prep practiceTest1PS 196

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

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

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

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

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

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

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)

(B)

(C) 1

(D)

(E)

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

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)

(B)

(C) 2.9

(D)

(E)

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)

(B)

(C)

(D)

(E)

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)

(B)

(C)

(D)

(E)

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

3 teaspoons = 1 tablespoon

4 tablespoons = [?] cup

According to the information above, how many teaspoons are equal to [?] 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

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

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

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

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

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

If a > b > 0, then

(A)

(B)

(C)

(D)

(E)

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

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

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

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

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

[?]

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

(A)

(B)

(C)

(D)

(E)

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

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

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

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

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)

(D)

(E)

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)

(C) 2y + 3z

(D) 3y + z

(E)

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

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

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)

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?

(A) $1.75

(B) $1.85

(C) $2.00

(D) $2.15

(E) $2.30

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

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

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

(D) 6 hr

(E) 6 hr 20 min

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

If x [?] 0, then [?]

(A) -1

(B) 0

(C) 1

(D) x

(E)

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

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

(E) 8.0

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

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

(D) $10

(E) $12

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

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)

(B)

(C)

(D)

(E)

56. 6998-!-item-!-187;#058&005424

A small water pump would take 2 hours to fill an empty tank. A larger pump would take 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)

(B)

(C)

(D)

(E)

57. 7044-!-item-!-187;#058&005427

If n is a multiple of 5 and n = (p^2)q, where p and q are prime numbers, which of the following must be a multiple of 25 ?

(A) p^2

(B) q^2

(C) pq

(D) (p^2)(q^2)

(E) (p^3)q

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

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)

(B) 1

(C)

(D)

(E)

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

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)

(B)

(C)

(D)

(E)

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)

(B)

(C)

(D)

(E)

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)

(D)

(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

65. 7870-!-item-!-187;#058&005675

For how many integers n is 2^n = n^2 ?

(A) None

(B) One

(C) Two

(D) Three

(E) More than three

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

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

[?]

In the rectangular coordinate system above, the area of triangular region PQR is

(A) 12.5

(B) 14

(C)

(D) 16

(E) 25

68. 8012-!-item-!-187;#058&005726

The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?

(A) 17

(B) 16

(C) 15

(D) 14

(E) 13

69. 8112-!-item-!-187;#058&005781

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

70. 8158-!-item-!-187;#058&005842

The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2 : 3, what is the ratio of the area of region R to the area of region S ?

(A) 25 : 16

(B) 24 : 25

(C) 5 : 6

(D) 4 : 5

(E) 4 : 9

71. 8312-!-item-!-187;#058&005967

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%

72. 8363-!-item-!-187;#058&005969

A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r ?

(A)

(B)

(C)

(D)

(E)

73. 8845-!-item-!-187;#058&006119

A certain company has 18 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?

(A) 18

(B) 72

(C) 180

(D) 1,260

(E) 3,060

74. 8893-!-item-!-187;#058&006120

40, 45, 45, 50, 50, 60, 70, 75, 95, 100

The scores on a certain history test are shown above. How many scores were greater than the median score but less than the mean score?

(A) None

(B) One

(C) Two

(D) Three

(E) Four

75. 8939-!-item-!-187;#058&006136

A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Two groups are considered different if at least one group member is different.)

(A) 48

(B) 100

(C) 120

(D) 288

(E) 600

76. 8985-!-item-!-187;#058&006184

Susan drove at an average speed of 30 miles per hour for the first 30 miles of a trip and then at an average speed of 60 miles per hour for the remaining 30 miles of the trip. If she made no stops during the trip, what was Susan's average speed, in miles per hour, for the entire trip?

(A) 35

(B) 40

(C) 45

(D) 50

(E) 55

77. 9031-!-item-!-187;#058&006222

At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

(A) 5

(B) 10

(C) 24

(D) 32

(E) 120

78. 9077-!-item-!-187;#058&006227

From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than [?] that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?

(A) 17

(B) 18

(C) 19

(D) 20

(E) 21

79. 9123-!-item-!-187;#058&006238

A certain builder is selling five homes for the following prices: $157,000, $168,000, $195,000, $235,000, and $256,000. If the price of the most expensive home is increased $10,000, which of the following statements best describes the change in the mean and the median of the home prices? (A) The mean and the median will remain unchanged.

(B) The mean will remain unchanged but the median will increase.

(C) The mean will increase but the median will remain unchanged.

(D) The mean and the median will increase by the same amount. (E) The mean and the median will increase by different amounts.

80. 9169-!-item-!-187;#058&006279

[?]

(A) If r and s are integers and rs + r is odd, which of the following must be even?

(B) r

(C) s

(D) r + s

(E) r^2 + s

81. 9215-!-item-!-187;#058&006304

If each term in the sum a1 + a2 + . . . + an is either 7 or 77 and the sum equals 350, which of the following could be equal to n ?

(A) 38

(B) 39

(C) 40

(D) 41

(E) 42

82. 9378-!-item-!-187;#058&006496

An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a

3-year period?

(A)

(B)

(C)

(D)

(E)

83. 9589-!-item-!-187;#058&006669

[?]

The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 73 scores?

(A) 60-69

(B) 70-79

(C) 80-89

(D) 90-99

(E) It cannot be determined from the information given.

84. 9689-!-item-!-187;#058&006710

If a quality control check is made by inspecting a sample of 2 lightbulbs from a box of 12 lightbulbs, how many different samples can be chosen?

(A) 6

(B) 24

(C) 36

(D) 66

(E) 72

85. 9735-!-item-!-187;#058&006716

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%

86. 9944-!-item-!-187;#058&006984

Which of the following is equal to x^18 for all positive values of x ?

(A) x^9 + x^9

(B) (x^2)^9

(C) (x^9)^9

(D) (x^3)^15

(E) x+18

87. 9993-!-item-!-187;#058&007019

[?]

In the addition table shown above, what is the value of m + n ?

(A) -19

(B) 4

(C) 5

(D) 6

(E) 22

88. 10039-!-item-!-187;#058&007071

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

89. 10086-!-item-!-187;#058&007098

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

(A) 3

(B) 4

(C) 6

(D) 9

(E) 12

90. 10132-!-item-!-187;#058&007125

A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average rate of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?

