2026年GMAT數(shù)學(xué)難題解析及答案考試時(shí)長(zhǎng)：120分鐘滿分：100分班級(jí)：__________姓名：__________學(xué)號(hào)：__________得分：__________試卷名稱：2026年GMAT數(shù)學(xué)難題解析及答案考核對(duì)象：GMAT考試備考者、商科研究生入學(xué)考試應(yīng)考生題型分值分布：-判斷題（總共10題，每題2分）：總分20分-單選題（總共10題，每題2分）：總分20分-多選題（總共10題，每題2分）：總分20分-案例分析（總共3題，每題6分）：總分18分-論述題（總共2題，每題11分）：總分22分總分：100分---一、判斷題（每題2分，共20分）1.Ifxandyareintegersandxy=1,thenx=1andy=1.（如果x和y是整數(shù)且xy=1，那么x=1且y=1。）A.正確B.錯(cuò)誤2.Theequation|x-3|=4hasexactlytwosolutions.（方程|x-3|=4有且僅有兩個(gè)解。）A.正確B.錯(cuò)誤3.Asetofdatawithastandarddeviationof0mustcontainonlyoneelement.（標(biāo)準(zhǔn)差為0的數(shù)據(jù)集必須只包含一個(gè)元素。）A.正確B.錯(cuò)誤4.Ifatrianglehastwosidesoflengths5and12,thethirdsidemustbelessthan17.（如果一個(gè)三角形的兩邊長(zhǎng)度分別為5和12，第三邊必須小于17。）A.正確B.錯(cuò)誤5.Thesumoftheinterioranglesofahexagonis720degrees.（六邊形的內(nèi)角和為720度。）A.正確B.錯(cuò)誤6.Afunctionf(x)iseveniff(-x)=f(x)forallx.（函數(shù)f(x)是偶函數(shù)，如果對(duì)所有x都有f(-x)=f(x)。）A.正確B.錯(cuò)誤7.Themedianofadatasetisalwaysequaltoitsmean.（數(shù)據(jù)集的中位數(shù)總是等于其均值。）A.正確B.錯(cuò)誤8.Ifaandbarepositiveintegers,thena+bisalwaysgreaterthana2+b2.（如果a和b是正整數(shù)，那么a+b總是大于a2+b2。）A.正確B.錯(cuò)誤9.Theprobabilityofrollingasumof7withtwofairsix-sideddiceis1/6.（用兩個(gè)公平的六面骰子擲出點(diǎn)數(shù)和為7的概率是1/6。）A.正確B.錯(cuò)誤10.TheareaofacirclewithradiusrisgivenbytheformulaA=πr2.（半徑為r的圓的面積由公式A=πr2給出。）A.正確B.錯(cuò)誤---二、單選題（每題2分，共20分）1.If3x+7=22,whatisthevalueofx?（如果3x+7=22，x的值是多少？）A.5B.6C.7D.82.Whichofthefollowingisafactorof120?（以下哪個(gè)是120的因數(shù)？）A.11B.13C.15D.173.Iff(x)=x2-4x+3,whatisf(2)?（如果f(x)=x2-4x+3，f(2)的值是多少？）A.1B.3C.5D.74.Theaverageofthefirstfivepositiveintegersis:（前五個(gè)正整數(shù)的平均值是：）A.2.5B.3C.3.5D.45.Aboxcontains5redballs,4blueballs,and3greenballs.Iftwoballsaredrawnatrandomwithoutreplacement,whatistheprobabilitythatbothballsarered?（一個(gè)盒子中有5個(gè)紅球、4個(gè)藍(lán)球和3個(gè)綠球。如果隨機(jī)抽取兩個(gè)球且不放回，兩個(gè)球都是紅色的概率是多少？）A.5/36B.10/36C.15/36D.20/366.Theslopeofthelinepassingthroughthepoints(2,3)and(5,11)is:（通過(guò)點(diǎn)(2,3)和(5,11)的直線的斜率是：）A.2B.3C.4D.57.Ifa=2andb=3,whatisthevalueofa3+b3?（如果a=2且b=3，a3+b3的值是多少？）A.35B.36C.37D.388.Thevolumeofacubewithedgelength4is:（邊長(zhǎng)為4的立方體的體積是：）A.16B.24C.32D.649.IftheprobabilityofeventAis0.6andtheprobabilityofeventBis0.3,whatistheprobabilityofbotheventsoccurringifAandBareindependent?（如果事件A的概率是0.6，事件B的概率是0.3，如果A和B獨(dú)立，兩個(gè)事件同時(shí)發(fā)生的概率是多少？）