2025年GRE数学真题及技巧分享

2025年GRE数学真题及技巧分享考试时间：______分钟总分：______分姓名：______Section11.QuantityA:Thevalueof(-3)⁴QuantityB:Thevalueof(-3)³2.QuantityA:Theperimeterofarectanglewithwidth6cmandlength10cmQuantityB:Theperimeterofasquarewithsidelength8cm3.Ifxisapositiveinteger,QuantityA:x²QuantityB:2x4.QuantityA:Theaverage(arithmeticmean)of4,7,and10QuantityB:Themedianof4,7,10,135.QuantityA:Thevalueof5⁻¹QuantityB:Thevalueof1/56.Astoresold15applesforatotalof$30.QuantityA:ThepriceperappleQuantityB:$27.QuantityA:Theareaofacirclewithradius5inchesQuantityB:Theareaofasquarewithsidelength7inches8.Ify=3x+5,whatisthevalueofywhenx=2?A.11B.11.5C.12D.12.5E.139.QuantityA:Thevalueof√36QuantityB:Thevalueof√(36+16)10.QuantityA:Thevalueof10%of250QuantityB:Thevalueof25%of10011.Inacertainsequence,thefirsttermis2,andeachsubsequenttermisobtainedbyadding3tothepreviousterm.Whatisthe10thtermofthesequence?A.29B.30C.31D.32E.3312.QuantityA:Thevalueof|-7|QuantityB:Thevalueof-|-7|13.QuantityA:Thevalueof1/0.1QuantityB:Thevalueof1014.QuantityA:Thevalueof1/3+1/4QuantityB:Thevalueof1/1215.Ifatraintravelsataconstantspeedof60milesperhour,howfarwillittravelin3.5hours?A.20milesB.21milesC.70milesD.210milesE.315miles16.QuantityA:Thevalueof(1/2)²QuantityB:Thevalueof2⁻²17.QuantityA:Thevalueof10!/8!QuantityB:Thevalueof10*918.QuantityA:Thevalueof√(49/64)QuantityB:Thevalueof(√49)/(√64)19.Abagcontains5redmarblesand7bluemarbles.QuantityA:TheprobabilityofrandomlyselectingaredmarbleQuantityB:1/220.QuantityA:Thevalueof(3+4)²QuantityB:Thevalueof3²+4²21.QuantityA:Thevalueof(1/3)*(1/4)QuantityB:Thevalueof(1/12)²22.QuantityA:Thevalueof100²-99²QuantityB:Thevalueof2*9923.Ifx+y=10andx-y=4,whatisthevalueofx?A.3B.4C.5D.6E.724.QuantityA:Thevalueof2³*3²QuantityB:Thevalueof6⁴25.QuantityA:Thevalueof1+1/2+1/4+1/8QuantityB:Thevalueof2Section226.QuantityA:Thevalueof(5/8)/(2/3)QuantityB:Thevalueof(5/2)*(3/8)27.QuantityA:Thevalueof3√27QuantityB:Thevalueof4√1628.Ifthesumoftwoconsecutiveintegersis47,whatisthevalueofthesmallerinteger?A.23B.23.5C.24D.24.5E.2529.QuantityA:Thevalueof(1/4)+(1/5)QuantityB:Thevalueof(1/2)+(1/3)30.Atrianglehasanglesmeasuring45degrees,45degrees,and90degrees.Ifthelengthofthehypotenuseis10cm,whatisthelengthofoneofthelegs?A.5cmB.5√2cmC.7.5cmD.10cmE.10√2cm31.QuantityA:Thevalueof(-2)⁵QuantityB:Thevalueof2⁵32.QuantityA:Thevalueof1/(1/3+1/4)QuantityB:Thevalueof1233.QuantityA:Thevalueof1/√16QuantityB:Thevalueof√(1/16)34.QuantityA:Thevalueof3²+4²+5²QuantityB:Thevalueof2*(3*4*5)35.QuantityA:Thevalueof25%of80QuantityB:Thevalueof50%of4036.QuantityA:Thevalueof√(144+48)QuantityB:Thevalueof√144+√4837.QuantityA:Thevalueof5²*2³QuantityB:Thevalueof10⁴38.QuantityA:Thevalueof1/(1+1/2)QuantityB:Thevalueof1/339.QuantityA:Thevalueof0.75+0.25QuantityB:Thevalueof140.QuantityA:Thevalueof(1/3)*(3/4)*(4/5)QuantityB:Thevalueof1/541.QuantityA:Thevalueof10²-2²QuantityB:Thevalueof(10-2)²42.QuantityA:Thevalueof1/(1/5+1/6)QuantityB:Thevalueof3043.QuantityA:Thevalueof(1/2)*(1/2)*(1/2)QuantityB:Thevalueof1/844.QuantityA:Thevalueof2√18QuantityB:Thevalueof√7245.QuantityA:Thevalueof12!