(A) 0.5 < t < 0.75

(B) 1.75 < t < 2.0

(C) 2.0 < t < 2.5

(D) 2.5 < t < 3.0

(E) 3 < t < 3.5

91. 10183-!-item-!-187;#058&007129

[?]

In the rectangular coordinate system above, the area of ??PQR is what fraction of the area

of ??LMN ?

(A)

(B)

(C)

(D)

(E)

92. 10232-!-item-!-187;#058&007135

[?]

In the rectangular coordinate system above, for which of the shaded regions is the area 2 ?

(A) None

(B) Q only

(C) Q and R only

(D) P, Q, and R only

(E) P, Q, R, and S

93. 10285-!-item-!-187;#058&007154

[?]

In the figure above, a square is inscribed in a circle. If the area of the square region is 16, what is the area of the circular region?

(A)

(B)

(C)

(D)

(E)

94. 10331-!-item-!-187;#058&007190

A company plans to assign identification numbers to

its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different

identification numbers are possible?

(A) 3,024

(B) 4,536

(C) 5,040

(D) 9,000

(E) 10,000

95. 10545-!-item-!-187;#058&007280

[?]

Which of the following statements can be inferred from the data above?

(A) I only

(B) II only

(C) I and III only

(D) II and III only

(E) I, II, and III

96. 10591-!-item-!-187;#058&007292 According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

(A) 25

(B) 34

(C) 50

(D) 67

(E) 100

97. 10643-!-item-!-187;#058&007319

If [?], then [?] =

(A)

(B)

(C)

(D)

(E)

98. 10689-!-item-!-187;#058&007329

If x is a negative integer, which of the following expressions has the LEAST value?

(A) x2 - 0.50

(B) x2 - 0.51

(C) x3 - 0.502

(D) x3 - 0.511

(E) x4 - 0.512

99. 10738-!-item-!-187;#058&007352

[?] 100. 10784-!-item-!-187;#058&007372

At a constant rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?

(A) 10

(B) 12

(C) 15

(D) 25

(E) 50

101. 10830-!-item-!-187;#058&007415

If xy + z = x(y + z), which of the following must be true?

(A) x = 0 and z = 0

(B) x = 1 and y = 1

(C) y = 1 and z = 0

(D) x = 1 or y = 0

(E) x = 1 or z = 0

102. 10931-!-item-!-187;#058&007448

If -3 is 6 more than x, what is the value of [?]

(A) -9

(B) -6

(C) -3

(D) -1

(E) 1

103. 10978-!-item-!-187;#058&007477

A list of measurements in increasing order is 4, 5, 6, 8, 10, and x. If the median of these measurements is [?] times their arithmetic mean, what is the value of x ?

(A) 16

(B) 15

(C) 14

(D) 13

(E) 12

104. 11026-!-item-!-187;#058&007480

If the average (arithmetic mean) of the 4 numbers n + 2, 2n - 3, 4n + 1, and 7n + 4 is 15, what is the value of n ?

(A) 3.5

(B) 4

(C) 6.5

(D) 11

(E) 13

105. 11075-!-item-!-187;#058&007490

Two water pumps, working simultaneously at their respective constant rates, took exactly 4 hours to fill a certain swimming pool. If the constant rate of

one pump was 1.5 times the constant rate of the

other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?

(A) 5

(B)

(C)

(D) 6

(E)

106. 11122-!-item-!-187;#058&007588

If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than

2.5 standard deviations from the mean?

(A) 12.0

(B) 13.5

(C) 17.0

(D) 23.5

(E) 26.5

107. 11225-!-item-!-187;#058&007613

[?]

In the figure above, equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?

(A) 5

(B) 8

(C) 11

(D) 15

(E) 19

108. 11272-!-item-!-187;#058&007635

In the arithmetic sequence t1, t2, t3, . . . , tn, . . . , t1 = 23 and tn = tn - 1 - 3 for each n > 1. What is the value of n when tn = -4 ?

(A) - 1

(B) 7

(C) 10

(D) 14

(E) 20

109. 11318-!-item-!-187;#058&007641

Last year, a certain public transportation system sold an average (arithmetic mean) of 41,000 tickets per day on weekdays (Monday through Friday) and an average of 18,000 tickets per day on Saturday and Sunday. Which of the following is closest to the total number of tickets sold last year?

(A) 1 million

(B) 1.25 million

(C) 10 million

(D) 12.5 million

(E) 125 million 110. 11364-!-item-!-187;#058&007646

The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?

(A) 30

(B) 20

(C) 18

(D) 12

(E) 6

111. 11411-!-item-!-187;#058&007682

If n is a positive integer less than 200 and [?] is an integer, then n has how many different positive prime factors?

(A) Two

(B) Three

(C) Five

(D) Six

(E) Eight

112. 11460-!-item-!-187;#058&007729

[?]

What is the sum of the integers in the table above?

(A) 28

(B) 112

(C) 336

(D) 448

(E) 784

113. 11514-!-item-!-187;#058&007740

For all positive integers m, [?] when m is odd and [?] when m is even. Which of the following is equivalent to [?] ?

(A)

(B)

(C)

(D)

(E)

114. 11561-!-item-!-187;#058&007757

If 0 < x < 1, what is the median of the values x, x-1, x^2, [?], and x^3 ?

(A) x

(B) x-1

(C) x^2

(D) [?]

(E) x^3

115. 11608-!-item-!-187;#058&007787

A used-car dealer sold one car at a profit of 25 percent of the dealer's purchase price for that car and sold another car at a loss of 20 percent of the dealer's purchase price for that car. If the dealer sold each car for $20,000, what was the dealer's total profit or loss, in dollars, for the two transactions combined?

(A) $1,000 profit

(B) $2,000 profit

(C) $1,000 loss

(D) $2,000 loss

(E) $3,334 loss

116. 11659-!-item-!-187;#058&007807

A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

(A)

(B)

(C)

(D)

(E)

117. 11706-!-item-!-187;#058&007820

A certain office supply store stocks 2 sizes of

self-stick notepads, each in 4 colors: blue, green, yellow, or pink. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of

3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

(A) 6

(B) 8

(C) 16

(D) 24

(E) 32

118. 12240-!-item-!-187;#058&008164

For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?

