TS are two-hoursimulated exams with completeMathematical and Verbal sections timedand formatted to be representative ofthE}e latest SATs and scored on the SATscale. After reviewing your weakareas& take these Practice Tests andsee how your perforE}mance would measureup on the actual exam.~RAThe VERBAL MODULE provides tutorials,drill and analysis in the verbal areasnE}ormally covered on the SAT.The VOCABULARY SECTION provides athorough review of antonyms& analogiesand sentence completionE}s& as well asan on-screen dictionary with 1000words.~RAThe READING COMPREHENSION SECTIONoffers strategies and practice iE}nresponding to questions about thematerial just read. Working withpassages drawn from the mostup-to-date sources in a varE}iety offields will help you improve yourability to determine main ideas& torecognize logical implications and toextract fE}actual information from whatyou read.~RAEach topic in a given section can beapproached in three ways~`acquiring backgroE}und with`DEFINITIONS& ANALYSIS AND STRATEGIES`gaining practice and instruction with`EXAMPLES WITH TUTORMODE`drilling wiE}th`EXAMPLES WITHOUT TUTORMODE~ET~ETEGIES`gaining practice and instruction with`EXAMPLES WITH TUTORMODE`drilling wiD)~Q1. Find the ratio between 10 inches and(1) one yard.(a) 5/9 (b) 1/2 (c) 5/18 (d) 5/8(e) 3/8~RCC1. (c) 5/18 Ans.N} Each of the questions in this section consist of two quantities& one in Column A and one in Column B. You are to compareI} the two quantities and choose the correct answer A if the quantity in A is greater; B if the quantity in B is greater; I}C if the two quantities are equal; D if the relationship cannot be determined from the information given. ~RA Notes~ I}1. In certain questions& information concerning one or both of the quantities to be compared is centered. 2. In a given I}question& a symbol that appears in both columns represents the same thing in Column A as it does in Column B. 3. LetterI}s such as k& n& and a stand for real numbers. ~RA ~Q ` COLUMN A COLUMN B 1. 1/y > 0 ` yI} -1 ~RCA ~Q ` COLUMN A COLUMN B ` 1 ` 1 - 1 1 2. - / 1 I} - x - ` y - y y ` y ~RCC ~Q ` COLUMN A COLUMN B ` I} 0.17 3. 0.85 ---- ` 2 ~RCA ~Q ` COLUMN A COLUMN B 4. I} 2 > a > -2 ` 1 > b > -2 ` a b ~RCD ~Q ` COLUMN A COLUMN B ` I} _ 5. (10)(7)(9)(8)(78)(\/2)(15) ` (24)(36)(100)(17)(4) ~RCA ~Q ` COLUMN A COLUMN I}B ` 0.8 1 6. --- --- ` 4 0.2 ~RCB ~Q ` COLUMN A COI}LUMN B ` 2 2 7. A /B = 1 ` 2 2 ` A B ~RCC ~Q ` I} COLUMN A COLUMN B ` ___ ` / 1 8. Reciprocal of 17 / I}--- ` \/ 289 ~RCC ~Q ` COLUMN A COLUMN B ` 2 2 9. k = 36 yI} = 49 ` k y ~RCD ~Q ` COLUMN A COLUMN B ` 1 1 ` - + -- ` 2 J} 2 ` x x x + 1 10. ------ ------ ` 1 2 ` 1 - -- x - 1 J}` 2 ` x ~RCB ~Q ` COLUMN A COLUMN B ` 0.39 11. .18 J} ---- ` 2 ~RCB ~Q ` COLUMN A COLUMN B 12. 