加拿大研究生留学考试如何攻克数学应用题中的长难句

加拿大研究生留学考试如何攻克数学应用题中的长难句

　　GRE和GMAT数学考试中经常会有人因为题目中的一些词语表达或者复杂的句式结构而理解错或者读不懂题目，下面总结了数学考试中经常会出现的一些词语、短语以及复杂句式，帮助大家扫除应用题中的理解障碍。加拿大GRE

　　常见数学词语和数学表达的转换

　　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

　　需要特别注意的词语

　　1.Fraction of

　　what fraction of a is b转换成数学表达是b/a（记住是后面除以前面）

　　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

　　选C

　　2.Other than

　　除了（指包含了这些对象在内）

　　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：

　　根据左边的图可以知道所有场合售出的卡片总数大约为5.6/1.25=4.48 billion张

　　根据右边表格，10个场合的卡片数量为3.9 billion张。

　　问题问的是，除了这十种场合之外，还卖出了多少张卡片？

　　除上述十种场合外的卡片销售量：4.48-3.9=0.58 billion张

　　问比0.58 billion少的，注意单位换算，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是数字还是数量

　　number既有数字也有数量的意思，很多人数学题做错就是因为把意思弄错了

　　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：

　　这里的number是数量的意思，Quantity A，能够被9整除的质数不存在，所以number是0

Quantity B，能够被19整除的质数有1个，就是19本身，所以number是0，答案选B

加拿大研究生留学考试如何攻克数学应用题中的长难句

　　需要特别注意的表达

　　1.成对出现的词：

　　看到add去找to，add后面的数值+and后面的数值

　　看到of去找and，of后面的数值+（或者-，x，÷）and后面的数值

　　看到ratio of去找to，ratio of后面的数值÷to后面的数值

　　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.倍数表达

　　很多人刚刚接触数学容易把英文中的倍数关系理解错了

　　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，选B

　　复杂的句子结构

　　1.平行结构

　　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? 学在加拿大

　　(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.限定性定语从句

　　限定性定语从句就是that前面没有逗号的句子，注意在理解的时候应该先去理解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生产的rakes是4x

　　三月的储存费用(4x-x/2)*0.10

　　四月的储存费用(4x-x/2-x/2)*0.10

　　根据规律可以算出总的费用

　　[(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

　　选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.比较结构

　　看到比较结构去找more/less和than，找到比较对象分别是什么

　　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：

　　假设有a个employees

　　average salary是b

　　TOTAL payroll=ab

　　After the decrease：

　　employees数量变成0.9a

　　Average salary变成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? 加拿大研究生留学考试

　　0.99ab/ab=99%，选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%