(A) 74

(B) 76

(C) 78

(D) 80 (E) 82

119. 12289-!-item-!-187;#058&008361

[?]

The figure shows seven train stations and the distances, in miles, along the railways that connect these stations. Beginning at one of the stations, a train takes 25 hours to travel directly to station W at an average rate of 50 miles per hour. At which of the stations did the train begin?

(A) T

(B) U

(C) V

(D) Y

(E) Z

120. 12390-!-item-!-187;#058&008396

Which of the following is closest to the value of [?]

(A) 10

(B) 1

(C) 0.1

(D) 0.01

(E) 0.001

121. 12439-!-item-!-187;#058&008408

[?]

A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data. If the 1,000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

(A) Four

(B) Six

(C) Nine

(D) Ten

(E) Eleven

122. 12485-!-item-!-187;#058&008472

Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities?

(A) 3

(B) 6

(C) 8

(D) 9

(E) 12

123. 12532-!-item-!-187;#058&008676

Of the following integers, which is the closest approximation to [?]

(A) 7

(B) 10

(C) 13

(D) 15

(E) 17

124. 12632-!-item-!-187;#058&008905

Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?

(A) 22

(B) 35

(C) 56

(D) 70

(E) 105

125. 12681-!-item-!-187;#058&008922

[?]

The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

(A) 278

(B) 341

(C) 357

(D) 400

(E) 441

126. 12727-!-item-!-187;#058&008936

Which of the following is equal to the value of 2^5+ 2^5 + 3^5 + 3^5 + 3^5 ?

(A) 5^6

(B) 13^5

(C) 2^6 + 3^6

(D) 2^7 + 3^8

(E) 4^5 + 9^5

127. 12774-!-item-!-187;#058&008957

The total cost of a vacation was divided equally among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost of the vacation?

(A) $200

(B) $300

(C) $400

(D) $500

(E) $600 128. 12878-!-item-!-187;#058&009011

[?]

The table shows the number of red blood cells per cubic millimeter of blood for each of five people. What is the median number of red blood cells per cubic millimeter of blood for these people?

(A) 4,600,000

(B) 5,000,000

(C) 5,020,000

(D) 5,150,000

(E) 5,300,000

129. 12981-!-item-!-187;#058&009035

[?]

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?

(A) 50

(B) 51

(C) 56

(D) 57

(E) 60

130. 13409-!-item-!-187;#058&009269

[?]

According to the table, the median acreage managed by the Federal Land Management agencies is how many million acres?

(A) 87

(B) 92

(C) 133

(D) 191

(E) 270

131. 13459-!-item-!-187;#058&009437

If the speed of x meters per second is equivalent to the speed of y kilometers per hour, what is y in terms of x ?

(1 kilometer = 1,000 meters)

(A)

(B)

(C)

(D)

(E)

132. 13505-!-item-!-187;#058&009469

If d is the standard deviation of x, y, and z, what is the standard deviation of x + 5, y + 5, and z + 5 ?

(A) d

(B) 3d

(C) 15d

(D) d + 5

(E) d + 15

133. 13554-!-item-!-187;#058&009480

[?]

A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the median amount of money that the student earned per day for the 20 days?

(A) $96

(B) $84

(C) $80

(D) $70

(E) $48

134. 13655-!-item-!-187;#058&009647

A 4-person task force is to be formed from the 4 men and 3 women who work in Company G's human resources department. If there are to be 2 men and 2 women on this task force, how many different task forces can be formed?

(A) 14

(B) 18

(C) 35

(D) 56

(E) 144

135. 13701-!-item-!-187;#058&009670

For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 30 percent of the total amount of the sale in excess of $500. If the total amount of one of her sales was $800, the saleswoman's commission was approximately what percent of the total amount of the sale?

(A) 22%

(B) 24%

(C) 25%

(D) 27%

(E) 28%

136. 13806-!-item-!-187;#058&009738

If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?

(A) (B)

(C)

(D)

(E)

137. 13906-!-item-!-187;#058&009755

If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a - b ?

(A) 1

(B) 10

(C) 19

(D) 20

(E) 21

138. 14007-!-item-!-187;#058&009795

The cost to park a car in a certain parking garage is $8.00 for up to 2 hours of parking and $1.75 for each hour in excess of 2 hours. What is the average (arithmetic mean) cost per hour to park a car in the parking garage for 9 hours?

(A) $1.09

(B) $1.67

(C) $2.25

(D) $2.37

(E) $2.50

139. 14108-!-item-!-187;#058&009811

A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?

(A) 32

(B) 37

(C) 40

(D) 43

(E) 50

140. 14208-!-item-!-187;#058&009862

If x and y are integers and 3^(x - 4) = 3^(y + 2), what is y in terms of x ?

(A) x - 6

(B) x - 5

(C) x - 2

(D) x + 2

(E) x + 6

141. 14419-!-item-!-187;#058&009981

If (5^21)(4^11) = 2(10^n) what is the value of n ?

(A) 11

(B) 21

(C) 22

(D) 23

(E) 32

142. 14580-!-item-!-187;#058&010013

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

143. 14954-!-item-!-187;#058&010212

In a survey of students, each student selected from a list of 12 songs the 2 songs that the student liked best. If each song was selected 4 times, how many students were surveyed?

(A) 96

(B) 48

(C) 32

(D) 24

(E) 18

144. 15002-!-item-!-187;#058&010239

If m = [?], w = [?], and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order?

(A) c, m, w

(B) c, w, m

(C) m, w, c

(D) w, c, m

(E) w, m, c

145. 15048-!-item-!-187;#058&010243

Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, to complete the job is 16 hours. How many hours would be needed if only 8 of the machines, working together, were used to complete the job?

(A) 18

(B) 20

(C) 22

(D) 24

(E) 26

146. 15203-!-item-!-187;#058&010262

Machine A, working alone at its constant rate, manufactures 280 bolts per hour, and machine B, working alone at its constant rate, manufactures 220 bolts per hour. How many hours will it take for machines A and B, working together at their respective constant rates, to manufacture 1,000 bolts?

