2025年GRE数学算术真题解析

2025年GRE数学算术真题解析考试时间：______分钟总分：______分姓名：______Section11.If3x+7=16,whatisthevalueofx?2.Thesumoftwoconsecutiveintegersis47.Whatisthesmallerinteger?3.Aboxcontains12redmarbles,8bluemarbles,and5greenmarbles.Ifamarbleisdrawnatrandom,whatistheprobabilitythatitisnotblue?4.Evaluate:(1/3+1/4)*125.Whichofthefollowingisequalto25%of144?A)36B)40C)45D)606.Convert0.625toafractioninsimplestform.7.Ifatraintravelsataspeedof60milesperhour,howfarwillittravelin3.5hours?8.Arectanglehasalengthof12cmandawidthof5cm.Whatisitsperimeter,incentimeters?9.Thepriceofabookis$18.Ifitisdiscountedby25%,whatisthesaleprice?10.Whichofthefollowingnumbersisdivisiblebyboth3and5?A)30B)45C)56D)7211.Findtheleastcommonmultiple(LCM)of6and9.12.Simplify:|-7|-|-3|13.Ify=3x-5andx=2,whatisthevalueofy?14.Amixturecontainswaterandalcoholintheratio3:2.Ifthereare15litersofwaterinthemixture,howmanylitersofalcoholarethere?15.Whatis30%of80?16.Iftheareaofasquareis81squareunits,whatisthelengthofitsside?17.Divide:(5/8)/(2/3)18.Acartraveled300milesusing15gallonsofgas.Howmanymilespergallondidthecarget?19.Findtheabsolutevalue:|-12-5|20.Whichofthefollowingfractionsisgreaterthan1/2?A)1/3B)3/5C)2/5D)1/4Section221.If4x-7=11,whatisthevalueof2x?22.Theaverage(arithmeticmean)offivenumbersis10.Iffourofthenumbersare8,9,10,and12,whatisthefifthnumber?23.Abagcontains10redballsand15whiteballs.Ifaballisdrawnatrandomandnotreplaced,whatistheprobabilityofdrawingaredballfollowedbyawhiteball?24.Evaluate:(3/4-1/8)*1625.Whatis120%of50?26.Convert5/8toadecimal.27.Abustravels240kilometersin4hours.Whatisitsaveragespeedinkilometersperhour?28.Theperimeterofaregularhexagonis42cm.Whatisthelengthofoneside?29.Theoriginalpriceofashirtis$24.Itisonsalefor30%off.Whatisthediscountamount?30.Whichofthefollowingintegersisaprimenumber?A)21B)29C)35D)4931.Findthegreatestcommondivisor(GCD)of18and24.32.Simplify:3*|-4|+5*|2|33.If4x+5y=20andx=1,whatisthevalueofy?34.Inaclassof30students,18areboys.Whatfractionofthestudentsaregirls?35.Whatis5%of$100?36.Ifthesidelengthofacubeis3cm,whatisthevolumeofthecubeincubiccentimeters?37.Multiply:(2/3)*(3/5)*(5/4)38.Amotorcycletraveled180milesusing6gallonsofgas.Howmanymilespergallondidthemotorcycleget?39.Findtheabsolutevalue:|8+2|40.Whichofthefollowingexpressionshasavaluelessthan-5?A)-8+3B)-3*4C)5/-1D)-1-6试卷答案1.32.233.8/254.75.C6.5/87.210miles8.34cm9.$13.5010.A11.1812.413.114.10liters15.2416.9units17.15/1618.20milespergallon19.1720.B21.922.1123.3/2624.525.6026.0.62527.60km/h28.7cm29.$7.2030.B31.632.2233.334.3/535.