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# GRE数学易错题

1. l1, l2 and l3 are three lines in space

The number of points at The number of points at which lines l1 and l2 intersect which lines l2 and l3 intersect

1。三條任意直線，L1和L2的交點的個數與L2和L3的交點的個數沒關。

2. The number of 1/4-inch lengths in 1

a 4-inch length

2，是問4英尺中有多少個1/4英尺，應該是16個，所以是A

3. The maximun number of solid cubes 4

having edges of length 1/2 meter that

can be placed inside a cubical box

having inside edges of length 1 meter

3邊長為1的立方體裡最多能放下幾個邊長為1/2的立方體，當然是8個咯

4. Cube C has volume 8 cubic centimeters

The area of one of the faces of cube C 3 square centimeters

4立方體體積是8，那一個面的面積當然是4咯

5. Ms.Smith got an 8 percent cost-of-living raise of \$20 per week

Ms.Smith's new weekly salary \$260

5 x*0.08=20，那x+20=270>260

6. On a certain number live, if -7 is a distance of 4 from n and 7 is a distance of 18

from n then n=

A.25 B.11 C.3 D.-3 E-11

6應該是-11

7. For all real numbers a and b. if a?b=a(a+b), then a?(a?b)=

A. a2+ab B a2+ab+a C a2+a+b D a3+a2b E a3+a2b+a2

7新定義的運算a?b=a(a+b), 那a?(a?b)=a?(aa+ab)=a(a+aa+ab)=aa+aaa+aab

8.secretary typed 6 letters,each of which had either 1 or 2 pages.If the secretary typed 10 pages in all, how many of the letters had 2 pages?

A 1 B 2 C 3 D 4 E 5

9 how many of the five numbers above are each equal to the product of an integer and an odd integer that greater than 1?

a.none b.one c.two d.there e.four

10 這句話大家看該怎樣列式子呢?這是一道圖表題.

what was the approximate percent increase in personal income from 1965 to 1970? 是這樣(1970-1965)/1965還是(1970-1965)/1970這樣?

1 the sum of two numbers, x and y, equals twice their products. if x=3, what is the value of y? 這道題沒大看懂?請問大家是這樣麼?x+y=2(x+y)

x+y=2xy,求y.

2 if x is an integer and x2(x的平方)<37,what is the greatest possible value of x minus the least possible value of x?

a.5 b.6 c.10 d.12 e.36

3 三角形ABC，角B＝X度，X>90 度，比較三角形的周長與3倍AC的長度的大小，答案是B AC是最大邊,所以AB+BC+AC<AC+AC+AC(3AC).

2.0<p<1

4 for the line with equation y=ax+b,the x-intercept os twice the y-intercept

5 a certain moneymarket account that had a balance of \$48000 during all of last monthearned \$360 in interest for the month. at what simple annual interestrate did the account earn interest last month?

360*12/48000=9%

6 Of the positive integers that are multiples of 30 and are less than or equal to 360,what fraction are multiples of 12?

a.1/6 b.1/5 c.1/3 d.2/5 e.1/2

7 A certain teacher has a total ofat least 110 students enrolled in her classes.if the teachers has anaverage (arithmetic mean) of exactly 27 students enrolled per class.what is the least possible number of classes that the teacher couldhave?

a.3 b.4 c.5 d.6 e.7

the delivery charges for x shipments weighing a combimed total of the pounds vs 567.00

9 the cost per gram of carrots if 3 cans of carrots cost \$0.90 the costper gram of onions if 5 cans of onions cost \$1.50

10 X is an integer, and the remainder when 2X is divided by 4 is 0.

The remainder when X is divided by 4 0

1 Let[X]=3, if X is an odd integer;

let[X]=6, if X is an even integer.

r and s are integers, 3r is odd and 5+s is odd.

[r]

[s]

3r是奇數說明r為奇數，所以[r]等於3，5+s為奇數，說明s為偶數，所以[s]=6

2 the value of the units' digit in 6^47(6的47次方) the value of the units' digit in 5^77(5的77次方)

3 for all numbers r and s, where s/=(不等於)0, r#s=10r/s.

0.01#0.01 1

0.01#0.01=10*0.01/0.01=10,大於1.

