GMAT考试PREP-MATH-PS1完整详解版-V2[1].0

PP-Problem Solving1 (PS1)

完整詳解版

V2.0

作者: pauline_chiou

william0625

gman

yuma168

備註：本版權內容歸作者和論壇共有，嚴禁任何未經允許的商業使用。

Revised History

由於這是眾人一起完成的,難免會有疏失,希望大家可以一起修正錯誤,讓這份詳解變得更完整! 版本增加規則如下:

1)修正算式錯誤or提出更好的算法, 請把版本小數+1 (Ex: V1.0 -> V1.1)

2)增加or補齊題目,請把版本個位數+1 (Ex: V2.0 ->V3.0)

Practice Test #1 Problem Solving

(196 Questions)

1. 409-!-item-!-187;#058&000306

A grocery store purchased crates of 40 oranges each for $5.00 per crate and then sold each orange for $0.20. What was the store's gross profit on each crate of oranges?

(A) $3.00

(B) $6.00

(C) $8.00

(D) $10.00

(E) $13.00

------------------------------------------------------------------------------------------------------------------------------------ 【答案】A

【思路】revenue=cost+profit,

假設X為the store's gross profit on each crate of oranges

0.2x40(sold each orange for $0.20)=5( per crate)+X

8=5+X, X=3

------------------------------------------------------------------------------------------------------------------------------------ 2. 455-!-item-!-187;#058&000316

The product P of two prime numbers is between 9 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then P =

(A) 15

(B) 33

(C) 34

(D) 46

(E) 51

------------------------------------------------------------------------------------------------------------------------------------ 【答案】E

【思路】前提是p是兩個”質數”的乘積

one of the prime numbers is greater than 2 but less than 6 包含3,5

the other is greater than 13 but less than 25 包含17,19,23

p 可能為51,57,69,85,95,115 (又9

------------------------------------------------------------------------------------------------------------------------------------

3. 664-!-item-!-187;#058&000504

A certain taxi company charges $3.10 for the first [?] of a mile plus $0.40 for each additional of a mile. What would this company charge for a taxi ride that was 8 miles long?

(A) $15.60

(B) $16.00

(C) $17.50

(D) $18.70

(E) $19.10

4. 765-!-item-!-187;#058&000550

In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack. How many boards are in the stack?

(A) 38

(B) 36

(C) 35

(D) 34

(E) 32

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】上面數下來第20個剛好在由下往上數第16個的下面→上面數下來第20個是下面數來第15個（下面有14個,上面有19個,在加上中心點那一個19+14+1＝34

------------------------------------------------------------------------------------------------------------------------------------ 5. 812-!-item-!-187;#058&000553

If , then m =

(A) 17

(B) 18

(C) 34

(D) 35

(E) 36

6. 859-!-item-!-187;#058&000568

The value of is closest to which of the following?

(A) 1

(B) 10

(C) 102

(D) 103

(E) 104

7. 905-!-item-!-187;#058&000575

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

(A) between 2 and 10

(B) between 10 and 20

(C) between 20 and 30

(D) between 30 and 40

(E) greater than 40

------------------------------------------------------------------------------------------------------------------------------------

8. 1221-!-item-!-187;#058&000650

A flower arrangement consists of 30 roses, each of which is either white or red. If a rose is to be selected at random from the flower arrangement, the probability that the rose selected will be white is twice the probability that it will be red. How many white roses are in the flower arrangement?

(A) 5

(B) 10

(C) 15

(D) 20

(E) 25

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】假設w=the probability of white rose, r= the probability of red rose

23030

w r

=?又w+r=30,得w=20 ------------------------------------------------------------------------------------------------------------------------------------

9. 1700-!-item-!-187;#058&001066

Last year the range of the annual salaries of the 100 employees at Company X was $30,000. If the annual salary of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual salaries of the 100 employees this year?

(A) $27,000 (B) $30,000 (C) $33,000 (D) $36,000 (E) $63,000

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C

【思路】Last year the range of the annual salaries of the 100 employees at Company X ＝30,000

（假設最大annual salaries=50,000,最小annual salaries=20,000）

又今年比去年annual salary 漲10％ 表示the range of the annual salaries of the 100

employees this year=50,000x(1.1)-20,000x(1.1)=33,000

------------------------------------------------------------------------------------------------------------------------------------ 10. 1746-!-item-!-187;#058&002343

If a = 7 and b = -7, what is the value of 2a - 2b + b^2 ?

