GMAT数学考试中余数精讲.doc

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1、Introduction  (赶时间的童鞋可以略过。。。只是一些概念帮助童鞋们回忆余数~~~)DefinitionIfxandyarepositiveintegers,thereexistuniqueintegersqandr,calledthequotientandremainder,respectively,suchthaty=divisor*quotient+remainder=xq+r;and0<=r

2、ince15=6*2+3.Noticethat0<=r

3、enasmallerintegerisdividedbyalargerinteger,thequotientis0andtheremainderisthesmallerinteger.Forexample,7dividedby11hasthequotient0andtheremainder7since7=11*0+7Thepossibleremainderswhenpositiveintegeryisdividedbypositiveintegerxcanrangefrom0tox-1.Forexample,possibleremaind

4、erswhenpositiveintegeryisdividedby5canrangefrom0(whenyisamultipleof5)to4(whenyisonelessthanamultipleof5).Ifanumberisdividedby10,itsremainderisthelastdigitofthatnumber.Ifitisdividedby100thentheremainderisthelasttwodigitsandsoon.Forexample,123dividedby10hastheremainder3and1

5、23dividedby100hastheremainderof23.1.  CollectionofMethodsMethod1：小数法（妹纸自己取的名字，包括后面的方法也都是妹纸取的~欢迎讨论）AwaythattheGMATwilltestremaindersiswhatyouwouldtypicallyjustdividebackintotheproblemtodeterminethedecimals:25/4=6remainder1Dividethat1backby4toget0.25,sotheansweris6.25.Anynu

6、mberwitharemaindercouldbeexpressedasadecimal.Theremainderprovidesthedataafterthedecimalpoint,andthequotientgivesyouthenumbertotheleftofthedecimalpoint.Considerthisproblem(whichappearscourtesyofGMAC):Example： Whenpositiveintegerxisdividedbypositiveintegery,theremainderis9.

7、Ifx/y=96.12,whatisthevalueofy?(A)96   (B)75   (C)48   (D)25   (E)12Sol：Goingbacktotheconceptoftheremainder,theremainderof9iswhatwillgiveusthat0.12afterthedecimalplace.Theanswertothedivisionproblemx/yiseither:96remainder9Or96.12Therefore,whentheremainderof9isdividedbackove

8、ry,weget0.12.Mathematically,thismeansthat:9/y=0.120.12y=912y=900y=900/12y=300/4y= 75Thecorrectan