2025年經(jīng)企管理研究生入學(xué)考試（GMAT）定量推理真題卷2025年經(jīng)企管理研究生入學(xué)考試（GMAT）定量推理真題卷

姓名：______班級(jí)：______學(xué)號(hào)：______得分：______

（考試時(shí)間：90分鐘，滿分：100分）

**一、問(wèn)題解決（共5題，每題2分，共10分）**

1.If3x+4y=17andx=3,whatisthevalueofy?

2.Astoresold1200itemsinaweek.Ifthenumberofitemssoldeachdaywas20%morethanthepreviousday,howmanyitemsweresoldonthefirstday?

3.Atrianglehastwosidesoflengths5cmand7cm.Iftheperimeterofthetriangleis18cm,whatisthelengthofthethirdside?

4.Ifa=2andb=3,whatisthevalueofa2+b2?

5.Acartravelsataconstantspeedof60km/h.Howfarwillittravelin3hours?

**二、數(shù)據(jù)充分性分析（共5題，每題3分，共15分）**

6.Isx>5?

(1)x2>25

(2)x+3>8

7.Ifaandbareintegers,isabanevennumber?

(1)aiseven

(2)bisodd

8.Istheaverageof5numbersgreaterthan10?

(1)Thesumofthe5numbersis50

(2)Thelargestnumberis15

9.Inaclassof30students,isthemedianheightgreaterthan160cm?

(1)Theaverageheightis165cm

(2)Therangeofheightsis20cm

10.Ifarectanglehasaperimeterof30cm,whatisitsarea?

(1)Thelengthoftherectangleis10cm

(2)Thewidthoftherectangleis5cm

**三、圖表分析（共3題，每題4分，共12分）**

11.Refertothefollowingbargraphshowingmonthlysales(inthousandsofdollars)foracompanyover6months:

|Month|Sales|

|-------|-------|

|Jan|20|

|Feb|25|

|Mar|30|

|Apr|22|

|May|28|

|Jun|35|

Whatistheaveragesalesforthe6months?

12.Alinegraphshowsthepriceofastockover5years.Ifthestockpriceincreasedby20%fromYear1toYear2,andthendecreasedby30%fromYear2toYear3,whatwasthestockpriceinYear3ifitwas$100inYear1?

13.Refertothefollowingpiechartshowingthedistributionofemployeesinacompanybydepartment:

|Department|Percentage|

|-----------|-----------|

|HR|15%|

|Marketing|25%|

|Finance|30%|

|IT|20%|

|Other|10%|

Ifthereare200employees,howmanyemployeesworkintheFinancedepartment?

**四、文字描述問(wèn)題（共3題，每題5分，共15分）**

14.Afactoryproduces1000unitsofaproductin8hours.Iftheproductionrateincreasesby25%,howmanyunitscanbeproducedin6hours?

15.Amixturecontains30%salt.If20litersofthemixtureisreplacedwithpurewater,whatisthenewconcentrationofsaltinthemixture?

16.Aprojectrequires3workerstocompleteitin10days.If2additionalworkersarehired,howmanydayswillittaketocompletetheproject?

**五、綜合推理（共2題，每題10分，共20分）**

17.Aboxcontains4redballs,3blueballs,and2greenballs.Iftwoballsaredrawnatrandomwithoutreplacement,whatistheprobabilitythatbothballsarered?

18.Acompanyofferstwosalaryplans:

-PlanA:$50,000basesalary+10%commission

-PlanB:$60,000basesalary+5%commission

AfterhowmanysaleswouldtheearningsfromPlanAbeequaltotheearningsfromPlanB,assumingthesamenumberofsales?

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（以下為剩余題目，因字?jǐn)?shù)限制分批輸出）

**六、代數(shù)方程（共3題，每題5分，共15分）**

19.Solveforx:2x+5=3x-7

20.Ifa=2bandb=3c,whatisthevalueofaintermsofc?

21.Aquadraticequationhasroots4and-2.Whatistheequation?

**七、幾何問(wèn)題（共3題，每題5分，共15分）**

22.Acirclehasaradiusof5cm.Whatistheareaofthecircle?

23.Asquarehasadiagonalof10cm.Whatistheperimeterofthesquare?

24.Inarighttriangle,thelegsare6cmand8cm.Whatisthelengthofthehypotenuse?

**八、概率與組合（共2題，每題5分，共10分）**

25.Afairdieisrolledtwice.Whatistheprobabilityofrollingasumof7?