(A) 1

(B) 1.3

(C) 1.5

(D) 1.8

(E) 2

147. 15249-!-item-!-187;#058&010285

A long-distance telephone company charges a monthly fee of $4.95 plus $0.07 per minute for long-distance telephone calls. If a person's

long-distance telephone calls for a certain month totaled 320 minutes, what was the total amount that the telephone company charged the person for that month?

(A) $22.90

(B) $24.06

(C) $25.87

(D) $26.67

(E) $27.35

148. 15563-!-item-!-187;#058&010376

[?]

(A) 28

(B) 27

(C) 26

(D) 25

(E) 24

149. 15609-!-item-!-187;#058&010412

A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?

(A) $0.60

(B) $0.70

(C) $0.80

(D) $0.90

(E) $1.00

150. 15710-!-item-!-187;#058&010468

[?]

151. 15756-!-item-!-187;#058&010486

A lawyer charges her clients $200 for the first hour of her time and $150 for each additional hour. If the lawyer charged her new client $1,550 for a certain number of hours of her time, how much was the average (arithmetic mean) charge per hour? (A) $155

(B) $160

(C) $164

(D) $172

(E) $185

152. 15857-!-item-!-187;#058&010522 Company C has a machine that, working alone at its constant rate, processes 100 units of a certain product in 5 hours. If Company C plans to buy a new machine that will process this product at a constant rate and if the two machines, working together at their respective constant rates, are to process 100 units of this product in 2 hours, what should be the constant rate, in units per hour, of the new machine?

(A) 50

(B) 45

(C) 30

(D) 25

(E) 20

153. 15903-!-item-!-187;#058&010559

A boat traveled upstream a distance of 90 miles at an average speed of (v - 3) miles per hour and then traveled the same distance downstream at an average speed of (v + 3) miles per hour. If the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

(A) 2.5

(B) 2.4

(C) 2.3

(D) 2.2

(E) 2.1

154. 16003-!-item-!-187;#058&010661

If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n ?

(A) 10

(B) 11

(C) 12

(D) 13

(E) 14

155. 16103-!-item-!-187;#058&010667

If 2^x - 2^(x - 2) = 3(2^13), what is the value of x ?

(A) 9

(B) 11

(C) 13

(D) 15

(E) 17

156. 16149-!-item-!-187;#058&010698 If a, b, c, and d are consecutive even integers and a < b < c < d, then a + b is how much less than c + d ?

(A) 2

(B) 4

(C) 6

(D) 8

(E) 10

157. 16358-!-item-!-187;#058&010761

To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?

(A) 6

(B) 8

(C) 10

(D) 15

(E) 30

158. 16572-!-item-!-187;#058&010847

The perimeter of a certain isosceles right triangle is [?]. What is the length of the hypotenuse of the triangle?

(A) 8

(B) 16

(C)

(D)

(E)

159. 16781-!-item-!-187;#058&010906

At a repair shop, the total cost of a repair consists of the charge for parts and a charge of $22.00 per hour for labor. If the total cost of a certain repair at the shop was $249.75 and the charge for parts was $150.75, then the labor charge was for how many hours of labor?

(A) 4.5

(B) 5

(C) 5.5

(D) 6.5

(E) 9

160. 16827-!-item-!-187;#058&010940 Committee X has 4 members, committee Y has 5 members, and these committees have no members in common. If a task force is to be formed consisting of one member of X and one member of Y, how many different task forces are possible?

(A) 6

(B) 9

(C) 10

(D) 20

(E) 36

161. 16873-!-item-!-187;#058&010944

Which of the following must be equal to

(x^6)(x^4) ?

(A) x^10

(B) x^12

(C) x^20

(D) x^24

(E) x^48

162. 17030-!-item-!-187;#058&010961

If n and y are positive integers and 450y = n^3, which of the following must be an integer?

[?]

(A) None

(B) I only

(C) II only

(D) III only

(E) I, II, and III

163. 17076-!-item-!-187;#058&010995

In 1990 the budgets for projects Q and V were $660,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?

(A) 1992

(B) 1993

(C) 1994

(D) 1995

(E) 1996

164. 17177-!-item-!-187;#058&011044

A certain scholarship committee awarded scholarships in the amounts of $1,250, $2,500, and $4,000. The committee awarded twice as many $2,500 scholarships as $4,000 scholarships, and it awarded three times as many $1,250 scholarships as $2,500 scholarships. If a total of $37,500 was awarded in $1,250 scholarships, how many $4,000 scholarships were awarded?

(A) 5

(B) 6

(C) 9

(D) 10

(E) 15

165. 17227-!-item-!-187;#058&011060

If [?], which of the following statements could be true? [?]

(A) I only

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

166. 17437-!-item-!-187;#058&011130

The architects of a certain type of building estimate construction costs to be $2.0 million per floor for each of the first 5 floors, $2.5 million per floor for each of the next 3 floors, and $3.5 million per floor for any additional floors. What would the architects estimate the construction costs to be for a building of this type with 10 floors?

(A) $23.0 million

(B) $23.5 million

(C) $24.0 million

(D) $24.5 million

(E) $25.0 million

167. 17541-!-item-!-187;#058&011147

If x is positive, which of the following could be the correct ordering of 2^x, and x^2 ?

[?]

(A) None

(B) I only

(C) III only

(D) I and II only

(E) I, II, and III

168. 17696-!-item-!-187;#058&011204

For which of the following functions f is f (x) = f (1 - x) for all x ?

(A) f (x) = 1 - x

(B) f (x) = 1 - x^2

(C) f (x) = x^2 - (1 - x)^2

(D) f (x) = (x^2)(1 - x)^2

(E)

169. 17796-!-item-!-187;#058&011312

The total price of a basic computer and a printer was $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been [?] of that total. What was the price of the basic computer?

(A) $1,500

(B) $1,600

(C) $1,750

(D) $1,900

(E) $2,000

170. 18117-!-item-!-187;#058&011424

Of the 13 employees in a certain department, 1 has an annual salary of $38,000, 2 have an annual salary of $45,000 each, 2 have an annual salary of $42,500 each, 3 have an annual salary of $40,000 each, and 5 have an annual salary of $48,500 each. What is the median annual salary for the 13 employees?