(A) - 49 (B) 21 (C) 49 (D) 63 (E) 77

------------------------------------------------------------------------------------------------------------------------------------ 【答案】E

【思路】代入法, 222a b b

-+2

272(7)(7)

=?-?-+-

=14+14+49=77

------------------------------------------------------------------------------------------------------------------------------------ 11. 1799-!-item-!-187;#058&002415

In the figure above, the radius of the circle with center O is 1 and BC = 1. What is the area of triangular region ABC ?

(A) √2/2 (B) √3/2 (C) 1 (D) √2 (E) √3

12. 1845-!-item-!-187;#058&002416

Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest. If that interest was approximately 6.5 percent of the bond's selling price, approximately what was the bond's selling price?

(A) $4,063

(B) $5,325

(C) $5,351

(D) $6,000

(E) $6,154

------------------------------------------------------------------------------------------------------------------------------------ 【答案】E

【思路】the interest=5,000x0.08=400

400=selling pricex0.065, selling price=6,154

------------------------------------------------------------------------------------------------------------------------------------ 13. 1898-!-item-!-187;#058&002486

If m lies between the integers p and s on the number line shown, which of the following is a possible value for m ?

(A)√17

(B) √4

(C) 2.9

(D) 20/4

(E) 10/3

14. 1999-!-item-!-187;#058&002494

(A) 3

(B) 6

(C) 9

(D) 12

(E) 18

15. 2160-!-item-!-187;#058&002594

At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?

(A) 3/25

(B) 11/36

(C) 7/12

(D) 2/3

(E) 25/36

16. 2206-!-item-!-187;#058&002619

When [?] of the garments in a shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the uninspected garments must pass inspection in order that

90 percent of the garments in the shipment pass?

(A) 10

(B) 9

(C) 8

(D) 7

(E) 5

17. 2311-!-item-!-187;#058&002635

In a certain board game, a stack of 48 cards, 8 of which represent shares of stock, are shuffled and then placed face down. If the first 2 cards selected do not represent shares of stock, what is the probability that the third card selected will represent a share of stock?

(A) 1/8

(B) 1/6

(C) 1/5

(D) 3/23

(E) 4/23

18. 2417-!-item-!-187;#058&002747

3 teaspoons = 1 tablespoon

4 tablespoons = 1/4 cup

According to the information above, how many teaspoons are equal to 3/8 cup?

(A) 3

(B) 4

(C) 9

(D) 12

(E) 18

19. 2463-!-item-!-187;#058&002761

For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 ?

(A) One

(B) Two

(C) Three

(D) Four

(E) Five

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C

【思路】題目What is the number of variations in sign for the sequence,所以題目已經給sequence,不用再排序,variation:當下個一數字正負號與自己不同時,則算一次

故(1,-3)(-3,2)(5,-4),共三次

------------------------------------------------------------------------------------------------------------------------------------ 20. 2563-!-item-!-187;#058&002787

It takes Carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour. How many minutes will it take Carlos to cycle from home to work along the same route at an average rate of 6 miles per hour?

(A) 26

(B) 33

(C) 36

(D) 44

(E) 48

------------------------------------------------------------------------------------------------------------------------------------ 【答案】B

【思路】

tan

dis ce

speed

time

先求Carlos home to work的距離d, carlos花了9分鐘以速率22miles/per

hour,

229603.3

d d ==,若carlos 騎cycle

6 3.360time

= time=33

------------------------------------------------------------------------------------------------------------------------------------ 21. 2609-!-item-!-187;#058&002849

If a = 1 and b = -2, then (2a^2 + b)(x + y) + (a + b)(x - y) =

(A) 0 (B) 2x (C) y - x (D) x - y (E) x + y

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C 【思路】

[]2(2)()()()21(2)()(12)()0(1)()a b x y a b x y x y x y x y y x

++++-=?+-++--=+--=-

------------------------------------------------------------------------------------------------------------------------------------ 22. 2710-!-item-!-187;#058&002886

The formula F = 9C/5 + 32 gives the relationship between the temperature in degrees Fahrenheit, F, and the temperature given in degrees Celsius, C. If the temperature is 85 degrees Fahrenheit, what is the temperature, to the nearest degree, in degrees Celsius?

