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GRE数学易错题

发布时间:2014-07-11 13:20:34  

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

注:a2表示a平方,a3表示a立方

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

答案是D,題目我都看不懂,是啥意思呢?

這是說秘書打六封信,沒一封信要1頁或者兩頁。如果秘書總共打了10頁,那麼有多少封信是兩頁?

解答:設有x封,則2x+(6-x)=10,解得x=4.

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?

這五個數是:2 6 8 14 16

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

我覺得這道題除了2不可能,其它四個數都有可能.可答案是c,想問大家為什麼?

題目意思是這5個數哪些可以是2個>1的數的積,一個是奇數,一個是整數,只有6和14的因數中有奇數,所以C.

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?

是這樣:(1970-1965)/1965

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?

我覺得這道題x的最大值為6,最小值為0,所以選6.

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

選D,最大為6,最小為-6.

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

比較the greatest value of p(1-p)與1/2的大小,答案是C

答案錯了,選B p+(1-p)>=2p(1-p)^1/2 => p(1-p)<=1/4 < 1/2

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

比較the slope of the line 與1/2的大小,答案是D,但算出來是-1/2呀

還有截距為零的情況,所以D.

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?

答案是9%,題目沒看懂

意思是一個貨幣市場上個月共結餘48000,用它賺了360的利息,問以年單利計算每年利率是多少?

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

首先這道題我是對multilples of ....不大明白,這是什麼意思啊?其次這道題怎麼解呢?

在小於360的30的公倍數中,也是12的公倍數的占多少?30N≤360, 得N≤12,所以共有12個數滿足題幹.

又12與30的最小公倍數為60,其實此題是求是60的倍數又小於等於360所占比例,同理求出為6

所以,6/12=答案E

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

我覺得這道題就是用110除以27就好了,可是答案是選c的

是呀,110/27=4.04,如果是4個班,那麼總人數為108,還剩2個。當然是5個班了。 8 a delivery service charges $0.02 per ounce for the first 16 ounces ofa shipment and $0.15 for each

additional ounce of theshipment,(1pound=16ounce)

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

這道題答案選的是D,不明白怎麼會無法確定呢?我是這樣算的:16×0.2+(25*16-16)×0.15...這樣對麼? 因為x是個未知數,所以你無法確定它的值。

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

無法確定,沒有告訴1can有多少克?

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

選D,當x=2,-2時,餘數為2,-2,其它情況為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)

比較兩個數的個位,6不管多少次方個位都為6,5不管多少次方個位都為5.

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

說的是n個大於零的奇數和。

當n=2,1+3=4;n^2-1=3;

當n=3,1+3+5=9;n^2-1=8;

當n=4,1+3+5+7=16;n^2-1=15

所以選A

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

注是a的7次方,類推呵呵

比較大小題

後-前=a^7(a-1)+a^14(1-a)

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

然後討論,最後結果是後-前的差<0,但當a=1時,相等。所以選D.

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

誰能把題目翻譯以下?謝謝

就是N^2的個位數不能為幾,應該選B吧

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?

還有,黃皮書的答案是全對的嗎?怎麼有些明顯好怪的,望指點哈~

這是比較6的47次方的個位數與5的77次方的個位數的大小。

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

同問此題,不明白題目說什莫

我理解的阿:打折20%後再打折40%,結果等於打一個X折,比較X和52的關係 (100-20)*(100-40) = 48

X = 100 - 48 = 52

10.已知:y=x^2-16x+64

比較"the least value of y"和"0"的大小

答案是C, y 沒有最小直呀?

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"

答案是A, 我覺得應該是B呀?

奇數除2餘數必為1,偶數除2餘數必為零,選A

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

答案是D,如果是D的話,那麼3+4+5也不是奇數呀?我覺得C和E怎麼都對呀?

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?

我沒頭緒 沒學過概率,怎麼辦呢?

這裡24個學幾何,40個學生物,20個全學。問兩個都沒學占多少比例。

單學幾何的有24-20=4個,單學生物的有40-20=20個,所以學了這兩門的任何一門的有:20+4+20=44個。所以沒學的就是80-44=36個。

所以概率為:36/80=9/20.

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'

三角形ABC的面積:AC的長度乘以AB的長度。

三角形AB'C'的面積:1.2AC的長度乘以0.8AB的長度=0.96三角形ABC的面積

所以選A

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?