(A) $38,000

(B) $40,000

(C) $42,500

(D) $45,000

(E) $48,500

171. 18163-!-item-!-187;#058&011426

Julia purchased a car on an installment plan. She made a down payment of $2,550 and then made n monthly payments of $155 each. If Julia paid a total of $9,060 for the car, how many monthly payments did she make?

(A) 30

(B) 36

(C) 42

(D) 48

(E) 54

172. 18209-!-item-!-187;#058&011433

A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 300 bolts?

(A) 36

(B) 72

(C) 120

(D) 144

(E) 180

173. 18259-!-item-!-187;#058&011463

In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 4 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?

(A) d = p - 0.22

(B)

(C) (D)

(E)

174. 18305-!-item-!-187;#058&011469

The main ingredient in a certain prescription drug capsule costs $500.00 per kilogram. If each capsule contains 600 milligrams of the ingredient, what is the cost of the ingredient in a capsule? (1 kilogram = 10^6 milligrams)

(A) $0.30

(B) $0.83

(C) $1.20

(D) $3.00

(E) $3.33

175. 18356-!-item-!-187;#058&011490

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)

(B)

(C)

(D)

(E)

176. 18407-!-item-!-187;#058&011575

If the operation [?] is defined for all integers a and b by [?] which of the following statements must be true for all integers a, b, and c ?

[?]

(A) I only

(B) II only

(C) I and II only

(D) I and III only

(E) I, II, and III

177. 18457-!-item-!-187;#058&011601

When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year? [?]

(A)

(B)

(C)

(D)

(E)

178. 18885-!-item-!-187;#058&011972

Adam and Beth each drove from Smallville to Crown City by different routes. Adam drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than Adam to complete the trip. How many miles per hour was Beth's average speed on this trip?

(A) 24

(B) 30

(C) 48

(D) 54

(E) 75

179. 19312-!-item-!-187;#058&012220

If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

[?]

(A) None

(B) I only

(C) II only

(D) II and III only

(E) I, II, and III

180. 19628-!-item-!-187;#058&012404

List K consists of 12 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K ?

(A) 5

(B) 6

(C) 7

(D) 11

(E) 12

181. 19782-!-item-!-187;#058&012457

Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. What is the maximum possible weight, in kilograms, of the lightest box?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

182. 19831-!-item-!-187;#058&012571

[?]

The table shows the number of shares of each of the 5 stocks owned by Mr. Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 24 shares of Stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?

(A) 4

(B) 6

(C) 9

(D) 15

(E) 20

183. 19877-!-item-!-187;#058&012576

A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $38 to ship a certain package, which of the following was the weight of the package, in pounds?

(A) 16

(B) 17

(C) 19

(D) 20

(E) 22

184. 19923-!-item-!-187;#058&012581

A certain kennel will house 24 dogs for 7 days. Each dog requires 10 ounces of dog food per day. If the kennel purchases dog food in cases of 30 cans each and if each can holds 8 ounces of dog food, how many cases will the kennel need to feed all of the dogs for 7 days?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9

185. 20023-!-item-!-187;#058&012617

Each year Mark works 40 hours per week for 50 weeks. Last year Mark was paid a total of $20,000. If this year his hourly pay rate is raised by $0.50, what is the total amount that Mark will be paid this year?

(A) $30,000

(B) $25,000

(C) $22,500

(D) $21,000

(E) $20,020

186. 20069-!-item-!-187;#058&012630

A retailer sold an appliance for $80. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit?

(A) $10

逻辑推理

每题给出一段陈述，这段陈述被假设为正确的，不容置疑的。要求你根据这段陈述，选择一个答案。注意，正确的答案应与所给的陈述相符合，不需要任何附加说明即可从陈述中直接推出。 例题： 对于穿鞋来说，正合脚的鞋子比过大的好。不过，在寒冷的天气，尺寸稍大点的毛衣与正合身的毛衣的差别不大。这意味着： A．不合脚的鞋不能在冬天穿 B．毛衣的大小只不过是式样的问题，与其功能无关 C．不合身的衣服有时仍有穿用价值 D．在买礼物时，尺寸不如用途那样重要 解答：只有C是可以从陈述中直接推出的，故选c。 请开始答题： 1．有甲、乙、丙、丁四个果园，其中甲园的各种果树都能在乙园找到，丙园的果树种类包含所有的乙园果树种类，而丙园中有一些果树在丁园也有种植，则： A．甲园中有二些果树能在丁园中找到 B．甲园中所有的果树都能在丙园中找到 C．丁园中所有的果树都能在乙园中找到 D．乙园中有一些果树能在丁园中找到 2．在一次社会调查中发现，A市的人均国民生产总值高于B市和c市，而D市的人均国民生产总值比C市高又低于E市，由此可以推出： A．E市的人均国民生产总值高于A市 B．B市的人均国民生产总值高于C市 C．A市的人均国民生产总值高于D市 D．在五个城市的人均国民生产总值中，C市最多名列第四 3．有A、B、C、D、E五个亲戚，其中4人每人讲了一个真实情况，如下：①B是我父亲的兄弟，②E是我的岳母，⑧c是我女婿的兄弟，④A是我兄弟的妻子。上面提到的每个人都是这五个人中的一个(例如，①中“我父亲”和“我父亲的兄弟”都是A、B、C、D、E五人中的一个)，则由此可以推出 A．B和D是兄弟关系 B．A是B的妻子 C．E是C的岳母 D. D是B的子女

逻辑三大基本规律(原本)