26.Howmanywayscanacommitteeof3peoplebeformedfromagroupof5people?

**九、數(shù)列與級(jí)數(shù)（共2題，每題5分，共10分）**

27.Thefirsttermofanarithmeticsequenceis3,andthecommondifferenceis2.Whatisthe10thterm?

28.Whatisthesumofthefirst20termsofthegeometricsequencewithafirsttermof2andacommonratioof3?

**十、應(yīng)用題（共2題，每題5分，共10分）**

29.Atraintravels400kmin5hours.Whatisitsaveragespeed?

30.Ifthecostofaproductis$20,anditissoldata25%markup,whatisthesellingprice?

**十一、邏輯推理（共1題，10分）**

31.Ifallstudentspasstheexam,thentheteacherwillbehappy.Iftheteacherishappy,thenshewillgiveabonus.Didtheteachergiveabonusif80%ofthestudentspassedtheexam?

**十二、數(shù)據(jù)分析（共1題，10分）**

32.Adatasethasthefollowingvalues:5,7,7,9,10.Whatisthevarianceofthedataset?

**十三、函數(shù)問(wèn)題（共1題，10分）**

33.Iff(x)=x2-4x+3,whatisthevalueoff(2)?

**十四、數(shù)論問(wèn)題（共1題，10分）**

34.Findthesmallestpositiveintegerthatisdivisiblebyboth12and18.

**十五、綜合應(yīng)用（共1題，10分）**

35.Abusinessinvests$10,000atanannualinterestrateof5%.After3years,howmuchinterestisearnediftheinterestiscompoundedannually?

**七、幾何問(wèn)題（共3題，每題5分，共15分）**

22.Acirclehasaradiusof5cm.Whatistheareaofthecircle?

23.Asquarehasadiagonalof10cm.Whatistheperimeterofthesquare?

24.Inarighttriangle,thelegsare6cmand8cm.Whatisthelengthofthehypotenuse?

**八、概率與組合（共2題，每題5分，共10分）**

25.Afairdieisrolledtwice.Whatistheprobabilityofrollingasumof7?

26.Howmanywayscanacommitteeof3peoplebeformedfromagroupof5people?

**九、數(shù)列與級(jí)數(shù)（共2題，每題5分，共10分）**

27.Thefirsttermofanarithmeticsequenceis3,andthecommondifferenceis2.Whatisthe10thterm?

28.Whatisthesumofthefirst20termsofthegeometricsequencewithafirsttermof2andacommonratioof3?

**十、應(yīng)用題（共2題，每題5分，共10分）**

29.Atraintravels400kmin5hours.Whatisitsaveragespeed?

30.Ifthecostofaproductis$20,anditissoldata25%markup,whatisthesellingprice?

**十一、邏輯推理（共1題，10分）**

31.Ifallstudentspasstheexam,thentheteacherwillbehappy.Iftheteacherishappy,thenshewillgiveabonus.Didtheteachergiveabonusif80%ofthestudentspassedtheexam?

**十二、數(shù)據(jù)分析（共1題，10分）**

32.Adatasethasthefollowingvalues:5,7,7,9,10.Whatisthevarianceofthedataset?

**十三、函數(shù)問(wèn)題（共1題，10分）**

33.Iff(x)=x2-4x+3,whatisthevalueoff(2)?

**十四、數(shù)論問(wèn)題（共1題，10分）**

34.Findthesmallestpositiveintegerthatisdivisiblebyboth12and18.

**十五、綜合應(yīng)用（共1題，10分）**

35.Abusinessinvests$10,000atanannualinterestrateof5%.After3years,howmuchinterestisearnediftheinterestiscompoundedannually?

**十六、線性方程組（共2題，每題5分，共10分）**

36.Solvethesystemofequations:

2x+3y=12

4x-y=5

37.IfthecostfunctionofaproductisC(x)=50x+2000andtherevenuefunctionisR(x)=80x,whatisthebreak-evenpoint?

**十七、三角函數(shù)（共1題，10分）**

38.Aladderisleaningagainstawall.Iftheladderis10meterslongandthebaseis6metersawayfromthewall,whatistheanglebetweentheladderandtheground?

**十八、數(shù)列應(yīng)用（共1題，10分）**

39.ThesumofthefirstntermsofanarithmeticsequenceisgivenbyS(n)=n2+2n.Findthefirsttermandthecommondifference.