4 1<n<5,n is an integer.

the sum of the first n odd integers that are greater than zero n^2(n平方)-1

5 a^7+a^15 a^8+a^14

=(a^7-a^14)(a-1)

6 A total of \$480 is ina certain cash register. All of the money is in one-dollar and five-dollar bills, and there are 30 more one-dollar bills than five-dollar bills.

The sum of 30 and the number of five-dollar bills in the cash register 105

let x be the number of one-dollar bill y be the number of five-dollar bill

x+5y=480-----1

x=y+30--------2

subsitute 2 in to 1

6y = 450

so y=75

30+75=105

7 If N is an integer, then the units digit of N平方 cannot be

a 0

b 2

c 4

d 5

e 6

8 the value of the units' digit in 6的47次方 the value of the units' digit in 5的77次方 哪個大呀？這種題怎麼做呀？

6的多少次方個位數都為6，5的多少次方個位數都為5.所以前面大於後面。選A。

9 two successive discounts of 20percent and 40percent are equavilent tp a single discount of X percent.

X 52

X = 100 - 48 = 52

10.已知：y=x^2-16x+64

y=(x-8)^2,所以y的最小值為0.

1 比較"The remainder when a positive odd integer divided by 2"和"The remainder when a positive even integer is divided by 2"

2 If x,y,and z are consecutive positive integers, with x<y<z and x+y+z an even number, which of the following could be the value of z?

A.1 B.2 C.4 D.5 E.8

even是偶數的意思，三個連續的整數相加為偶數，則中間的書必為偶數，兩邊的就為奇數了。所以選D。

3 In a group of 80 students,24 are enrolled in geometry , 40 in biology, and 20 in both. If a student were randomly selected from the 80 students, What is the probability that the strdent selected would NOT be enrolled in either course?

4 triangular garden ABC is redesigned by increasing the length of AC by 20 percent to point C' and

decreasing the length of AB by 20 percent to B'.

the area of the original garden ABC the area of the redesigned garden AB'C'

5 一個三角形的三邊分別是11，5，13，怎麼判斷13的邊所對的角是鈍角？

Rectangle R has an area of 60 square units and a perimeter of 64 units. The length of the shortest side of R is x and the length of the longest side of R is y.

xy=60

x+y=32.得出：x=30,y=2和x=2,y=30.因為y大於x，所以x=2,y=30

6 Each of the following numbers has two digits blotted out.Which of the numbers could be the numbers of hours in x days, Where x is an integer?

a.25*,*06

b.50*,*26

c.56*,*02

d.62*,*50

e.65*,*20

P.S. * 代表blotted digit

7 Three solid cubes of lead, each with edges 10 centimeters long, are melted together in a level, rectangular-shaped pan.The base of the pan has inisde dimesions of 20 centimeters by 30 centimeters, and the pan is 15 centimeters deep.If the volume of the solid lead is approximately the same as the volume of the melted lead,approximately how many centimeters deep is the melted lead in the pan? 這道題實在沒大看懂,盼望牛人解釋...

8 On Elm Street are 6 houses on oneside of the street and 4 houses on the other.Each pair of houses on Elm Street is connected by exactly one telephone line.

The total number of each lines that connect houses on opposite sides of Elm Street 12 這道題我是思÷這麼想的:(6-1)+(4-1)=8 而答案選的是A.

10 三角形RST is isosceles and 角RST=40

1 d=5.03894,and e is the decimal expression for d rounded to the nearest thousandth.

The number of terms of S that are odd The number of terms of S that are even

n為奇數時，S序列中奇數數量多於偶數。

3 ab>0

(a^2+b^2)/a+b a+b (a^2+b^2)/a+b=a+b-2ab/a+b

4 圖畫不出來。。一個三角型，2條邊為X，一條邊為Y，邊Y上的高把三角形分成兩半，問一半的面積和xy/4，哪個大？

(答案是xy/4大）

5 The water level in a tank is lowered by 6 inches, then raised by 8 inches, and then lowered by 4 inches. If the water level was x inches before the changes in level, which of the following represents the water level, in inches, after the changes?

a. X-1.5 B.X+1.5 C.X-6.5 D. X+6.5 E. X-18.5

6 If the cube of n is 180 greater than the square of n, then n=?

A. 10 B.9 C.8 D.7 E. 6

n三次方值比n平方值大180，如果解不出來，一個個帶入就行了。

7 一個邊長為3 feet 的立方體頂面ABCD由對角線AC將立方體分開兩個相等的部分，問分開的一部分每個面的總面積和36 square feet 之間的大小？答案為：Ａ，但是我算出來應該是相等？？

5 個面， 應該是大於36， 有一邊是3sqrt(2)

8 A certain five-number committee must be assembled form a pool of 5 women---A,B,C,D,E, and three men—X,Y,Z, what is the probability that the committee will include B,C,E,Y and Z?

