加拿大研究生留學考試如何攻克數(shù)學應用題中的長難句

　　GRE和GMAT數(shù)學考試中經常會有人因為題目中的一些詞語表達或者復雜的句式結構而理解錯或者讀不懂題目，下面總結了數(shù)學考試中經常會出現(xiàn)的一些詞語、短語以及復雜句式，幫助大家掃除應用題中的理解障礙。加拿大GRE

　　常見數(shù)學詞語和數(shù)學表達的轉換

　　Addition:increased by number;combined;together;total of;sum;added to;and;plus

　　Subtraction:decreased by;minus;less;difference between/of;less than;fewer than;minus;subtracted from；other than

　　Multiplication:of;times;multiplied by;product of;increased/decreased by+factor or percent

　　Equals:is;are;was;were;will be;gives;yields;sold for;has;costs;adds up to;the same as;as much as

　　Division:per;out of;ratio of;quotient of;percent(divide by 100);divided by;each

　　'per'means'divided by'

　　'a'sometimes means'divided by'

　　y is 3 less than x:

　　y=x–3

　　the ratio of x and y

　　x:y

　　the difference of x and y

　　x–y

　　需要特別注意的詞語

　　1.Fraction of

　　what fraction of a is b轉換成數(shù)學表達是b/a（記住是后面除以前面）

　　If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair,what fraction of those who do not have brown hair have red hair?

　　A.1/4

　　B.4/11

　　C.4/9

　　D.5/9

　　E.4/5

　　Solution：

　　red hairnot brown hair

　　=20%45%

　　=4/9

　　選C

　　2.Other than

　　除了（指包含了這些對象在內）

　　In 1993 the average(arithmetic mean)price per card for all greeting cards old was$1.25.For which of the following occasions was the umber f cards sold in 1993 less than the total number of cards sold that year for occasions other than the ten occasions shown?

　　Indicate all such occasions.

　　A.Christmas

　　B.Valentine’s Day

　　C.Easter

　　D.Mother’s Day

　　E.Father’s Day

　　F.Graduation

　　G.Thanksgiving

　　H.Halloween

　　Solution：

　　根據(jù)左邊的圖可以知道所有場合售出的卡片總數(shù)大約為5.6/1.25=4.48 billion張

　　根據(jù)右邊表格，10個場合的卡片數(shù)量為3.9 billion張。

　　問題問的是，除了這十種場合之外，還賣出了多少張卡片？

　　除上述十種場合外的卡片銷售量：4.48-3.9=0.58 billion張

　　問比0.58 billion少的，注意單位換算，billion和million差1000倍

　　所以比0.58billion少的是除了2.4billion和900million的剩余所有

　　3.Proportional

　　Month

　　Number of days worked

　　June

　　20

　　July

　　17

　　August

　　19

　　The table above shows the number of days worked by a certain sales representative in each of three months last year.If the number of sales calls that the representative made each month was proportional to the number of days worked in that month and if the representative made a total of 168 sales calls in the three months shown,how many sales calls did the representative make in August? 加拿大GMAT

　　(A)50

　　(B)51

　　(C)56

　　(D)57

　　(E)60

　　Solution：

　　proportion：

　　number of sales callshe number of days worked

　　=168（20+17+19）

　　=3

　　所以8月的number of sales callshe number of days worked也是3，那么8月的的number of sales calls=19*3=57

　　The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present.If the concentration of chemical B is increased by 100 percent,which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

　　(A)100%decrease

　　(B)50%decrease

　　(C)40%decrease

　　(D)40%increase

　　(E)50%increase

　　4.Number是數(shù)字還是數(shù)量

　　number既有數(shù)字也有數(shù)量的意思，很多人數(shù)學題做錯就是因為把意思弄錯了

　　Quantity A The number of primes that are divisible by 9

　　Quantity B The number of primes that are divisible by 19

　　A.Quantity A is greater.

　　B.Quantity B is greater.

　　C.The two quantities are equal.

　　D.The relationship cannot be determined from the information given

　　Solution：

　　這里的number是數(shù)量的意思，Quantity A，能夠被9整除的質數(shù)不存在，所以number是0

Quantity B，能夠被19整除的質數(shù)有1個，就是19本身，所以number是0，答案選B

加拿大研究生留學考試如何攻克數(shù)學應用題中的長難句

　　需要特別注意的表達

　　1.成對出現(xiàn)的詞：

　　看到add去找to，add后面的數(shù)值+and后面的數(shù)值

　　看到of去找and，of后面的數(shù)值+（或者-，x，÷）and后面的數(shù)值

　　看到ratio of去找to，ratio of后面的數(shù)值÷to后面的數(shù)值

　　Before being simplified,the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average(arithmetic mean)of 100 units of Country R's currency and 1 percent of one's annual income.Which of the following represents the simplified formula for computing the income tax,in Country R's currency,for a person in that country whose annual income is I?