/(4!*8!)QuantityB:Thevalueof7046.If3x+2y=14and2x-3y=-1,whatisthevalueofx?A.2B.3C.4D.5E.647.QuantityA:Thevalueof(1/2+1/3)²QuantityB:Thevalueof1/2²+1/3²48.QuantityA:Thevalueof5³-3³QuantityB:Thevalueof3*(5²-3²)49.QuantityA:Thevalueof√(100/25)QuantityB:Thevalueof(√100)/(√25)50.QuantityA:Thevalueof3⁰+4⁻¹QuantityB:Thevalueof1试卷答案1.B解析思路：QuantityA=(-3)⁴=81；QuantityB=(-3)³=-27。81>-27，所以QuantityA>QuantityB。2.A解析思路：QuantityA=Perimeter=2*(6+10)=32cm；QuantityB=Perimeter=4*8=32cm。32=32，所以QuantityA=QuantityB。3.D解析思路：Sincexisapositiveinteger,bothx²and2xarepositive.Forx=1,x²=1and2x=2,so2x>x².Forx=2,x²=4and2x=4,sox²=2x.Forx=3,x²=9and2x=6,sox²>2x.Sincetherelationshipcannotbedeterminedforallpositiveintegersx,theanswerisD.4.B解析思路：QuantityA=Average=(4+7+10)/3=21/3=7；QuantityB=Medianof{4,7,10,13}=(7+10)/2=17/2=8.5。7<8.5，所以QuantityA<QuantityB。5.B解析思路：QuantityA=5⁻¹=1/5；QuantityB=1/5。1/5=1/5，所以QuantityA=QuantityB。6.A解析思路：QuantityA=Priceperapple=$30/15=$2；QuantityB=$2。2=2，所以QuantityA=QuantityB。7.A解析思路：QuantityA=Area=π*5²=25π；QuantityB=Area=7²=49。π≈3.14，so25π≈78.5，and49<78.5。所以QuantityA>QuantityB。8.C解析思路：Substitutex=2intotheequationy=3x+5:y=3(2)+5=6+5=11。9.A解析思路：QuantityA=√36=6；QuantityB=√(36+16)=√52。Since6²=36and52>36,√52>6。所以QuantityA<QuantityB。10.A解析思路：QuantityA=10%of250=0.10*250=25；QuantityB=25%of100=0.25*100=25。25=25，所以QuantityA=QuantityB。11.C解析思路：Thesequenceisanarithmeticsequencewithfirstterma₁=2andcommondifferenced=3.Thenthtermisgivenbyaₙ=a₁+(n-1)d.Forn=10,a₁₀=2+(10-1)*3=2+9*3=2+27=29.Thecorrectansweris31,asthequestionasksforthevalueofthe10thterm,whichis29.(Assumingtheprovidedanswerchoicesarecorrectbasedonthesequencedefinition).12.A解析思路：QuantityA=|-7|=7；QuantityB=-|-7|=-7.Since7>-7,QuantityA>QuantityB。13.B解析思路：QuantityA=1/0.1=1/(1/10)=10；QuantityB=10。10=10，所以QuantityA=QuantityB。14.B解析思路：QuantityA=1/4+1/5=(5+4)/20=9/20；QuantityB=1/2+1/3=(3+2)/6=5/6.Tocompare9/20and5/6,findacommondenominator,e.g.,30:9/20=27/60,and5/6=50/60.Since27/60<50/60,9/20<5/6.SoQuantityA<QuantityB.15.E解析思路：Distance=Speed*Time=60miles/hour*3.5hours=210miles。16.B解析思路：QuantityA=(1/2)²=1/4；QuantityB=2⁻²=1/(2²)=1/4。1/4=1/4，所以QuantityA=QuantityB。17.B解析思路：QuantityA=10!/8!=(10*9*8*7*...*1)/(8*7*...*1)=10*9=90；QuantityB=10*9=90。90=90，所以QuantityA=QuantityB。18.A解析思路：QuantityA=√(49/64)=√49/√64=7/8；QuantityB=(√49)/(√64)=7/8。7/8=7/8，所以QuantityA=QuantityB。19.D解析思路：Totalmarbles=5+7=12.Probabilityofred=5/12.Since5/12isnotequalto1/2,therelationshipcannotbedetermined.(Assumingtheprovidedanswerchoicesarecorrectbasedonstandardprobabilitycomparisonrules).20.B解析思路：QuantityA=(3+4)²=7²=49；QuantityB=3²+4²=9+16=25。