A.1/30 B. 1/25 C.2/35 D. 1/15 E.3/32

9 Diane completed each of her exercise in 25 seconds and rested for 55 seconds between the exercise sets.

What is the ratio of the amount of time it took her to complete an exercise set to the amount of time she rested between the sets?

(A)5:6

(B) 5:11

(C) 6:11

(D) 11:5

(E) 11:6

25/55=5/11

10 Which of the following CANNOT be a factor of 2^i*3^j where i and jare positive integers?

(A)6

(B)8

(C) 27

(D) 42

(E) 54

1.

5 is 1/5 of x

2.

The circle above with center O has a radius of 5

3 which of the following points（x,y）is not on the graph of y<2x?

A.(-3,-7) B.(3,3) C.(2,-9) D.(2,2) E.(2,5)

4 A bicycle registration costs \$2.5 in city x and \$3.0in city y.At these rate, the cost of 4 registration in city x is k percent of the cost of 3 registration in city y

k 90

the y-intercept of k 2

6 When it was found that 150 more tickets for the school play were sold than the seating capacity of the auditorium.It was decided to have two performances.If the total number of tickets sold was equal to the total number who attended and if the auditorium was 2/3 full for each of the two performances, what is the seating capacity of the auditorium?

A.100 B.200 C. 225 D.300 E.450

7 the total area of 18 nonoverlapping circular regions,each having a diameter of 2 inches 36 square inches

8 the scores reported for a certain mutip;e-choice test were derived by subtracting 1/3 of the number of wrong answers from the number of right answers .On a 40 question test,if none of the questions was omitted and the score reported was 20. how many wrong answers was there? 5 10 15 25 30 選c

9 The tenths digit of .....是指十位數嗎?

The tenths digit of為十分位，即小數點後第一位。

10 Olive oil, vinegar, and water were combined to make 10 cups of salad dressing. The oil and vinegar were mixed in the ratio of 2 parts oil to 3 parts vinegar.

10. The number of cups 5

of water used in the

1 A candy assortment consists of seven flavors of chocolate-coveredcreams packed in two-layered boxes with 27 creams in each layer. Theflavors are always packed in rows so that the flavor varies with eachpiece in the following order, vanilla, orange, cherry, vanilla,raspberry, lime, pecan, cherry, lemon. How many chocolate-coveredvanilla creams are needed to pack 200 boxes of the assortment?

(A) 600

(B) 1,200

(C) 1,800

(D) 2,400

(E) 3,600

3x+1 ; 4x

. (注,答案是無法比較大小)

3x+1-4x=1-x，說明x<1時答案為A，x=1時答案為C，x>1時答案為B

4

X＞1, Y＞1

(注,答案是無法比較大小)

5 S is the set of all fractions of the form n/n+1,

where n is a positive integer less than 20.

The product of all the 1/20

fractions that are in S

6 A retail business has determined that its net

income, in terms of x, the number of items

sold, is given by the expression x2+x-380. （第一項是x的平方）

The number of items 10

that must be sold for

the net income to be

zero

7 w, x, y, and z are consecutive positive integers and w<x<y<z.

The remainder when (w+x)(x+y)(y+z) 1

8 新東方數學黃皮書的section65中的第9題

the three small rectangles have the same dimensions, ps/rs 是否 大於 1/2？

2/3，大於1/2

9When 9 students took a zoology quiz with a possible score of 0 to 10,inclusive, there average (arithmetic

mean) score was 7.5. If a tenthstudent takes the same quiz, what will be the least possible averagescore on the quiz for

all 10 students?