逻辑三大基本规律： 一、容：（同一律、矛盾律、排中律）； 二、作为逻辑三大基本规律的原因： １、最普遍地适用于各种概念、命题、推理和论证； ２、正确的思维应当具备确定性、无矛盾性和明确性，而三大基本规律集中反映之； ３、逻辑规律是思维规律，逻辑三大规律是总结的结果； ·同一律： 一、同一律的容和要求： １、容：同一个思维过程中，每一思想与其自身是同一的；既“Ａ就是Ａ”； ２、要求：同一个思维过程中，概念都要确定，并保持自身的同一，不得随意变更； 二、违反同一律要求的逻辑错误： １、混淆概念或偷换概念：把两个不同的概念混淆起来，并用一个概念代替已经使用的另一个概念； 表现为：１）随表达需要而随意变更概念的涵和外延； ２）将同一词语在不同语境中表达的不同概念混为一谈； ２、转移论题或偷换论题：在同一思维过程中，改变原来的断定同，或者用另一断定代替之； 表现为：１）在思维中，用一个与原来相似但不同的命题代替原来的待断定命题； ２）思考或谈论问题时，没有中心论题或者远离中心论题； 三、同一律的作用及其运用时应注意的问题： １）只要求在一个思维过程中保持确定； ２）并不否认思维的发展变化； ３）仅仅在思维领域里起作用； ·矛盾律： 一、矛盾律的容和要求： １、容：同一思维过程中，两个互相否定的思想不能同真，必有一假；既“非（既Ａ又非Ａ）”； ２、要求：同一思维过程中，不能对不能同真的命题（矛盾关系、反对关系）同时加以肯定； 二、违反矛盾律要求的逻辑错误： １、自相矛盾：同时肯定了互相矛盾的命题； ２、悖论：一种特殊的逻辑矛盾，即通过一个命题的真，可以推假，而通过它的假，又可推真； 三、矛盾律的作用及其运用时应注意的问题： １）仅对于一个思维过程，即同一个时间、地点的同一对关系； ２）并不否认客观世界事物之间的矛盾； ３）矛盾律对于下反对关系没有制约作用； ·排中律 一、排中律的容和要求： １、容：同一个思维过程中，两个相互矛盾的思想不能同假，必有一真，即“要么Ａ要么非Ａ”； ２、要求：同一思维过程中，不能对不能同假的命题（矛盾关系、下反对关系）同时加以否定； 二、违反排中律要求的逻辑错误： １、两不可：对于相互矛盾的命题同时不予肯定，或者含糊其辞； ２、复杂问语的回答与排中律：回答复杂问语时可以通过否定前提同时加以否定； 三、排中律的作用及其运用过程中应注意的问题： １）应对于一个思维过程，即同一个时间、地点的同一对关系； ２）排中律述不可同假，矛盾律述不可同真； ３）排中律并不否认事物相互转化的中间形态； 之所以说因为矛盾律，就因为两个辩题是相互否定的，所以不可能同真；而作为辩题又不能有任意一个为必然真，所以只可能在某种层面上两个命题都假，只有在各自的不同角度和维度上才可能各自为“真”

第二章 逻辑思维规律

第二章逻辑思维的基本规律 教学目的和要求： 通过本章的学习，使学生了解逻辑思维的基本规律的内容和要求，正确理解逻辑基本规律的性质和作用范围，并能在实际思维过程中自觉运用和遵守逻辑基本规律，发现并纠正违反逻辑规律的各种逻辑错误。 教学重点： 逻辑思维基本规律的要求和违反基本规律的逻辑错误是本章的教学重点。 教学难点： 逻辑规律之间的关系，逻辑规律之间既有联系又有区别。 教学时间：6学时 章节结构：全章共分六部分内容，第一节是逻辑基本规律概述；第二节是同一律；第三节是矛盾律；第四节是排中律；第五节是充足理由律；第六节是逻辑规律之间的关系。下面先讲第一节。 教学内容： 第一节逻辑基本规律概述 关于逻辑规律一章的章次安排，不同的逻辑教材安排也不同。有的把它放在前面讲，讲完绪论以后就将逻辑思维的基本规律，我们的教材就是如此。有的把它放在论证之后讲，有的放在推理之后讲。不论如何安排次序，其基本内容是一样的。 一、什么是逻辑思维的基本规律 逻辑学是以思维形式为主要研究对象的科学，逻辑思维的规律主要是关于思维形式的规律。下面我们讲词项（概念）、命题（判断）即运用词项（概念）、命题（判断）进行推理，我们还讲词项（概念）、命题（判断）、推理的规则，这些都是形式逻辑的特殊规则。这一章讲的是逻辑思维的基本规律，通过学习我们知道了逻辑的基本规律是人们在运用概念、做出判断（命题）、进行推理和论证时，所必须遵守的最起码的思维规律。人们正确运用逻辑思维形式的最一般的规律，包括：同一律、矛盾律、排中律、充足理由律。 充足理由律在学术界有争论，有两种观点，一种观点认为，充足理由律不是一条基本规律，它是论证的特殊规律或规则，比如河海大学、高等教育出版社出版的教材。另一种观点认为它是一条规律，我同意第二种观点，因为充足理由律不仅在人们论证时必须遵守，运用概念进行判断时也必须有充足的理由，给概念下定义不也需要有充足的理由吗？所以，它是一条基本规律，应该把充足理由律放在基本规律一章来讲。 为什么这四条规律是逻辑学的基本规律呢？ 第一，它们适用于并制约着各种思维形式。

逻辑推理

判断推理解题技巧——寻找逻辑词 充分假言命题：如果A，那么B；只要A，就B；要想A，就必须B。 必要假言命题：只有A，才B；除非A，否则B。 一般来说，充分假言命题的推理规则是A→B；必要假言命题的推理规则是B →A。但其中比较特殊的是“除非A，否则B”，它的推理规则被称为“否一推一”，即￢A→B或者￢B→A。 例 经理说：“有了自信不一定赢。”董事长回应说：“但是没有自信一定会输。”以下哪项与董事长的意思最为接近？ A.只有赢了，才可能更自信 B.如果自信，则一定会赢 C.除非自信，否则不可能输 D.只有自信，才可能不输 【答案】D。解析：题干的论证可写成：没有自信→一定输。否前不能否后，B项错误；A项与B项等值，也错误；C项等值于只有自信，才可能输，显然不对；题干转化为必要条件假言命题即为D项。故选D。 【解题关键】考生应理解充分假言命题和必要假言命题的含义、因果关系及推理规则等，并学会综合运用，将相同的条件连接在一起，化难为简。 第四部分判断推理 1.党政机关公文是党政机关实施领导、履行职能、处理公务的具有特定效力的文书。其中命令(令)适用于公布行政法规和规章、宣布施行重大强制性措施、批准

