1) If (1/5)m(1/4)18 = 1/2(10)35, m?a. 18b. 17c. 21d. 35 e. 3

2) (-1)k+1(½k). T is the sum of the first 10 k, is t a. > 2b. between 1 and 2c. between ½ and 1d. between ¼ and ½ e. < ¼

3) What is m+n?a. 3b. 4c. 5 d. 6e. 7

+ x y z4 1 -5 me 7 n 10f 2 -4 5

4) Perimeter of isosceles right triangle is 16 +16√2, what is hypotenuse?a. 8b. 16 c. 4√2d. 8√2e. 16√2

5) If it took Carlos 1/2hr from home to library, is distance greater than 6 miles? (1mile = 5280 feet) E

a. Average speed was greater than 16 feet/secondb. Average speed was less than 18 feet/second

6) Does line k intersect quadrant II? Aa. Slope of k is -1/6b. Y intercept of k is -6

7) r and s are integers and rs + r is odd, which MUST be even?a. rb. s c. r + sd. rs – re. r2 + s

8) Two machine types, Type R and Type S, operate at a constant rate. R does a job in 36 hours. S does same job in 18. If we use the same number of each type to do the job in 2 hours, how many Type r machines do we need?

a. 3b. 4c. 6 d. 9e. 12

9) If x ≠ 0, then √x2/x =a. -1b. 0c. 1d. xe. |x|/x

10) 2x – 2x-2 = 3(213), what is x?a. 9b. 11c. 13d. 15 e. 17

11) Is integer r divisible by 3? Aa. R is the product of 4 consecutive positive integersb. r < 25

12) If # is defined by a # b = a + b – ab, then which is true?a # b = b # aa # 0 = a(a # b) # c = a # (b # c)

a. I b. IIc. I & IId. I & IIIe. I, II & III

13) Lines n and p lie in xy plane. Is slope of line n less than slope of line p? Ca. Lines n and p intersect at (5, 1)b. Y-intercept of line n is greater than y intercept of line p

14) Six machines working at the same rate constant rate complete a job in 12 days. How many additional machines working at same rate will be needed to complete the job in 8 days?

a. 2b. 3 c. 4d. 6e. 8

15) 108 – 102 / 107 – 103 is closest to which of the following?a. 1b. 10 c. 102

d. 103

e. 104

16) A basket has 5 apples, one is spoiled. If Henry picked 2 apples simultaneously and at random, what is probability that the 2 selected apples will include the spoiled one.

a. 1⁄5b. 2⁄10c. 2⁄5 d. 1⁄2e. 3⁄5

17) On the 1st day the late fine is 0.1. Each additional day the total fine is either increased by 0.3 or doubled whichever is the lesser amount. What is total fine on the 4th day?

a. 0.6b. 0.7 c. 0.8d. 0.9e. 1.0

18) Of 25 cars sold, some had automatic and some had antilock. How many had automatic but not antilock E

a. All cars that had antilock also had automaticb. 2 of the cars that had neither automatic nor antilock

19) Is x between 0 and 1? Ba. x is between -1⁄2 and 3⁄2b. 3⁄4 is 1⁄4 more than x

20) If m, r, x & y are positive, is the ratio of m to r equal to the ratio of x to y? Ba. Ratio of m to y is equal to ratio of x to rb. Ratio of m + x to r + y equals ratio of x to y

21) How long did it take Helen to drive from home to her parents? C

a. Helen’s ave speed was 72Km/hb. If Helen’s ave speed had been 8km/h faster it would have taken her 1 hour

less

22) Each row has same number of chairs and number of rows is 1 less than the number of chairs in a row. How many chairs are in each row? D

a. There are a total of 72 chairsb. After 1 chair is removed from last row, there are 17 chairs in the last 2

rows

23) Alice’s take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home 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. 1⁄2b. 1⁄3c. 1⁄4d. 1⁄5 e. 1⁄6

24) n is an integer between 10 and 99, is n< 80? Ba. Sum of the two digits on n is a prime numberb. Each of the two digits of n is a prime number

25) During a one day sale, a store sold each sweater for $30 more than the cost of purchase. How many were sold during the sale? C

a. Total revenue for sweaters is $270b. Store sold each sweater for 50% more than the cost of purchase.