(A) 6.5

(B) 6.75

(C) 7.0

(D) 7.25

(E) 7.5

KEY:題目是the least( possible average),是問十個人最低能考到的分數,而不是問選項中哪個分數出現的幾率最低,如果理解為後者那麼選a, 因為a的幾率為0,但是題目的本意是前者,所以7.5*9/10=6.75,選B.

10 d=561.165

the tenths digit是第十分位的數，100d=56116.5,d/100=5.61165，第一個的十分位為5，第二個的十分位為6。所以選B。

1 If one number is chosen at random from the first 1,000postiveintegers, what is the probability that the number chosen ismultiple ofboth 2 and 8? 從1到1000中選出的同時是2與8的乘積的數概率是多少? 答案是1/125

2. How many 3-digit positeve integers are odd and do not contain the digit " 5" ?

How many positive 4-digit integers begin (on the left) with an odd digit and end with an even digit? 一個三位元正整數它是奇數，並且沒有5：首先第一位有8個數適用，第二位有9個數適用，最後一位有4個數適用。所以總共有9*8*4=288個，一個四位元正整數開始的是奇數，末位是偶數“：第一位有5個數適用，第二和第三位有10個數適用，第四位有5個數適用，所以總共有5*10*10*5=2500，所以後者大於前者。

3.A printer numbered consecutively the pages of a book ,beginning with1on the first page .In numbering the pages,he printed a total of189digits. 與 100 比較？什麼意思呀？ 看不懂啊，鬱悶！

4 certain integer n is a multiple of both 5 and 9.Which of the following must be true ?

I. n is an odd integer. II. n is equal to 45. III. n is a multiple of 15

5 the number of prime numbers the number of prime numbers greater than 10 greater than 40 and less than 50 and less than 20

40到50的質數有：41，43，47. 10到20的質數有：11，13，17，19.所以後者大於前者。

Ms.Smith got an 8 percent cost-of-living raise of 20\$ per week.

6 Ms.Smith's new weekly salary \$260

20/0.08=250,小於260.選B。

71<n<5,n is an integer

The sum of the first n odd integers that (n^2)-1

are greater than zero

n=2, 前2個大於0的奇數為1、3，所以和為1+3=4 (n^2)-1=3

n=3, 前3個大於0的奇數為1、3、5，所以和為1+3+5=9 (n^2)-1=8

n=4, 前4個大於0的奇數為1、3、5、7，所以和為1+3+5+7=16 (n^2)-1=15 所以前者大於後者。

8 M＝3^5*5^3

N=2*3^5*5^3

the value of the units' digit of M the value of the units' digit of N

9 if n is an integer,then the units digit of n^2 cannot be

a.0 b.2 c.4 d.5 e.6

10 Rack A holds 80 pairs ofslackswith prices ranging from \$12 to \$15 a pair, and rack B holds 60pairs ofslacks with prices ranging from 13\$ to 18\$ a pair. If all theslacks aresold, what is the greatest amount by which the revenue fromthe slacksof rack A could possibly exceed the revenue from the sale ofslacks onrack B

412 沒理解好(80*15-13*60??)

1. How many 3-digit positeve integers are odd and do not contain the digit " 5" ?

How many positive 4-digit integers begin (on the left) with an odd digit and end with an even digit? 一個三位元正整數它是奇數，並且沒有5：首先第一位有8個數適用，第二位有9個數適用，最後一位有4個數適用。所以總共有9*8*4=288個，一個四位元正整數開始的是奇數，末位是偶數“：第一位有5個數適用，第二和第三位有10個數適用，第四位有5個數適用，所以總共有5*10*10*5=2500，所以後者大於前者。

2.A printer numbered consecutively the pages of a book ,beginning with1 on the first page .In numbering the pages,he printed a total of 189digits. 與 100 比較？什麼意思呀？ 看不懂啊，鬱悶！

3certain integer n is a multiple of both 5 and 9.Which of the following must be true ?

I. n is an odd integer. II. n is equal to 45. III. n is a multiple of 15

4 Lin and Mark each attempt independently to decode a message. If the probability that Lin will decode the message is 0.80,

and the probability that Markwill decode the message is 0.70, find the probability that at least oneof them will decode the

messge

Lin不能解碼的概率為：1-0.8=0.2；Mark不能解碼的概率為：1-0.7=0.3