$5.0036.27cubiccm37.1/638.30milespergallon39.1040.B每道题解析思路1.Subtract7frombothsides:3x=9.Divideby3:x=3.2.Letthesmallerintegerben.Thenthelargerisn+1.n+(n+1)=47.2n+1=47.2n=46.n=23.Thesmallerintegeris23.3.Totalmarbles=12+8+5=25.Probability(notblue)=1-Probability(blue)=1-(8/25)=17/25.Alternatively,Probability(notblue)=(12+5)/25=17/25.4.Findacommondenominatorforthefractions:(4/12+3/12)*12=(7/12)*12=7.5.25%=1/4.(1/4)*144=144/4=36.6.0.625=625/1000.Simplifybydividingnumeratoranddenominatorby125:5/8.7.Distance=Speed*Time=60miles/hour*3.5hours=210miles.8.Perimeter=2*(Length+Width)=2*(12cm+5cm)=2*17cm=34cm.(Note:Thepromptaskedforcm,calculationyields34cm,finalansweris34).9.Discountamount=25%of$18=(1/4)*18=$4.50.Saleprice=Originalprice-Discountamount=$18-$4.50=$13.50.Alternatively,Saleprice=75%of$18=(3/4)*18=$13.50.10.30isdivisibleby3(3+0=3,sumdivisibleby3)andby5(endsin0).45isdivisibleby3(4+5=9,sumdivisibleby3)andby5(endsin5).56isdivisibleby3(5+6=11,notdivisibleby3)butnotby5.72isdivisibleby3(7+2=9,sumdivisibleby3)butnotby5.Only30fitsbothcriteria.11.Multiplesof6:12,18,24,30,...Multiplesof9:9,18,27,36,...TheLCMis18.12.|-7|=7.|-3|=3.7-3=4.13.Substitutex=2intotheequation:y=3(2)-5=6-5=1.14.Letthetotalpartsbe3+2=5.Ifwateris3parts,alcoholis2parts.Ifwater=15liters,then1part=15liters/3=5liters.Alcohol=2parts*5liters/part=10liters.15.30%of80=(30/100)*80=(3/10)*80=3*8=24.16.Letsidelengthbes.Area=s^2.s^2=81.s=√81=9units.17.Dividingfractionsisthesameasmultiplyingbythereciprocal:(5/8)/(2/3)=(5/8)*(3/2)=(5*3)/(8*2)=15/16.18.Milespergallon=Totalmiles/Totalgallons=300miles/15gallons=20milespergallon.19.|-12-5|=|-17|=17.20.A)1/3≈0.333.B)3/5=0.6.C)2/5=0.4.D)1/4=0.25.3/5isgreaterthan1/2.21.Add7tobothsides:4x=18.Divideby4:x=18/4=9/2=4.5.Thevalueof2xis2*(9/2)=9.22.Sumoffivenumbers=Average*Count=10*5=50.Sumofthefourgivennumbers=8+9+10+12=39.Thefifthnumber=Totalsum-Sumoffournumbers=50-39=11.23.Probability(Redfirst)=10/(10+15)=10/25.Probability(Whitesecond|Redfirst)=15/(25-1)=15/24.Probability(RedthenWhite)=(10/25)*(15/24)=(2/5)*(5/8)=10/40=1/4.Alternatively,usingcombinations:Totalways=C(25,2).WaystogetRedthenWhite=C(10,1)*C(15,1).Probability=[C(10,1)*C(15,1)]/C(25,2)=(10*15)/[25*24/2]=(150/600)=1/4.24.Findacommondenominatorforthefractions:(6/8-1/8)*16=(5/8)*16=5*(16/8)=5*2=10.25.120%=120/100=1.2.1.2*50=60.26.5/8=5÷8=0.625.27.Averagespeed=Totaldistance/Totaltime=240km/4hours=60km/h.28.Perimeter=6*sidelength.42=6*sidelength.Sidelength=42/6=7cm.29.Discountamount=30%of$24=(30/100)*24=0.3*24=$7.20.(Note:Thepromptaskedforamount,calculationyields$7.20,finalansweris$7.20).30.Primenumbershaveonlytwodistinctpositivedivisors:1andthemselves.21=3*7.29isonlydivisibleby1and29.35=5*7.49=7*7.Only29isprime.31.Factorsof18:1,2,3,6,9,18.Factorsof24:1,2,3,4,6,8,12,24.TheGCDis6.32.|-4|=4.|2|=