26) If the average of five numbers, x, 7, 2, 16, and 11 = the median, what is x? Da. 7 < x > 11b. x is median of the five numbers

27) If everyone was charged the same fee, how many people came? Ca. If the fee had been %0.75 less and 100 more people came the club would

have received the same amount.b. If fee had been $1.50 more and 100 fewer people came, the club would

have received the same amount

28) On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line? E

a. xyz < 0b. xy < 0

29) If xyz > 0, is x > 0? Ca. xy > 0b. xz > 0

30) 2(4-1)^2 / 23-2

a. 2 8 b. 27

c. 26

d. 25

e. 24

31) If n is a positive integer less than 200 and 14n⁄60 is also an integer, then n has how many different positive prime factors

a. 2b. 3 c. 5d. 6e. 8

32) Are at least 10% of people 65 and older employed? Ba. 11.3% of population is 65 or overb. Of those 65 and older, 20% of mean and 10% of women are employed.

33) The difference between Mary and Jim’s salary was twice the difference between Mary and Kate’s. If Mary had the highest salary, what was the average of the three? B

a. Jim’s salary was $30,000b. Kate’s was $40,000

34) If xy = 1, what is value of 2(x+y)^2 / 2(x-y)^2

a. 2b. 4c. 8d. 16 e. 32

35) If r and s are positive integers, is r/s an integer? Aa. Every factor of s is also a factor of rb. Every prime factor of s is also a prime factor of r

36) For a finite set 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 consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6?

a. 1b. 2c. 3 d. 4e. 5

37) Circular gears P & Q start rotating at the same time at constant speeds. Gear P rotates at 10 revs/min and gear Q at 40 revs/min. How many seconds after gears start rolling will Q have made exactly 6 more revs than P

a. 6b. 8c. 10d. 12 e. 15

38) Is x less than 20? Ea. Sum of x and y is less than 20b. y is less than 20

39) In isosceles triangle RST, what is measure of angle R? A a. Angle T is 100ºb. Angle S is 40º

40) Some water was removed from each of 6 tanks. If standard deviation of the volumes of water at the beginning was 10 gallons, what was the standard deviation of the volumes at the end? A

a. For each tank, 30% of water at the beginning was removedb. The average volume of water in the tanks at the end was 63 gallons

41) A serving requires 1½ cups of pasta. How many cups of pasta will he use this time? C

a. He makes half as many servings as he did last timeb. He used 6 cups of pasta the last time

42) L M

K NIn this figure, what is ratio KN/MN? B

a. Perimeter of KLMN is 30b. All three rectangles have the same dimensions

43) The rate of a reaction is directly proportional to the square of the concentration of A and inversely proportional to concentration of B. If B increases by 100%, which of the following is closest to the % change in concentration of A required to keep the rate unchanged?

a. 100% decreaseb. 50% decreasec. 40% decreased. 40% increase e. 50% increase

44) PQ is parallel to OR. OR = 18. What is the length of minor arc PQ [DON’T DO]a. 2π b. 9π⁄4c. 7π⁄2d. 9π⁄2e. 3π

45) A list of measurements in increasing order is 4, 5, 6, 8, 10, and x. If median of the measurements is 6/7 times the mean, what is the value of x?

a. 16 b. 10c. 12d. 13e. 15

46) Which of the following is and integer?12!/6!12!/8!12!/7!5!

a. Ib. IIc. IIId. I & IIe. I, II & III

47) Three grades of milk: 1%, 2%, and 3% fat by volume. X gallons of 1%, y gallons of 2%, and z gallons of 3% are mixed to give x + y + z gallons of 1.5%. What is x in terms of y and z?

a. y + 3z b. (y + z)/4c. 2y + 3zd. 3y + ze. 3y + 4z

48) n and m are positive integers, what is remainder when 34n + 2 + m is divided by 10? B

a. n = 2b. m = 1

49) In the xy plane, at what point does y = (x + a)(x + b) cross the x axis? Ca. a + b = -1 b. graph intersects y axis at (0, -6)

50) If x and y are integers greater than 1, is x a multiple of y? Aa. 3y2 + 7y = xb. x2 – x is a multiple of y

51) At 50 mph a car uses 1 gallon for every 30 miles. If the car starts with a full tank of 12 gallons and drives for 5 hrs at 50mph, the amount of gas used would be what fraction of the tank?