2y - 3 = 5 + y ` y J} 2 ~RCA ~Q ` COLUMN A COLUMN B ` _ 13. y = \/2 ` y J} 1 ~RCD ~Q ` COLUMN A COLUMN B ` __ ` / 3 14. / -- 5 ` \/ 49 ~RCB ~Q ` J} COLUMN A COLUMN B ` 3 3 15. k = 64 y = 343 ` y k ~RCA ~ET ~EJ}T Copyright ARROW INSTRUCTIONAL SYSTEMS ` July 1983 y = 343 ` y k ~RCA ~ET ~EHENote~ Keep your units the same` 1 yard = 36 inches` 10 5` -- = -- Ans. when reduced` 36 18 N} to lowest terms~RA~Q2. Find the value of y& if` 4~a = y~b(a) 4b/a (b) 2b/a (c) b/a (d) ab(e) b/a~RCA2. N }(a) 4b/a Ans.Note~ Re-write in fraction form.` 4 y` - = -` a b` ya = 4b` y = N }4b/a Ans.~RA~Q3. How many miles are there between 2cities& if the distance is representedby a 1.2 inch line on a map havN }ing ascale of 1/3 inches to 6 miles?(a) 20 (b) 21 (c) 21.5 (d) 21.6(e) 15~RCD3. (d) 21.6 Ans.` DIRECT PRON }PORTION` actual (mi.) map (in.)` y 1.2` - = ---` 6 1/3` N } 1/3y = 7.2` 21.6 miles = y Ans.~RA~Q4. How many cents will r books cost ift books cost m dollars?(a)N} 50rm/t (b) 10rm/t (c) 100rm/t(d) rm/t (e) 1000rm/t~RCC4. (c) 100rm/t Ans.` m dollars = 100m cents` DN}IRECT PROPORTION` books cents` r y` - = ----` t 100m` N} ty = 100rm` y = 100rm/t cents Ans.~RA~Q5. If apples cost 2 for 50 cents& findthe cost of 1 2/3 dozen N}apples?(a) $4 (b) $8 (c) $9 (d) $10(e) $5~RCE5. (e) $5 Ans.Note~ Convert dozen into individualapples by multiplyiN}ng by 12.` 1 2/3 x 12 = 5/3 x 12` = 20 apples` 2 50` -- = --` 20 y` N} 2y = 1000` y = 500 cents or $5 Ans.~RA~Q6. If it takes 10 minutes to walk 4/5miles& how many minutes will it N}take towalk the rest of the mile?(a) 2 min (b) 4 min (c) 2.4 min(d) 2.5 min (e) 1 min~RCD6. (d) 2.5 min Ans.Note~N} Find the rest of the distance` 10 y` --- = ---` 4/5 1/5` 4/5y = 2` N} 4y = 10` y = 2.5 min. Ans.~RA~Q7. If 5 people paint a house in khours& how many hours will it take pN}people to do the same job?(a) pk/5 (b) pk (c) 0 (d) pk/1(e) k/5~RCA7. (a) pk/5 Ans.` INVERSE PROPORTION`N} people hours` 5 y` - = -` P k` py = 5k` N} y = 5k/y hrs. Ans.~RA~Q8. If 8 tractors are needed to plow afield in 6 hours& how many tractors areneeded tN}o plow the field in 3 hours?(a) 10 (b) 5 (c) 8(d) 12 (e) 16~RCE8. (e) 16 tractors Ans.` INVERSE PROPORTIN}ON` tractors hours` 8 3` - = -` y 6` 3y =N} 48` y = 16 tractors Ans.~RA~Q9. A car that gets 15 miles per gallonof gasoline can travel 270 miles oN}n afull tank. If the same car got 30 milesper gallon& how many miles could ittravel on a full tank?(a) 54 mi. (b) 540 mN}i. (c) 500 mi.(d) 520 mi. (e) 440 mi.~RCB9. (b) 540 mi. Ans.` DIRECT PROPORTION` mpg miles` N} 15 270` -- = ---` 30 y` 15y = 8100` y = 540 miles AnsN }.~ET~ET 15 270` -- = ---` 30 y` 15y = 8100` y = 540 miles AnsL -?:A d,7 A D:QUANT.BASPRRESCANF1F2F3FLINTTLTXDSSCSKTMCPPMERWRSRTSRSSWCP*