**十九、概率應(yīng)用（共1題，10分）**

40.Abagcontains5redmarbles,3bluemarbles,and2greenmarbles.Ifthreemarblesaredrawnatrandomwithoutreplacement,whatistheprobabilityofdrawingexactly2redmarbles?

**二十、統(tǒng)計(jì)問(wèn)題（共1題，10分）**

41.Asampleof10studentshasheightsincm:160,165,170,155,162,168,170,160,165,158.Whatistheinterquartilerange(IQR)oftheheights?

**二十一、函數(shù)與導(dǎo)數(shù)（共1題，10分）**

42.Iff(x)=3x2-2x+1,findthederivativef'(x)andevaluateitatx=2.

**二十二、數(shù)論進(jìn)階（共1題，10分）**

43.Provethat30isamultipleof5usingthedefinitionofdivisibility.

**二十三、幾何綜合（共1題，10分）**

44.Arectanglehasaperimeterof30cmandanareaof50cm2.Findthelengthsofthesides.

**二十四、概率組合（共1題，10分）**

45.Inagroupof10people,howmanywayscanacommitteeof4beformedif2specificpeoplemustbeincluded?

**二十五、應(yīng)用經(jīng)濟(jì)（共1題，10分）**

46.Acompany'sprofitfunctionisP(x)=-x2+20x-100.Whatisthemaximumprofitandthecorrespondingnumberofunitssold?

**一、問(wèn)題解決答案**

1.y=2

2.600items

3.5cm

4.13

5.180km

**二、數(shù)據(jù)充分性分析答案**

6.E(Statementsalonearenotsufficient)

7.E(Statementsalonearenotsufficient)

8.E(Statementsalonearenotsufficient)

9.E(Statementsalonearenotsufficient)

10.B(Statement2aloneissufficient)

**三、圖表分析答案**

11.27.5thousanddollars

12.$140

13.60employees

**四、文字描述問(wèn)題答案**

14.1250units

15.20%

16.6days

**五、綜合推理答案**

17.6/35

18.1000sales

**六、代數(shù)方程答案**

19.x=12

20.a=6c

21.x2-2x-8=0

**七、幾何問(wèn)題答案**

22.78.5cm2

23.40cm

24.10cm

**八、概率與組合答案**

25.1/6

26.10ways

**九、數(shù)列與級(jí)數(shù)答案**

27.21

28.1048576

**十、應(yīng)用題答案**

29.80km/h

30.$25

**十一、邏輯推理答案**

31.No

**十二、數(shù)據(jù)分析答案**

32.9.2

**十三、函數(shù)問(wèn)題答案**

33.1

**十四、數(shù)論問(wèn)題答案**

34.36

**十五、綜合應(yīng)用答案**

35.$762.88

**十六、線性方程組答案**

36.x=3,y=2

37.50units

**十七、三角函數(shù)答案**

38.36.87°

**十八、數(shù)列應(yīng)用答案**

39.Firstterm=2,commondifference=2

**十九、概率應(yīng)用答案**

40.10/21

**二十、統(tǒng)計(jì)問(wèn)題答案**

41.11cm

**二十一、函數(shù)與導(dǎo)數(shù)答案**

42.f'(x)=6x-2,f'(2)=10

**二十二、數(shù)論進(jìn)階答案**

43.30=6*5,and6isaninteger,so30isdivisibleby5.

**二十三、幾何綜合答案**

44.5cm,10cm

**二十四、概率組合答案**

45.30ways

**二十五、應(yīng)用經(jīng)濟(jì)答案**

46.Maximumprofit=$150at10unitssold

**知識(shí)點(diǎn)分類和總結(jié)**

1.**算術(shù)與代數(shù)**

-基本運(yùn)算：加、減、乘、除

-代數(shù)方程：一元一次、一元二次方程求解

-數(shù)列：等差數(shù)列、等比數(shù)列的通項(xiàng)公式與求和公式

-不等式：解不等式與充分性判斷

2.**幾何**

-平面幾何：三角形（邊長(zhǎng)、角度、面積）、四邊形（矩形、正方形、平行四邊形）、圓（半徑、直徑、面積、周長(zhǎng)）

-立體幾何：體積、表面積計(jì)算

-幾何綜合：結(jié)合代數(shù)與幾何問(wèn)題的實(shí)際應(yīng)用

3.**概率與統(tǒng)計(jì)**

-概率：古典概率、條件概率、組合概率

-統(tǒng)計(jì)：均值、中位數(shù)、方差、標(biāo)準(zhǔn)差、四分位距（IQR）

-數(shù)據(jù)分析：圖表解讀、數(shù)據(jù)趨勢(shì)分析

4.**函數(shù)**

-代數(shù)函數(shù)：線性函數(shù)、二次函數(shù)、多項(xiàng)式函數(shù)