a. 3⁄25b. 11⁄36c. 7⁄12d. 2⁄3e. 25⁄36

52) If M = √4 + 3√4 + 4√4, the value of M isa. < 3b. = 3c. 3 < M < 4d. = 4e. > 4

53) 2 sizes of sticky pads. Each has 4 colors – Blue, Green, Yellow, and Purple. The pads are packed in packages that contain either 3 notepads of same size and same color or 3 notepads of same size and of 3 different colors. How many different packages of the types described are possible?

a. 6b. 8c. 16 d. 24e. 32

54) If the operation @ is one of + - * or /, is (6 @ 2) @ 4 = 6 @ (2 @ 4) Aa. 3 @ 2 > 3b. 3 @ 1 = 3

55) What is the value of n? Ba. N is between 0 and 1b. 7∕16 is 3∕8 more than n

56) Martha bought an armchair and a coffee table at an auction and sold both. Her gross profit from purchase and sale of armchair was what % greater than gross profit from purchase and sale of coffee table? E

a. She paid 10% more for armchair than tableb. She sold armchair for 20% more than she told the table

57) x, y, and z are integers greater than 1, what is value of x + y + z? Aa. xyz = 70b. x/yz = 7/10

58) Is z equal to the median of the 3 positive integers x, y & z? Ba. x < y + zb. y = z

59) M orders 50 computers and printers. N orders 60 computers and printers. How many computers did M order? E

a. M & N ordered the same number of computersb. N ordered 10 more printers than M

60) (82)(33)(24) / 962 = a. 3 b. 6c. 9d. 12e. 18

61) If xy + z = x(y + z), which must be true?a. x = 0; z = 0b. x = 1; y = 1c. y = 1; z = 0d. x = 1 or y = 0e. x = 1 or z = 0

62) Area of triangle PQR is what fraction of triangle LMN [DON’T DO]a. 1⁄9b. 1⁄8c. 1⁄6d. 1⁄5e. 1⁄3

63) S is finite set of numbers. Does S contain more negative numbers than positive numbers? E

a. Product of all numbers in S is -1200b. There are 6 numbers in S

64) Each employee is either a director or a manager. What % of the employees are directors? C

a. The average salary of managers is $5000 less than the average of all employees

b. The average salary of directors is $15000 greater than the average of all employees

65) The ratio of women to children on a tour is 5:2. How many men are there? Ca. Ratio of children to women is 5:11b. There are less than 30 women on the tour.

66) In the figure P and Q lie on circle with center Q, what is s? [DON’T DO]a. 1⁄2b. 1c. √2d. √3e. √2/2

67) n and y are positive integers and 450y = n3, which is an integer?y / 3 * 22 * 5y / 32 * 2 * 5y / 3 * 2 * 52

a. Noneb. I c. IId. IIIe. I, II, III

68) A thin piece of 40 m wire is cut in two. One piece is a circle with radius of r. Other is a square. No wire is left over. Which represents total area of circle and square in terms of r?

a. Πr2

b. Πr2 + 10

c. Πr2 + ¼ π2r2

d. Πr2 + (40 - 2πr)2

e. Πr 2 + (10 - ½ Πr) 2

69) Harry bought a desk for $150. Selling price was purchase price plus markup that was 40% of selling price. What is gross profit?

a. 40b. 60c. 80d. 90e. 100

70) If x4 + y4 = 100, the greatest possible value of x is between a. 0 and 3 b. 3 and 6c. 6 and 9d. 9 and 12e. 12 and 15

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

a. 38b. 39c. 40 d. 41e. 42

72) What is the remainder when positive integer x is divided by 3? Da. When x is divided by 6 remainder is 2b. When x is divided by 15, remainder is 2

73) In xy plane, what is y-intercept of l? Ea. Slope of l is 3 times the y interceptb. x-intercept of l is -⅓

74) Sum of positive integers x and y is 72. What is xy? Da. x = y + 1b. x and y have same tens digit