(A) 18 (B) 23 (C) 29 (D) 47 (E) 51

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C 【思路】

9325985325

9265,29.4444C

F C C C =

+=+==

------------------------------------------------------------------------------------------------------------------------------------ 23. 2976-!-item-!-187;#058&003069 [?]

For the 5 days shown in the graph, how many kilowatt-hours greater was the median daily electricity use than the average (arithmetic mean) daily electricity use?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5 24. 3022-!-item-!-187;#058&003084

In a certain game, the units of currency of three countries are the crown, the shield, and the pound,

respectively. If 2 crowns equal 3 shields and 3 shields equal 4 pounds, how many crowns equal 18 pounds?

(A) 9

(B) 16

(C) 18

(D) 32

(E) 36

------------------------------------------------------------------------------------------------------------------------------------ 【答案】A

【思路】2c=3s,3s=4p

4p=18,p=4.5

3s=18,s=6

代入2c=3s,c=9

------------------------------------------------------------------------------------------------------------------------------------ 25. 3236-!-item-!-187;#058&003282

26. 3282-!-item-!-187;#058&003293

There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?

(A) 100

(B) 90

(C) 50

(D) 45

(E) 25

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】

C(10,2)= 10!

8!2!=45

------------------------------------------------------------------------------------------------------------------------------------ 27. 3330-!-item-!-187;#058&003295

38, 69, 22, 73, 31, 47, 13, 82

Which of the following numbers is greater than three-fourths of the numbers but less than one-fourth of the numbers in the list above?

(A) 56

(B) 68

(C) 69

(D) 71

(E) 73

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】將上述的sequence由小到大重新排列13,22,31,38,47,69,73,82

假設題目要求的number為X,X大於數列的3

4

,小於數列的

1

4

數列共有8個數, 3

4X8=6,

1

4X8=2

so, 69

------------------------------------------------------------------------------------------------------------------------------------ 28. 3377-!-item-!-187;#058&003297

If xy = 1, what is the value of 2^[(x+y)^2] / 2^[(x-y)^2] ?

(A) 2

(B) 4

(C) 8

(D) 16

(E) 32

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】根據

r

r s

s

x

x

x

-

=,所以

222

2222

222

(2)

()(2)

224

()

22

22

22x xy y

x y x xy y

x xy y x xy y xy

x y-+

+++

++-+-

-

===

xy=1,故the value=42=16

------------------------------------------------------------------------------------------------------------------------------------29.

3426-!-item-!-187;#058&003323

The value of the expression above is closest to which of the following?

(A) 0.0001

(B) 0.001

(C) 0.1

(D) 1

(E) 10

30. 3528-!-item-!-187;#058&003455

A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus

a markup that was

40 percent of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?

(A) $40

(B) $60

(C) $80

(D) $90

(E) $100

------------------------------------------------------------------------------------------------------------------------------------ 【答案】E

【思路】selling price=the purchase price+ 40%selling price

selling price =150+0.4x selling price

0.6 selling price=150

selling price=250, the gross profit=250-150=100

------------------------------------------------------------------------------------------------------------------------------------31. 4014-!-item-!-187;#058&003590

The circle shown has center O and radius 4. What is the area of the shaded region?

(A) 3π (B) 4π (C) 6π (D) 8π (E) 12π 32. 4438-!-item-!-187;#058&003962

At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 3:80. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?

(A) 130 (B) 131 (C) 132 (D) 133 (E) 134

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D 【思路】

3

80

T S >, T=5代入 400>3S,S<133.3

so, the maximum number of students possible in the course that has 5 teaching

assistants=133

------------------------------------------------------------------------------------------------------------------------------------ 33. 4484-!-item-!-187;#058&004004

If x^4 + y^4 = 100, then the greatest possible value of x is between

(A) 0 and 3 (B) 3 and 6 (C) 6 and 9 (D) 9 and 12 (E) 12 and 15

------------------------------------------------------------------------------------------------------------------------------------ 【答案】B 【思路】

44

3813.1100

=<又,所以 the greatest possible value of x is between3 and 6

------------------------------------------------------------------------------------------------------------------------------------ 34. 4586-!-item-!-187;#058&004030 Of the following, which is least?