-函數(shù)性質(zhì)：?jiǎn)握{(diào)性、極值、導(dǎo)數(shù)應(yīng)用

-函數(shù)應(yīng)用：實(shí)際問(wèn)題的函數(shù)建模

5.**數(shù)論**

-基本概念：整除、最大公約數(shù)（GCD）、最小公倍數(shù)（LCM）

-進(jìn)階數(shù)論：同余、素?cái)?shù)判斷

6.**應(yīng)用題**

-經(jīng)濟(jì)學(xué)應(yīng)用：成本、收入、利潤(rùn)分析

-現(xiàn)實(shí)問(wèn)題：行程問(wèn)題、工程問(wèn)題、投資問(wèn)題

**各題型所考察學(xué)生的知識(shí)點(diǎn)詳解及示例**

**一、問(wèn)題解決**

-考察點(diǎn)：基本算術(shù)運(yùn)算與代數(shù)應(yīng)用

-示例：

-3x+4y=17,x=3→3(3)+4y=17→9+4y=17→4y=8→y=2

**二、數(shù)據(jù)充分性分析**

-考察點(diǎn)：信息充分性判斷，需要結(jié)合兩個(gè)條件才能得出結(jié)論

-示例：

-Isx>5?

(1)x2>25→x>5orx<-5→Insufficient

(2)x+3>8→x>5→Sufficient

→CorrectanswerisB(Statement2aloneissufficient)

**三、圖表分析**

-考察點(diǎn)：從圖表中提取數(shù)據(jù)并進(jìn)行分析

-示例：

-Bargraphofmonthlysales→Averagesales=(20+25+30+22+28+35)/6=170/6=27.5

**四、文字描述問(wèn)題**

-考察點(diǎn)：應(yīng)用數(shù)學(xué)模型解決實(shí)際應(yīng)用問(wèn)題

-示例：

-Productionrateincreasesby25%→Newrate=1000/8*1.25=1250unitsin6hours

**五、綜合推理**

-考察點(diǎn)：復(fù)雜概率與組合問(wèn)題

-示例：

-Drawing2redmarblesfromabag→P(R,R,B)=(5/10)*(4/9)*(3/8)+(5/10)*(3/9)*(4/8)+(3/10)*(5/9)*(4/8)=10/45=2/9→Totalprobability=6/35

**六、代數(shù)方程**

-考察點(diǎn)：一元一次與一元二次方程求解

-示例：

-2x+5=3x-7→5+7=3x-2x→x=12

**七、幾何問(wèn)題**

-考察點(diǎn)：平面幾何計(jì)算

-示例：

-Circlearea=π*52=78.5cm2

-Rectangleperimeter→2(5+10)=30cm→Solving2(l+w)=30andlw=50→l=5,w=10

**八、概率與組合**

-考察點(diǎn)：基本概率與組合計(jì)算

-示例：

-Rollingasumof7withtwodice→(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)→6/36=1/6

**九、數(shù)列與級(jí)數(shù)**

-考察點(diǎn)：等差數(shù)列與等比數(shù)列計(jì)算

-示例：

-Arithmeticsequence→a?=3,d=2→a??=3+2(10-1)=21

-Geometricsequence→a?=2,r=3→S??=2(32?-1)/(3-1)=1048576

**十、應(yīng)用題**

-考察點(diǎn)：實(shí)際問(wèn)題的數(shù)學(xué)建模

-示例：

-Trainspeed=400/5=80km/h

-Markupprice=20*1.25=$25

**十一、邏輯推理**

-考察點(diǎn)：條件推理與邏輯判斷

-示例：

-Ifallpass→happy→bonus→80%pass→notallpass→nobonus

**十二、數(shù)據(jù)分析**

-考察點(diǎn)：統(tǒng)計(jì)量計(jì)算

-示例：

-Variance=[(5-8)2+(7-8)2+(7-8)2+(9-8)2+(10-8)2]/5=9.2

**十三、函數(shù)問(wèn)題**

-考察點(diǎn)：函數(shù)值計(jì)算

-示例：

-f(x)=x2-4x+3→f(2)=22-4(2)+3=1

**十四