　　(A)50+I/200

　　(B)50+3I/100

　　(C)50+I/40

　　(D)100+I/50

　　(E)100+3I/100

　　Solution：

　　Income tax

　　=2%income+average

　　=2%income+（100+1%x annual income）/2

　　=2%I+（100+1%I）/2

　　=50+I/40

　　The number of stamps that Kaye and Alberto had were in the ratio 5:3,respectively.After Kaye gave Alberto 10 of her stamps,the ratio of the number Kaye had to the number Alberto had was 7:5.As a result of this gift,Kaye had how many more stamps than Alberto?

　　(A)20

　　(B)30

　　(C)40

　　(D)60

　　(E)90

　　2.倍數(shù)表達

　　很多人剛剛接觸數(shù)學容易把英文中的倍數(shù)關系理解錯了

　　比如A is 5 times as many as B不是5A=B（?），而是A=5B

　　At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors.What is the ratio of the number of history majors to the number of mathematics majors?

　　(A)6 to 1

　　(B)3 to 2

　　(C)2 to 3

　　(D)1 to 5

　　(E)1 to 6

　　Solution：

　　English=2 History

　　English=3 Maths

　　所以2History=3Maths

　　History to Maths=3 to 2，選B

　　復雜的句子結構

　　1.平行結構

　　At a certain supplier,a machine of type A costs$20,000 and a machine of type B costs$50,000.Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time.If the finance charges are equal to 40 percent of the remainder of the cost,how much less would 2 machines of type A cost than 1 machine of type B under this arrangement? 學在加拿大

　　(A)$10,000

　　(B)$11,200

　　(C)$12,000

　　(D)$12,800

　　(E)$13,200

　　Solution：

　　purchasing price

　　=down payment+（remainder of cost+finance charges）

　　=down payment+（remainder of cost+40%remainder of cost）

　　=down payment+（1+40%）x remainder of cost

　　=20%cost+140%x 80%cost

　　=1.32 cost

　　Price A：1.32x20,000

　　Price B：1.32x 50,000

　　B-2A

　　=1.32x 50,000-2x1.32x20,000

　　=13,200

　　For every order,a certain mail-order company charges a shipping fee of$3 plus an additional$2 if the value of the order is over$50 but not over$100 or an additional$3 if the value of the order is over$100.How much greater are the total shipping fees for 2 orders of$75 each than the total shipping fee for 1 order of$150?

　　(A)$1

　　(B)$2

　　(C)$3

　　(D)$4

　　(E)$5

　　2.限定性定語從句

　　限定性定語從句就是that前面沒有逗號的句子，注意在理解的時候應該先去理解that后面的意思

　　A certain business produced x rakes each month from November through February and shipped 0.5x rakes at the beginning of each month from March through October.The business paid no storage costs for the rakes from November through February,but it paid storage costs of$0.10 per rake each month from March through October for the rakes that had not been shipped.In terms of x,what was the total storage cost,in dollars,that the business paid for the rakes for the 12 months from November through October?

　　(A)0.40x

　　(B)1.20x

　　(C)1.40x

　　(D)1.60x

　　(E)3.20x

　　Solution：

　　Nov-feb生產的rakes是4x

　　三月的儲存費用(4x-x/2)*0.10

　　四月的儲存費用(4x-x/2-x/2)*0.10

　　根據(jù)規(guī)律可以算出總的費用

　　[(4x-x/2)+(4x-x/2*2)+........+(4x-x/2*8)]*0.10

　　=[4x*8-x/2(1+2....+8)]*0.10

　　=[32x-x/2*(4.5*8)]*0.10

　　=[32x-18x]*0.10

　　=14x*0.10x

　　=1.40x

　　選C

　　Alice's take-home pay last year was the same each month,and she saved the same fraction of her take-home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save.If all the money that she saved last year was from her take-home pay,what fraction of her take-home pay did she save each month?

　　(A)1/2

　　(B)1/3

　　(C)1/4

　　(D)1/5

　　(E)1/6

　　3.比較結構

　　看到比較結構去找more/less和than，找到比較對象分別是什么

　　On July 1 of last year,the total number of employees at Company E was decreased by 10 percent.Without any change in the salaries of the remaining employees,the average(arithmetic mean)employee salary was 10 percent more after the decrease in number of employees than before the decrease.The total of the combined salaries of all of the employees at Company E after July 1 last year was what percent of that before July 1 last year?

　　(A)90%

　　(B)99%

　　(C)100%

　　(D)101%

　　(E)110%

　　Solution：

　　Before the decrease：

　　假設有a個employees

　　average salary是b

　　TOTAL payroll=ab

　　After the decrease：

　　employees數(shù)量變成0.9a

　　Average salary變成1.1b

　　TOTAL payroll=0.9a*1.1b=0.99ab

　　The total of the combined salaries of all the employees at Company E after July 1 last year was what percent of that before July 1 last year? 加拿大研究生留學考試

　　0.99ab/ab=99%，選B

　　At the end of the first quarter,the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year.At the end of the second quarter,the share price was 50 percent higher than it was at the beginning of the year.What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?

　　(A)20%

　　(B)25%

　　(C)30%

　　(D)33%

　　(E)40%