(A)

(B) (0.2)2 (C) 0.02 (D) (E) 0.2

35. 4632-!-item-!-187;#058&004107

What is the sum of the different positive prime factors of 550 ?

(A) 10

(B) 11

(C) 15

(D) 16

(E) 18

------------------------------------------------------------------------------------------------------------------------------------ 【答案】E

【思路】550=5x5x2x11

the sum of the different positive prime factor=5+2+11=16(5只能加一次因為different)

------------------------------------------------------------------------------------------------------------------------------------ 36. 4841-!-item-!-187;#058&004235

In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be

(A) 3 and 15

(B) 3 and 20

(C) 4 and 13

(D) 4 and 14

(E) 5 and 14

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C

【思路】

題意應該是抽一張牌就要乘上這張牌和其下一個號碼

所以3x(3+1)=12. 4x(4+1)=20, 13x(13+1)=182, 14x(14+1)=210.

應該是4與13沒錯

------------------------------------------------------------------------------------------------------------------------------------ 37. 5000-!-item-!-187;#058&004365

For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by . If T is the sum of the first 10 terms in the sequence, then T is

(A) greater than 2

(B) between 1 and 2

(C) between 1/2 and 1

(D) between 1/4 and 1/2

(E) between 1/4

38. 5102-!-item-!-187;#058&004451

Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x + y + z gallons of a 1.5 percent grade, what is x in terms of y and z ?

(A) y + 3z

(B) (y + z) /4

(C) 2y + 3z

(D) 3y + z

(E) 3y + 4.5z

39. 5583-!-item-!-187;#058&004668

A certain stock exchange designates each stock with a one-, two-, or three-letter code, where each letter is selected from the

26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order

constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

(A) 2,951 (B) 8,125 (C) 15,600 (D) 16,302 (E) 18,278

------------------------------------------------------------------------------------------------------------------------------------ 【答案】E

【思路】題目有前提If the letters may be repeated and if the same letters used in a different order

constitute a different code,

所以one letter-26種

two letters-26x26種

three letters-26x26x26種

total=18,278

------------------------------------------------------------------------------------------------------------------------------------ 40. 5629-!-item-!-187;#058&004684

Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

(A) 2 (B) 3 (C) 4 (D) 6 (E) 8

------------------------------------------------------------------------------------------------------------------------------------ 【答案】B

【思路】速率x 時間=工作量(距離)

Sx12(days)=1,S= 112(six machines),表示一台的速率1

72(這個地方要小心！！)

假設x 台機器complete the job in 8 days

1

172??X 8＝,X=9,所以必須增加3台機器complete the job in 8 days

------------------------------------------------------------------------------------------------------------------------------------ 41. 5676-!-item-!-187;#058&004686

All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?

(A) 2(26^5) (B) 26(26^4) (C) 27(26^4) (D) 26(26^5) (E) 27(26^5)

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C

【思路】either a 4-letter or a 5-letter

454444262626262626(126)2726+=+?=+=?

------------------------------------------------------------------------------------------------------------------------------------

42. 5722-!-item-!-187;#058&004704

Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost $0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

(B) $1.85 (C) $2.00 (D) $2.15 (E) $2.30

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C

【思路】假設最小size cost X

比X 大一個size=X+0.25,大兩個size=x+0.5….依序

8.25＝X+(X+0.25)+(X+0.5)+(X+0.75)+(X+1)+(X+1.25),X=0.75 so, the largest pot costs 0.75+1.25=$2.00

------------------------------------------------------------------------------------------------------------------------------------ 43. 5768-!-item-!-187;#058&004705

A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

(A) 16 (B) 24 (C) 26 (D) 30 (E) 32

------------------------------------------------------------------------------------------------------------------------------------ 【答案】E

【思路】<作法1>committe 中不能有couple 的組合即 "全部的組合-committe 中有couple 的組合"

C(8,3)-4*6 =56-24

<作法2>

323!

= OOO → 一個蘿蔔一個坑，求組合!!（3!是因為 abc acb bac bca cba cab 是同一種組合）

------------------------------------------------------------------------------------------------------------------------------------ 44. 5871-!-item-!-187;#058&004763

A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 senior officers and 1 junior officer, how many different committees are possible?