75) Is x > 0.05? Da. x > 3/40b. x > 3% of 50

76) Al, Pablo, and Masha shared driving on a 1,500 mile trip. Who drove greatest distance? E

a. Al drove 1 hr longer than Pablo but at an average speed of 5 mph slower than Pablo

b. Masha drove 9 hrs and averaged 50 mph

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

a. d b. 3dc. 15dd. d + 5e. d + 15

78) x and y are positive, what is x + y? Da. 2x3y = 72b. 2x2y = 32

79) What is the % increase in population of City K from 1980 to 1990? Ba. In 1970 population of K was 160,000b. In 1980 population of K was 20% greater than 1970 and in 1990

population is 30% greater than in 1970

80) Which is equal to 25 + 25 + 35 + 35 + 35?a. 56

b. 135

c. 2 6 + 3 6 d. 27 + 38

e. 45 +95

81) If x is negative integer, which of the following has the least value?a. x2 – 0.50b. x2 – 0.51c. x3 – 0.502d. x 3 – 0.511 e. x4 – 0.512

82) The main ingredients in a capsule is $500/kilo. Each capsule has 600 milligrams per capsule, what is the cost of the ingredient in a capsule? (1 kilo = 106 milligrams)

a. $0.30 b. $0.83c. $1.20d. $3.00e. $3.33

83) Is x < 20? Ea. x + y < 20b. y < 20

84) PRS is how many degrees greater than PQR? [DON’T DO] Da. QPR is 30º b. PQR +PRQ is 150º

85) What fraction of graduating students at college X are male? Ca. 33% of males and 20% of females transferred from another collegeb. 25% of all students transferred

86) Did it take Pei more than 2 hours to walk a distance of 10 miles? (1 mile = 1.6km) D

a. Pei walked at an average rate of less than 6.4 kmhb. On average, it took Pei more than 9 mins/km to walk this distance

87) Equilateral triangle ABC is inscribed. If arc ABC is 24, what is diameter? [DON’T DO]

a. 2b. 8c. 11d. 15e. 19

88) For how many integers n is 2n = n2

a. Noneb. 1c. 2 d. 3e. More than 3

89) What is GCD of positive integers m and n? Ca. m is a prime numberb. 2n = 7m

90) For which of the following functions is f(x) = f(1-x) for all x?a. f(x) = 1 – xb. f(x) = 1 – x2

c. f(x) = x2 – (1 – x)2

d. f(x) = x 2 (1 – x) e. f(x) = x / x/1 – x

91) If zn = 1, what is value of z? Ca. n is a nonzero integerb. z > 0

92) If x > y2 > z4, which of the following could be true?x > y > zz > y > xx > z > y

a. Ib. I and IIc. I and IIId. II and IIIe. I, II, and III

93) Each stack is designated with a 1, 2, and 3 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 constitutes a different code, how many different stocks is it possible to uniquely designate with these codes?

a. 2951b. 8125c. 15600d. 16302e. 8278

94) Dealer sold 1 car at a profit of 25% of purchase price, and sold another car at a loss of 20% of purchase price. If dealer sold each car for $20000, what was dealer’s total profit or loss in dollars for the 2 transactions combined?

a. 1000 profitb. 2,000 profitc. 1000 loss d. 2000 losse. 3334 loss

95) Each employee of company Z is employed in either Division X or Division Y, but not both. If each division has some part time employees, is the ratio of the number of full-time employees to number of part-time employees greater for Division X than for Company Z? D

a. Ratio of number of full time employees to part-time employees is less for division Y than for company Z

b. More than ½ of full-time employees of company Z are employees of div X, and more than ½ of part-time employees of company Z are employees of div Y

96) X and Y work at constant rates, how many more hours does it take machine y, alone, to fill an order of a certain size than machine X alone. E

a. X and Y together fill order in 2⁄3 the time that X alone doesb. Y alone does it in twice the time as X alone does

97) When a tree was planted it was 4 feet. Its height increased by a constant amount each year for 6 years. After 6 years the tree was 1⁄5 taller than at the end of 4th year. By how many feet did the height of the tree increase each year?

a. 3⁄10b. 2⁄5c. 1⁄2d. 2⁄3 e. 6⁄5

98) Positive integers x, y, and z are such that x is a factor of y and y is a factor of z, if z even? D

a. xz is evenb. y is even

99) If x is a positive number less than 10, is z greater than average of x and 10? Aa. z is closer to 10 than x on the number lineb. z = 5x