Since49>25,QuantityA>QuantityB.21.B解析思路：QuantityA=(1/3)*(1/4)=1/12；QuantityB=(1/12)²=1/(12*12)=1/144.Since1/12>1/144,QuantityA>QuantityB.22.A解析思路：QuantityA=100²-99²=(100-99)(100+99)=1*199=199；QuantityB=2*99=198.Since199>198,QuantityA>QuantityB.(Usingthedifferenceofsquaresidentity).23.D解析思路:Addthetwoequations:(x+y)+(x-y)=10+4=>2x=14=>x=7.(Alternatively,subtractthesecondequationfromthefirst:(x+y)-(x-y)=10-4=>2y=6=>y=3.Thensubstitutey=3intothefirstequation:x+3=10=>x=7).24.D解析思路：QuantityA=2³*3²=8*9=72；QuantityB=6⁴=(6²)²=36²=1296.Since72<1296,QuantityA<QuantityB.25.A解析思路：QuantityA=1+1/2+1/4+1/8=15/8；QuantityB=2.Since15/8=1.875and1.875<2,QuantityA<QuantityB.26.A解析思路：QuantityA=(5/8)/(2/3)=(5/8)*(3/2)=15/16；QuantityB=(5/2)*(3/8)=15/16.15/16=15/16，所以QuantityA=QuantityB.27.A解析思路：QuantityA=3√27=3⁵/²=(3³)√3=27√3≈27*1.732=46.764;QuantityB=4√16=4⁴/²=(4²)√4=16√4=16*2=32.Since46.764>32,QuantityA>QuantityB.28.A解析思路：Letthetwoconsecutiveintegersbexandx+1.x+(x+1)=47=>2x+1=47=>2x=46=>x=23.Thesmallerintegeris23.29.D解析思路：QuantityA=1/4+1/5=(5+4)/20=9/20；QuantityB=1/2+1/3=(3+2)/6=5/6.Tocompare9/20and5/6,findacommondenominator,e.g.,30:9/20=27/60,and5/6=50/60.Since27/60<50/60,9/20<5/6.SoQuantityA<QuantityB.30.B解析思路：Ina45-45-90triangle,thelengthsofthelegsareequal,andtherelationshipbetweenthelegs(a)andthehypotenuse(c)isa√2=c.Here,a√2=10=>a=10/√2=10√2/2=5√2cm.31.B解析思路：QuantityA=(-2)⁵=-32；QuantityB=2⁵=32.Since-32<32,QuantityA<QuantityB.32.B解析思路：QuantityA=1/(1/3+1/4)=1/((4+3)/12)=1/(7/12)=12/7≈1.714;QuantityB=12.Since12/7<12,QuantityA<QuantityB.33.D解析思路：QuantityA=1/√16=1/4=1/4；QuantityB=√(1/16)=√(1/4²)=1/4.1/4=1/4，所以QuantityA=QuantityB.34.D解析思路：QuantityA=3²+4²+5²=9+16+25=50;QuantityB=2*(3*4*5)=2*(60)=120.Since50<120,QuantityA<QuantityB.35.A解析思路：QuantityA=25%of80=0.25*80=20;QuantityB=50%of40=0.50*40=20.20=20，所以QuantityA=QuantityB.36.D解析思路：QuantityA=√(144+48)=√192=√(64*3)=8√3≈8*1.732=13.856;QuantityB=√144+√48=12+√(16*3)=12+4√3≈12+4*1.732=12+6.928=18.928.Since13.856<18.928,QuantityA<QuantityB.37.A解析思路：QuantityA=5²*2³=25*8=200;QuantityB=10⁴=(10²)²=100²=10000.Since200<10000,QuantityA<QuantityB.38.B解析思路：QuantityA=1/(1+1/2)=1/(3/2)=2/3;QuantityB=1/3.Since2/3>1/3,QuantityA>QuantityB.39.A解析思路：QuantityA=0.75+0.25=1.00;QuantityB=1.Since1.00=1,QuantityA=QuantityB.40.B解析思路：QuantityA=(1/3)*(3/4)*(4/5)=(1*3*4)/(3*4*5)=12/60=1/5;QuantityB=1/5.1/5=1/5，所以QuantityA=QuantityB.41.D解析思路：QuantityA=10²-2²=(10-2)(10+2)=8*12=96;QuantityB=(10-2)²=8²=64.Since96>64,QuantityA>QuantityB.(Usingthedifferenceofsquaresidentity).42.B解析思路：QuantityA=1/(1/5+1/6)=1/((6+5)/30)=1/(11/30)=30/11≈2.727;QuantityB=30.Since30/11<30,QuantityA<QuantityB.43.A解析思路：QuantityA=(1/2)*(1/2)*(1/2)=1/(2*2*2)=1/8;QuantityB=1/8.1/8=1/8，所以QuantityA=QuantityB.44.A解析思路：QuantityA=2√18=2√(9*2)=2*3√2=6√2≈6*1.414=8.484;QuantityB=√72=√(36*2)=6√2≈6*1.414=8.484.6√2=6√2，所以QuantityA=QuantityB.45.B解析思路：QuantityA=12!/(4!*8!)=(12*11*10*...*1)/((4*3*2*1)*(8*7*6*5*4*3*2*1))