假設11, 5是兩條直角邊,斜邊的平方等於 146小於13的平方,所以13對的邊是鈍角

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.

問x/y大還是1/15大?

這種題怎麼算呀,答案是一樣大

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

咋做呀~~

這是求下麵哪個數能被24整除。當尾數為2,6時,倒數第二個數應該為奇數。當尾數為0,4,8時,倒數第二個數為偶數。所以選E。

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...

三個鉛塊,每個邊長10cm,熔了之後放在一矩形平底鍋內.鍋的底面積20×30,高15.問這三個熔了的鉛塊倒進鍋了有多深?

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.

你理解錯了,題目求連接街道兩面的電話線有幾根? 24個?,因為有一邊就4棟房子啊,4×6. 9 100x<y 1000x<2y

問:1100x y

這道題我是沒有什麼思路,請大家幫忙.

由上兩式知道x<y/500,所以1100x<2.2y;但是不一定小於y.所以無法確定。選D

10 三角形RST is isosceles and 角RST=40

問the sum of the measures of the two angles of 三角形RST that have equal measure 和120,哪個大?(題目講啥?)答案是不能比較

題目告訴了你等腰三角形有一個角是40,問你相等的兩個角的和和120比大小

如果40是頂角,那麼兩個相等角的和是140大於120,如果是底角,那麼兩個相等角的和是80小於120,所以不能比較

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

問the number of decimal places where d and e differ ,和 4比較 ,哪個大?(這個也不曉得題目在講啥)答案是4大

這道題是問你在哪一位小數位d和e不同,e=5.039,所以是在第三位不同,所以小於四 2 n is an odd integer, and S is the finite sequence of consecutive integers1,2,3,4,...,n

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

當a,b都大於零時,前者小於後者;當a,b都小於零時,前者大於後者。

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)

設Y上的高為h,一半的面積為:1/2*1/2*y*h=y/4*h.所以比較的就是h和x的大小。因為h是這個三角形的直角邊,而x是斜邊。所以h小於x,所以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

答案選A

題目沒有說明 x的大小。有可能X<6 .而除A外,其他答案都是不可能的。

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

答案選E

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

理解成3:2的組合,就選A

總體幾率應該是1/55

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

答案是B

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

答案是C

這個數必須是個偶數,所以選C。

1.

5 is 1/5 of x

比較x 與1大小?

答案是A 5是X的1/5,所以X=5X5=25 大於1

2.

一個圓上有一點(Z,y),半徑是5

The circle above with center O has a radius of 5

圓上的點(Z,y)的 y 與 20開根號比較

答案是A,因為無論Y 在哪裡都坐落於圓上,既它到O的距離為5>根號20

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)

首先是要問大家這是一個什麼樣子的graph呢?然後是對折刀題沒有什麼思路...

這道題是說x,y哪個不滿足y<2x。這裡只有E符合。

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

這道題我是這樣想的,4×2.5=k*3*3.0,課答案選的是A...

對呀你這樣算出來的k=1.1,人家問的是k percent,所以要乘以100,得110.所以選A。 5 In a rectangular coordinate system, line k has x-intercept 4 and slope -2

the y-intercept of k 2

這道題是因為我不能理解x(y)-intercept的意思...

可以列出方程式:y=-2(x-4)=-2x+8,當x=0時,y=8,即在y軸的截距為8.選A.

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

這道題我沒什麼思路,請牛人給出解釋.主要是讀題時頭都大了...

這道題的意思是:當學校演出所賣的票比劇院的容量多150個時,需要演兩場。如果賣票數等於參加的人數,那麼每場演出的人數為劇院容量的2/3.問劇院的容量?

設劇院容量為x,得:(x+150)/2=2/3 *x,得出x=450,選E.

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

答案選A 我怎麼覺得是D呢?

題目到底是什麼意思?

這句話是說:18個不重疊的圓的總面積為多少?每個圓的直徑為2.

所以18個圓的面積為:18派,大於36,所以選A

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

設錯了X個題,則對了40-X個,總分為40-X(對的題數)-1/3X(錯的1/3)=20

解出來X=15

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

salad dressing

這題什麼意思?

我的理解是,oil和vinegar的比例是2:3,即放2份的oil要放3份的vinegar,但由於並沒有涉及水的比率也並不知道配製1杯sd需要多少oil或vinegar或水,所以無法判斷配製10杯sd需要多少杯水。

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

這題看著暈的要命,不知道怎麼回事?