授予。意见适用于对重要问题提出见解和处理办法。批复适用于答复下级机关请示事项。函适用于不相隶属机关之间商洽工作、答复问题、请求批准。 根据上述定义，下列选项中应添加批复的是： A.《国务院关于同意设立陕西西咸新区的________》 B.《国务院办公厅关于进一步加强资本市场中小投资者合法权益保护工作的 ________》 C.《国务院办公厅关于黑龙江双鸭山经济开发区升级为国家级经济技术开发区的________》 D.《国务院关于在我国统一实行法定计量单位的________》 【答案】A。 【中公解析】批复定义的关键信息是：答复下级机关。A项是答复下级机关的文件，符合定义关键信息，其他三项均不存在答复的关系。故答案选A。 2.图灵测试是测试者在与被测试者隔开的情况下，通过一些装置向被测试者随意提问，问过一些问题后，如果被测试者有超过30%的答复确认不出哪个是人、哪个是机器，那么这台机器就通过了测试，并被认为具有人类智能。 根据上述定义，以下哪项中的测试一定通过了图灵测试? A.对机器甲40%的答复所有人都确认其为机器

逻辑思维规律简编

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第十二章思维的基本规律 1、教学基本要求：通过本章学习，使学生掌握逻辑思维各条规律的内容、要求以及违反逻辑规律的错误。 2、教学重点：同一律、矛盾律、排中律的实质、内容、要求；分析违反逻辑思维基本规律的逻辑错误 3、教学难点：矛盾律和排中律在实际思维中的应用 4、计划学时：6 第一节概述 思维形式是受逻辑规律制约的。逻辑规律中，有的是关于某种思维形式的特殊规律，有的是适用于一切思维形式的普遍规律。例如，三段论的规则，只适用于三段论推理，不适于性质判断对当推理和判断变形推理，也不适用于各种复合判断的推理，更不适用于有关概念和判断的问题。而逻辑基本规律是对于一切思维形式普遍有效的，即是说，它们是概念、判断、推理和论证所要共同遵守的。 逻辑思维的基本规律有三条：同一律、矛盾律、排中律。同一律保证思想的同一性，矛盾律保证思想的无矛盾性，排中律保证思想的明确性。而同一性、无矛盾性和明确性则是思维有确定性的不同角度的表现。在现实的思维过程中，思维的确定性即同一性、无矛盾性和明确性是人们正确思想的最超码的要求，所以，这三条规律在各类逻辑思维形式中普遍起作用，成为最基本的逻辑规律。 逻辑规律尽管只是思维规律，它不同于事物本身的规律，但是思维规律既不是先验的，也不是约定俗成的，它是客观事物固有的规定性经过人们亿万次的实践在人们头脑中的反映，是有其客观基础的。千变万化的客观事物，在一定时间和一定条件下，总是具有质的规定性，这种质的规定性反映在人类思维中，就表现为思维的确定性。逻辑基本规律恰恰是从不同角度表现了思维的确定性。所以，客观事物的质的规定性，就是逻辑基本规律的客观基础。 第二节同一律 一、同一律的内容与要求 同一律的基本内容是：在同一思维过程中，每一思想与自身具有同一性。可用公式表示为：“A是A”，即“A→A”。它表示在同一思维过程中，每一词项、每一判断都必须是确定的，都必须与自身保持同一。 根据同一律的基本内容，我们可以将同一律的基本要求归结为以下两点： 1、在同一思维过程，我们表达思想时所用的词项，必须保持其确定的内涵和外延。即是说，在同一思维过程中，一个词项，原来指称什么对象就要一直指称这一对象，而不能随意变更。这样，运用概念和判断进行推理的时候，才能保证思想内容的确定性，否则就会发生思维混乱并引起行动上的错误。 2、在同一思维过程中，不仅要保持词项内容的确定性，而且还必须保持判断的确定性。即是说，一个判断陈述什么就陈述什么，并且其前后的陈述应当一致。同样，一个判断是真的就真的，是假的就是假的，也不能随意变更，否则也会发生思维混乱。例如，“法律是统治阶级意志的体现”，这个判断的内容是确定的，我们运用它进行推理、论证的时候，必须保持其同一性，而不能时而认为它是这样的内容，时而又认为它是那样的内容；也不能一会儿说它是真的，一会儿又说是假的。在引论中，我们曾举出古希腊有名的“半费之讼”的例子。在这一例子中，普罗达哥拉斯最终陷人两难的境地。究其根源，就在于为了使自己在诉讼中处于有利地位，随意变更判定胜败的标准，即是说没有保持判定胜败标准的

逻辑思维的重要性(优.选)

逻辑思维的重要性 逻辑与我们的工作和生活息息相关，尤其是在思维和语言中意义重大。逻辑思维是人的理性认识阶段，人运用概念、判断、推理等思维类型反映事物本质与规律的认识过程。在工作中如果我们能正确运用逻辑思维的方法可以达到事半功倍的效果。 比较思维方法是确定研究对象之间异同点的一种逻辑方法。比较分为同类事物之间的比较和不同类事物之间的比较按照形式，比较分为求同比较和求异比较。运用比较思维方法，在同类事物之间的相似中，求不同处，例如：香港有一家经营粘合剂的商店，在推出一种新型的"强力万能胶"时，市面上也有各种形形色色的"万能胶"。老板决定从广告宣传入手，经过研究发现几乎所有的"万能胶"广告都有雷同。于是，他想出一个与众不同、别出心裁的"广告"，把一枚价值千元的金币用这种胶粘在店门口的墙上，并告示说，谁能用手把这枚金币抠下来，这枚金币就奉送给谁。果然，这个广告引来许多人的尝试和围观，起到了"轰动"效应。尽管没有一个人能用手抠下那枚金币，但进店买"强力万能胶"的人却日益增多。如果我们在工作中，在设计开发产品时，运用比较逻辑法，多了解其他厂家产品的特点，我们自己的产品与其他厂家产品多比较，开动脑筋，开发出自己具有特色的产品，才能使自己的产品更有市场和竞争力。 逆向思维法是指为实现某一创新或解决某一因为常规思路难以解决的问题，而采取反向思维寻求解决问题的方法。人类的思维具有方向性，存在着正向与反向之差异，由此产生了正向思维与反向思维