A.0.18B.0.24C.0.3D.0.910.Theequationofalinewithslope3andy-intercept-2is:（斜率為3且y軸截距為-2的直線方程是：）A.y=3x-2B.y=-3x+2C.y=3x+2D.y=-3x-2---三、多選題（每題2分，共20分）1.Whichofthefollowingarefactorsof72?（以下哪些是72的因數(shù)？）A.3B.4C.6D.8E.92.Ifx2-5x+6=0,whatarethepossiblevaluesofx?（如果x2-5x+6=0，x的可能值是什么？）A.2B.3C.-2D.-3E.03.Thefollowingfunctionsareeven:（以下函數(shù)是偶函數(shù)：）A.f(x)=x2B.f(x)=cos(x)C.f(x)=x3D.f(x)=|x|E.f(x)=sin(x)4.Thefollowingexpressionsareequivalentto(x+2)(x-2):（以下表達(dá)式與(x+2)(x-2)等價(jià)：）A.x2-4B.x2+4C.x2-2x+4D.x2-4x+4E.x?-165.Thefollowingstatementsaretrueabouttriangles:（以下關(guān)于三角形的陳述是正確的：）A.Thesumoftheanglesinatriangleis180degrees.B.Anequilateraltrianglehasthreeequalsides.C.Anisoscelestrianglehastwoequalsides.D.Arighttrianglehasone90-degreeangle.E.Atrianglecanhavetwoobtuseangles.6.Thefollowingarepropertiesofthemedianofadataset:（以下是對(duì)數(shù)據(jù)集的中位數(shù)的性質(zhì)：）A.Itisalwaystheaverageofthetwomiddlenumbers.B.Itisthemiddlenumberwhenthedatasethasanoddnumberofelements.C.Itisthelargestnumberinthedataset.D.Itisnotaffectedbyoutliers.E.Itisalwaysgreaterthanthemean.7.ThefollowingarevalidprobabilitydistributionsfortwoeventsAandB:（以下是對(duì)兩個(gè)事件A和B的有效概率分布：）A.P(A)=0.5,P(B)=0.3,P(A∩B)=0.1B.P(A)=0.7,P(B)=0.4,P(A∩B)=0.2C.P(A)=0.6,P(B)=0.5,P(A∩B)=0.3D.P(A)=0.4,P(B)=0.6,P(A∩B)=0.1E.P(A)=0.8,P(B)=0.2,P(A∩B)=0.58.Thefollowingarepropertiesofacircle:（以下是對(duì)圓的性質(zhì)：）A.Allradiiareequal.B.Thediameteristwicetheradius.C.ThecircumferenceisgivenbyC=2πr.D.TheareaisgivenbyA=πr2.E.Thetangentatanypointisperpendiculartotheradiusatthatpoint.9.Thefollowingarevalidsolutionstotheequation|x|=3:（以下是對(duì)方程|x|=3的有效解：）A.x=3B.x=-3C.x=0D.x=6E.x=-610.Thefollowingarepropertiesofasquare:（以下是對(duì)正方形的性質(zhì)：）A.Allsidesareequal.B.Allanglesare90degrees.C.Thediagonalsareequal.D.Thediagonalsbisecttheangles.E.TheareaisgivenbyA=s2,wheresisthesidelength.---四、案例分析（每題6分，共18分）1.CaseStudy:DataAnalysisAcompanycollectedthefollowingdailysalesdataoveraweek:50,60,70,80,90,100,110.a.Calculatethemeanandmedianofthedataset.b.Whatistherangeofthedataset?c.Ifthecompanywantstoincreasetheaveragesalesby10units,howmanyadditionalunitsmustbesolddailyonaverage?2.CaseStudy:ProbabilityAbagcontains4redballs,3blueballs,and2greenballs.Twoballsaredrawnatrandomwithoutreplacement.a.Whatistheprobabilitythatbothballsarered?b.Whatistheprobabilitythatoneballisredandoneballisblue?c.Whatistheprobabilitythatatleastoneballisgreen?3.CaseStudy:GeometryArighttrianglehaslegsoflengths6cmand8cm.a.Whatisthelengthofthehypotenuse?b.Whatistheareaofthetriangle?c.Ifthetriangleisinscribedinacircle,whatistheradiusofthecircle?