我的理解是,一塊box有兩層,每層有27creams,題中說口味是packedinrows,又給出了一個9個flavors的排列,我認為這一層是3行這樣的排列,按此計算,每層有3*2個vanila,一塊box有2*3*2個vanila,所以200boxes有200*2*3*2=2400個vanila的creams。 2一個八邊形,內角相等,橫邊得豎邊長都為1,斜邊長為根號2,面積是多少.答案是7

八邊形的面積分解成一個正方形+4個矩形+4個等邊直角三角形,此題那個正方形的面積為為豎邊與橫邊的乘積為1,斜邊為根號2,所以直角三角形的兩條直角邊為1,這樣4個三

角形的面積為1*1/2*4=2。4個矩形面積為1*1*2+1*1*2=4,所以總面積為7。 3 X是大於1的整數,下麵哪個大.

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

所以選B,答案錯誤!

4

X>1, Y>1

下麵哪個大:1/(1/x+1/y); 1/x+1/y

(注,答案是無法比較大小)

第一項太麻煩,化簡為xy/(x+y),而第二項合併為(x+y)/xy,由於未知x+y與xy的大小關係,無法比較原題中二者的大小。

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

這是說1/2*2/3*3/4*.......n/n+1,這裡n小於20.所以乘完以後為:1/n+1=1/20.所以相等。

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

這是求x^2+x-380=0,求得x=20.所以選擇A

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

答案是C , 不理解。題也不理解, 答案也不理解啊!

這道題的解法為:x=w+1,y=w+2,z=w+3.所以(w+x)(x+y)(y+z)=(2w+1)(2w+3)(2w+5),這三個數都為奇數,三個奇數相乘還為奇數。所以除2必餘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

小矩形設短邊長為1,則小矩形的長邊長為2;

所以大矩形的短邊長PS=小矩形的長邊長=2,大矩形的長邊長RS=小矩形短邊長+小矩形長邊長=3;

因此PS/RS=2/3>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

比較the tenths digit of 100d,和the tenths digit of d/100,答案是一樣大。

不懂the tenths digit是否指得是十位元上的數字?

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

我的解法是這樣的:: 只有滿足8*2 8*4...........8*124 可以滿足,也就是只有62個,概率就應該是62/1000. 錯在哪兒呢?

在1至1000中,8的倍數有125個,因為2和8的最小公倍數為8,則該數是2和8的倍數的概率為:125/1000=1/8.

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!

這道題是說:一個列印者數連續的頁數,從第一頁的1開始.數這些頁數,它總共打了189個數。

首先:1-9的單位數一共有9個,所以189-9=180為兩位數,180/2=90,說明一共有90個兩位數,從10到99.所以比100小。

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

答案 是 只有 第三個 對 , 第二個 為什麼不對呢?

這是問的是n是5和9的乘積,但並沒有說是幾個5和9的乘積,而且還有可能還有其它的數,所以不一定是45.

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

尾數為3的數的冪的個位數一定以3,9,7,1迴圈。所以3^5的個位數為3. 5^3的個位數為5. 所以3*5的個位數為5.

所以N的個位數為:2*5的個位數為0.

所以前者大於後者。

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

答案為b

這題的意思是:如果n為一個整數,那麼n的平方的個位數不能是哪個?

因為沒有兩個相同的數相乘為2,所以選2.

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??)

最大的差為:80*15-13*60=420,最小的差為:15*80-18*60=120.所以412在這個範圍內。

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!

這道題是說:一個列印者數連續的頁數,從第一頁的1開始.數這些頁數,它總共打了189

個數。

首先:1-9的單位數一共有9個,所以189-9=180為兩位數,180/2=90,說明一共有90個兩位數,從10到99.所以比100小。

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

答案 是 只有 第三個 對 , 第二個 為什麼不對呢?

這是問的是n是5和9的乘積,但並沒有說是幾個5和9的乘積,而且還有可能還有其它的數,所以不一定是45.

中的 integer 如果 前面 沒有加 positive 或 minus OR negative ,是不是 都算作是 正的整數啊? 不是,沒說的話,按整數處理包括正和負

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

這道題是這樣解的:問你它們兩個至少有一人可以解碼的概率。你只要算出他倆都不能解碼的概率,然後1減就是答案了。

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

倆人都不能解碼的概率為0.2*0.3=0.06

所以至少有一個可以解碼的概率為:1-0.06=0.94.

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