(A) 8 (B) 24 (C) 58 (D) 80 (E) 210

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】C(6,3)XC(4,1) =20X4=80

------------------------------------------------------------------------------------------------------------------------------------ 45. 5918-!-item-!-187;#058&004778

While working alone at their respective constant rates, computer X processes 240 files in 4 hours and computer Y processes 240 files in 8 hours. If all files processed by these computers are the same size, how long would it take the two computers, working at the same time and at their respective constant rates, to process a total of 240 files?

(A) 2 hr

(B) 2 hr 20 min (C) 2 hr 40 min

(E) 6 hr 20 min

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C

【思路】computer X processes 60 files in1 hour, and computer Y processes 30 files in 1 hour so, X和Y一起做可以完成90 files in 1 hour

若一起完成240files, 需花費T=2402

2

903

＝hours(2 hr 40 min)

------------------------------------------------------------------------------------------------------------------------------------ 46. 5966-!-item-!-187;#058&004795

If x ≠0, then

(A) -1

(B) 0

(C) 1

(D) x

(E) |x| / x

47. 6013-!-item-!-187;#058&004836

is between

(A) 300 and 400

(B) 400 and 500

(C) 500 and 600

(D) 600 and 700

(E) 700 and 800

48. 6225-!-item-!-187;#058&004914

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

(A) 10,700

(B) 10,800

(C) 10,900

(D) 11,000

(E) 11,100

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】假設the minimum possible population that the least population district could have=x 且假設其他10個voting district的人口more than10percent

x+(x+0.1x)x10=132,000

x=11,000

------------------------------------------------------------------------------------------------------------------------------------49. 6490-!-item-!-187;#058&005075

[?]

The table above shows the distribution of scores on a geography quiz given to a class of 25 students. Which of the following is closest to the average (arithmetic mean) quiz score for the class?

(A) 8.6

(B) 8.5

(C) 8.4

(D) 8.3

50. 6541-!-item-!-187;#058&005092

Which of the following is an integer?

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I, II, and III

51. 6587-!-item-!-187;#058&005111

Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 15

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】

P每1分鐘轉10次=> 60/10=6秒/次

Q每1分鐘轉40次=> 60/40=1.5秒/次

假設在T秒之後，Q比P多轉了6圈

(T/6) = (T/1.5) - 6

T=12

------------------------------------------------------------------------------------------------------------------------------------

52. 6641-!-item-!-187;#058&005112

[?]

In the circle above, PQ is parallel to diameter OR, and OR has length 18. What is the length of minor arc PQ ?

(A)

(B)

(C)

(D)

(E)

53. 6687-!-item-!-187;#058&005122

Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fourth theater ticket with a price of $16, what is the average price of all 4 theater tickets?

(A) $4

(B) $6

(C) $8

(E) $12

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D 【思路】 3×8＝24

(24＋16)÷4＝10

------------------------------------------------------------------------------------------------------------------------------------ 54. 6787-!-item-!-187;#058&005232

An auction house charges a commission of 15 percent on the first $50,000 of the sale price of an item, plus 10 percent on the amount of the sale price in excess of $50,000. What was the sale price of a painting for which the auction house charged a total commission of $24,000 ? (A) $115,000 (B) $160,000 (C) $215,000 (D) $240,000 (E) $365,000

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C 【思路】

plus 10 percent on the amount of the sale price in excess of $50,000 超過50000的部份收10%

設the amount of the sale price 為x

50000×15％＋(x-50000)×(10％)＝24000 X ＝215000

------------------------------------------------------------------------------------------------------------------------------------ 55. 6892-!-item-!-187;#058&005291

Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finite length?

(A) X 4 ≧ 1 (B) X 3 ≦ 27 (C) X 2 ≧ 16

(D) 2 ≦ |X| ≦ 5 (E) 2 ≦ 3X + 4 ≦ 6 56. 6998-!-item-!-187;#058&005424

A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?