---五、論述題（每題11分，共22分）1.Topic:FunctionsandTheirPropertiesExplainthefollowingpropertiesoffunctions:domain,range,andinjectivity.Provideexamplesoffunctionsthatdemonstrateeachproperty.Discusshowthesepropertiesarerelevantinreal-worldapplications,suchaseconomicsorphysics.2.Topic:StatisticsandDecisionMakingDescribetheimportanceofmean,median,andmodeindataanalysis.Provideascenariowherethemeanisthemostappropriatemeasureofcentraltendencyandanotherwherethemedianismoresuitable.Discussthelimitationsofusingonlyonemeasureofcentraltendencyandhowcombiningthemcanprovideamorecomprehensiveunderstandingofthedata.---標(biāo)準(zhǔn)答案及解析---一、判斷題1.B.錯(cuò)誤（xy=1時(shí)，x和y可以是1和1，也可以是-1和-1，或任何非零數(shù)的倒數(shù)對(duì)。）2.A.正確（|x-3|=4有兩個(gè)解：x=7和x=-1。）3.B.錯(cuò)誤（標(biāo)準(zhǔn)差為0時(shí)，所有數(shù)據(jù)元素相同，但數(shù)據(jù)集可以包含多個(gè)元素。）4.A.正確（三角形不等式：第三邊長(zhǎng)度必須小于兩邊之和且大于兩邊之差，即5+12>第三邊>12-5，即17>第三邊>7。）5.A.正確（六邊形內(nèi)角和為(6-2)×180=720度。）6.A.正確（偶函數(shù)定義：f(-x)=f(x)對(duì)所有x成立。）7.B.錯(cuò)誤（中位數(shù)是排序后中間的數(shù)，均值是所有數(shù)的和除以數(shù)量。只有當(dāng)數(shù)據(jù)對(duì)稱時(shí)，兩者相等。）8.B.錯(cuò)誤（例如a=1,b=1時(shí)，a+b=2,a2+b2=2，兩者相等。）9.A.正確（擲兩個(gè)六面骰子點(diǎn)數(shù)和為7的組合有(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)，共6種，概率為6/36=1/6。）10.A.正確（圓的面積公式為A=πr2。）---二、單選題1.B.6（3x+7=22→3x=15→x=5。）2.C.15（120的因數(shù)有1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120。）3.A.1（f(2)=22-4×2+3=4-8+3=1。）4.C.3.5（(1+2+3+4+5)/5=15/5=3。）5.A.5/36（P(第一球紅)=5/12,P(第二球紅|第一球紅)=4/11→5/12×4/11=20/132=5/36。）6.C.4（(11-3)/(5-2)=8/3=4/1.5=4。）7.A.35（a3+b3=(2+3)×(22-2×3+32)=5×(4-6+9)=5×7=35。）8.D.64（43=64。）9.A.0.18（P(A∩B)=P(A)P(B)=0.6×0.3=0.18。）10.A.y=3x-2（斜率截距式：y=mx+b，m=3,b=-2。）---三、多選題1.A,B,C,D（72的因數(shù)有1,2,3,4,6,8,9,12,18,24,36,72。）2.A,B（x2-5x+6=(x-2)(x-3)→x=2,3。）3.A,B,D（f(x)=x2,cos(x),|x|是偶函數(shù)；f(x)=x3,sin(x)是奇函數(shù)。）4.A,E（(x+2)(x-2)=x2-4,x?-16=(x2-4)(x2+4)。）5.A,B,C,D（三角形內(nèi)角和為180度；等邊三角形三邊相等；等腰三角形兩邊相等；直角三角形有一個(gè)90度角。）6.A,B,D（中位數(shù)是中間數(shù)或平均中間兩數(shù)；奇數(shù)個(gè)元素時(shí)中位數(shù)是中間數(shù)；中位數(shù)不受極端值影響。）7.A,B,D（概率非負(fù)且≤1，且P(A∩B)≤P(A),P(B)。）8.A,B,C,D,E（圓的性