两种形式。正向思维与反向思维只是相对而言的，一般认为，正向思维是指按照人们的习惯性思考路线去思考，而反向思维则是指背逆人们的习惯路线去思维。逆向思维法是指从事物的反面去思考问题的思维方法。这种方法常常使问题获得创造性的解决。例如金属腐蚀是一种坏事，但人们利用金属腐蚀原理进行金属粉末的生产，或进行电镀等其它用途，无疑是逆向思维法的一种应用。这是一种利用事物的缺点，将缺点变为可利用的东西，化被动为主动，化不利为有利的思维发明方法。这种方法并不以克服事物的缺点为目的，相反，它是将缺点化弊为利，找到解决方法。这使我联想到如果一个人在从事一项工作时，有很多时候，对于一个岗位而言的缺点，可能会成为另一个岗位的优点。比如说，如果你具备活泼好动的个性，往往不适合财务类工作而适合销售类工作。 从思维方向看，有直线思维和U型思维之分。在求解问题过程中，如果能用直线思维求解，那是再好不过的了，但是许多问题的求解，靠直线思维是难以如愿的，这时采用U型思维去观察思考，或许能使问题迎刃而解。U型思维的实质是：迂回前进。中国有一句古话：退一步海阔天空，其体现的恰恰就是U型思维的妙处。最通达的道路往往不是直线距离最短的道路，而是阻力最小的道路。这使我联想到在处理人际关系中，我们如果能运用U型思维，当在某些问题上与家人或同事发生矛盾时，不直接从正面冲突，而是谋求避开或越过障碍而解决问题的，即有利于人际关系和谐，又能最终达到目标。

第十章 逻辑思维及方法.

第十章逻辑思维及方法 一、逻辑思维的特征与作用 二、逻辑思维的形式 三、逻辑思维的方法 四、逻辑思维的训练 一、逻辑思维的特征与作用 (一)什么是逻辑思维 (二)逻辑思维的特征 (三)逻辑思维的作用 (一)什么是逻辑思维 逻辑思维，就是人在感性认识的基础上，以概念为操作的基本单元，以判断、推理为操作的基本形式，以辨证方法为指导，间接地、概括地反映客观事物规律的理性思维过程。 逻辑思维又称抽象思惟，是思维的一种高级形式。抽象思维既不同于以动作为支柱的动作思维，也不同于以表象为凭借的形象思维，它已摆脱了对感性材料的依赖.是以理论为依据，运用科学的概念、原理、定律、公式等进行判断和推理。 (二)逻辑思维的特征 普遍性、严密性、稳定性、层次性 (三)逻辑思维的作用 1.逻辑思维对创新目标的实现有引导和调控作用 2.创新结果的正确与否需要通过逻辑推理检验 3.逻辑思维可以直接产生创新结果 4.逻辑思维可以准确表达创新成果进入科学体系 5.创新成果推广应用需要逻辑思维 “西方科学的发展是以两个伟大的成就为基础，那就是：希腊哲学家发明的形式逻辑体系，以及通过系统的实验判断出因果关系”——爱因斯坦 “理论物理学的完整体系是由概念、被认为对这些概念是有效的基本定律，以及用逻辑推理得到的结论这三者所构成的。这些结论必须同我们的各个单独的经验相符合；在任何理论著作中，导出这些结论的逻辑演绎几乎占据了全部篇幅”——爱因斯坦 各门独立科学的系统体系都是由逻辑概念、逻辑判断、逻辑推理、逻辑证明建立起来的。在学术交流、教学实践、认知原理中、在科学家的思考过程中、在阐述各个学科的系统理论中，

不难看出逻辑思维在学习、工作中的重要性和核心地位。 (四)逻辑思维的形式 形式逻辑、数理逻辑、辨证逻辑 1．形式逻辑 抛开具体的思维内容，仅从形式结构上研究概念、判断、推理及其联系的逻辑体系，就是形式逻辑（又叫普通逻辑，我们平常说的逻辑，一般也指的是形式逻辑） 2．形式逻辑的基本规律 形式逻辑以保持思维的确定性为核心，帮助人们正确地思考问题和表达思想；思维要保持确定性，就要符合形式逻辑的一般规律即：同一律、矛盾律、排中律、充足理由律。 3．数理逻辑（定量的数理分析） 数理逻辑是在普通逻辑（形式逻辑）基础上发展起来的新的逻辑分支学科。数理逻辑是在深度和广度上推进了传统逻辑，使它更加精确和严密。由于数理逻辑使用了数学的语言和符号，揭示了事物和事物之间的数量关系，不仅深化了传统自然科学学科的研究，而且对计算机科学、控制技术、信息科学、生物科学等学科的发展有重要的意义。 4．辨证逻辑 “不是关于思维的外在形式的学说，而是关于一切物质的、自然的和精神的事物的发展规律的学说，即关于世界的全部具体内容及对它的认识的发展规律的学说。”——列宁辨证逻辑就是按照辨证唯物主义哲学对客观世界的认识方法和思维方式。它的思维原则主要有：全面性原则、动态性原则、实践性原则、具体性原则。 (五)逻辑思维的方法 演绎推理法、归纳推理法、实验法、比较研究法、证伪法 1．演绎推理法 演绎推理就是由一般性前提到个别性结论的推理。按照一定的目标，运用演绎推理的思维方法，取得新颖性结论的过程，就是演绎推理法 例如：一切化学元素在一定条件下发生化学反应。惰性气体是化学元素，所以，惰性气体在一定条件下确实能够发生化学反应。这里运用的就是演绎推理方法。 演绎推理的主要形式是三段论法。三段论法就是从两个判断中进而得出第三个判断的一种推理方法。上面的例子就是包含着三个判断。第一个判断是一切化学元素都在一定条件下发生化学反应"-提供了一般的原理原则，叫做三段论式的大前提。第二个判断是"惰性气体是化学元素"--指出了一种特殊情况，叫做小前提。联合这两种判断，说明一般原则和特殊情况间的联系，因而得出第三个判断："惰性气体在一定条件下确定能够发生化学反应"--结论。 只要作为前提的判断是正确的，中间的推理形式是合乎逻辑规则的，那么，必然能够推出