(A) 1/4 (B) 1/3 (C) 2/5 (D) 5/4 (E) 3/2 57. 7044-!-item-!-187;#058&005427 If n is a multiple of 5 and ()2n p q = , where p and q are prime numbers, which of the following must rt

be a multiple of 25 ? (A) 2p

(B)

2q (C) pq

(D) 22

p q

(E) 3p q

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】

題目給的是n的質因式分解因為n為5的乘數那麼n的質因式中必定包含5這個因子所以有兩種可能p=5或

q=5

如果p=5 q不一定那麼n可以被25整除因為這裡已經有兩個5的因子

但是如果q=5 p不一定此時只有增加一個質因子p 才能保證為25整除

[另解]

題目說:p^2q=5k

這邊就要先推論一下,有兩種可能情形:

(1)p=5,k=pq

(2)q=5,k=p^2

直接看答案D

(p^2)(q^2)=5kq (由題目推的)

再帶入剛剛的兩種情形

(1)5kq=5(pq)(q)=25q^2

(2)5kq=5(p^2)(5)=25p^2

所以只有22

p q符合條件!

------------------------------------------------------------------------------------------------------------------------------------ 58. 7090-!-item-!-187;#058&005463

In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the graduating class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?

(A) 0.90

(B) 0.70

(C) 0.45

(D) 0.30

(E) 0.25

------------------------------------------------------------------------------------------------------------------------------------ 【答案】B

【思路】

設the graduating class 共有x位學生

Male 有

48 100

x人

Female有

52 100

x人

Male且25 years old or older有

40

100

48

100

x＝0.192x

Female且25 years old or older有

20

100

52

100

x=0.104x

求少於25歲的人數比例，(0.1920.104)

0.296

x x

x

+

=

1-0.296=0.704

------------------------------------------------------------------------------------------------------------------------------------ 59. 7143-!-item-!-187;#058&005466

In the figure above, points P and Q lie on the circle with center O. What is the value of s ?

(A) 1/2

(B) 1

(C) √2

(D) √3

(E) √2/2

60. 7189-!-item-!-187;#058&005472

Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?

(A) $430

(B) $620

(C) $650

(D) $680

(E) $770

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】

(1005)(403)(1023)680

?+?+??=

------------------------------------------------------------------------------------------------------------------------------------ 61. 7409-!-item-!-187;#058&005546

As shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. What is the distance, in feet, between the centers of the two wheels?

(A) (15 -π) / 2

(B) 5π/4

(C) 15 - 2π

(D) 15 -π

(E) 2π

62. 7564-!-item-!-187;#058&005577

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 63. 7612-!-item-!-187;#058&005607

For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b ?

(A) f(x) = x 2 (B) f(x) = x + 1 (C) f(x) = √x (D) f(x) = 2/x (E) f(x) = -3x 64. 7659-!-item-!-187;#058&005610

If in a certain population, people are born at an average rate of 9 people every 2 seconds and people die at an average rate of 3 people every 2 seconds, by approximately how many people does the population increase in 1 day? (A) 17,280 (B) 25,920 (C) 129,600 (D) 259,200 (E) 388,800

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D 【思路】

born at an average rate of 9 people every 2 seconds 且die at an average rate of 3 people every 2 seconds 得知人口每兩秒增加6個人

60

660242592002

?

??= ------------------------------------------------------------------------------------------------------------------------------------ 65. 7870-!-item-!-187;#058&005675 For how many integers n is 2

2n

n =? (A) None (B) One (C) Two (D) Three

(E) More than three

------------------------------------------------------------------------------------------------------------------------------------ 【答案】C 【思路】

2 and 4 兩個整數

------------------------------------------------------------------------------------------------------------------------------------ 66. 7916-!-item-!-187;#058&005701

The manager of a theater noted that for every 10 admission tickets sold, the theater sells 3 bags of popcorn at $2.25 each, 4 sodas at $1.50 each, and 2 candy bars at $1.00 each. To the nearest cent, what is the average (arithmetic mean) amount of these snack sales per ticket sold? (A) $1.48 (B) $1.58 (C) $1.60 (D) $1.64 (E) $1.70

------------------------------------------------------------------------------------------------------------------------------------ 【答案】A 【思路】

(3×2.25)＋(4×1.5)＋(2×1)=14.75 即10 admission tickets sold 會有14.75的收入 14.75÷10=1.475

------------------------------------------------------------------------------------------------------------------------------------ 67. 7966-!-item-!-187;#058&005724