Problem Solving |

# | ID | Difficulty | Primary Category | Question Text |

1 | PS | Easy | Work/Rate Problems | Working at a constant rate a copy machine makes 20 copies of a one pa |

2 | PS | Easy | Algebra | If x y 2 and x 2 y 2 2 what is the value of xy |

3 | PS | Easy | Arithmetic | The sum s of the first n consecutive positive even integers is given |

4 | PS | Easy | Graphs and Illustrations/Word Probl | A certain harbor has docking stations along its west and south docks |

5 | PS | Easy | Arithmetic | |

6 | PS | Easy | Arithmetic | Points a b c and d in that order lie on a line if ab 3 cm ac |

7 | PS | Easy | Algebra | What is the value of x 2yz xyz 2 if x 2 y 1 and z |

8 | PS | Easy | Word Problems | A souvenir vendor purchased 1 000 shirts for a special event at a pric |

9 | PS | Easy | Inequalities | If x y and y z which of the following represents the greatest num |

10 | PS | Easy | Word Problems | To order certain plants from a catalog it costs 3 00 per plant |

11 | PS | Easy | Word Problems | A rug manufacturer produces rugs at a cost of 75 per rug what is the |

12 | PS | Easy | Percents and Interest Problems | The value of maureen s investment portfolio has decreased by 5 8 perce |

13 | PS | Easy | Word Problems | Company c produces toy trucks at a cost of 5 00 each for the first |

14 | PS | Easy | Words Problems | The annual profit or loss for the three divisions of company t for the |

15 | PS | Easy | Fractions/Ratios/Decimals | If the following which is least |

16 | PS | Easy | Arithmetic | If the average arithmetic mean of 5 numbers j j 5 2j 1 4j |

17 | PS | Easy | Geometry | Guadalupe owns 2 rectangular tracts of land one is 300 m by 500 m and |

18 | PS | Easy | Algebra/Word Problems | There are five sales agents in a certain real estate office one month |

19 | PS | Easy | Algebra/Word Problems | In a field day at a school each child who competed in n events and sc |

20 | PS | Easy | Work/Rate Problems | A certain work plan for september requires that a work team working |

21 | PS | Easy | Word Problems | A company sells radios for 15 00 each it costs the company 14 00 pe |

22 | PS | Easy | Arithmetic | Which of the following represent positive numbers |

23 | PS | Easy | Geometry | Point x lies on side bc of rectangle abcd which has length 12 and wid |

24 | PS | Easy | Mixture Problems | A grocer has 400 pounds of coffee in stock 20 percent |

25 | PS | Easy | Word Problems | The toll t in dollars for a truck using a certain bridge is given by |

26 | PS | Easy | Algebra | For what value of x between 4 and 4 inclusive is the value of x |

27 | PS | Easy | Algebra | If x 5 8 and y 1 2 what is the value of the expression 2x y |

28 | PS | Easy | Algebra | If x y r and xy s then x 2 y |

29 | PS | Medium | Must or Could be True Questions/Rem | For positive integers a and b the remainder when a is divided by b is |

30 | PS | Easy | Divisibility/Multiples/Factors/Stat | List s consists of the positive integers that are multiples of 9 and |

31 | PS | Easy | Arithmetic | A rope 20 6 meters long is cut into two pieces |

32 | PS | Easy | Must or Could be True Questions/Num | If x and y are integers and x y is odd which of the following must |

33 | PS | Medium | Percents and Interest Problems | On monday the opening price of a certain stock was 100 per share and |

34 | PS | Easy | Coordinate Geometry | In the rectangular coordinate system shown above points o p and q r |

35 | PS | Easy | Geometry | What is the perimeter in meters of a rectangular garden 6 meters |

36 | PS | Medium | Arithmetic | |

37 | PS | Easy | Absolute Values/Modulus/Arithmetic | |

38 | PS | Easy | Word Problems | If the total amount that jill spent on a shopping trip excluding taxe |

39 | PS | Easy | Inequalities | How many integers x satisfy both 2 x 4 and 0 x |

40 | PS | Easy | Percents and Interest Problems | At the opening of a trading day at a certain stock exchange the price |

41 | PS | Easy | Algebra/Word Problems | As shown in the diagram above a lever resting on a fulcrum has weight |

42 | PS | Medium | Algebra/Exponents/Powers | If r and s are positive integers such that 2 r 4 s 16 then 2r |

43 | PS | Easy | Word Problems | Three people each contributed x dollars toward the purchase of a car |

44 | PS | Easy | Word Problems | Last week jack worked 70 hours and earned 1 260 if he earned his re |

45 | PS | Easy | Exponents/Powers | If a and b are positive integers and 2 a b 23 what is the value |

46 | PS | Medium | Work/Rate Problems | Five machines at a certain factory operate at the same constant rate |

47 | PS | Hard | Word Problems | A certain toll station on a highway has 7 tollbooths and each tollboo |

48 | PS | Hard | Number Properties/Divisibility/Mult | How many integers between 1 and 16 inclusive have exactly 3 differen |

49 | PS | Easy | Fractions/Ratios/Decimals/Mixture P | Stephanie has 9 4 cups of milk on hand and makes 2 batches of cookies |

50 | PS | Easy | Algebra | The expression n is defined as the product of the integers from 1 thr |

51 | PS | Medium | Fractions/Ratios/Decimals | A school club plans to package and sell dried fruit to raise money th |

52 | PS | Medium | Word Problems | A nursery sells fruit trees priced as shown in the chart above in its |

53 | PS | Medium | Distance/Rate Problems | A certain bridge is 4 024 feet long approximately how many minutes |

54 | PS | Easy | Percents and Interest Problems | The annual interest rate earned by an investment increased by 10 perce |

55 | PS | Medium | Fractions/Ratios/Decimals/Percents | A total of 5 liters of gasoline is to be poured into two empty contain |

56 | PS | Easy | Algebra | What is the larger of the 2 solutions of the equation x 2 4x |

57 | PS | Medium | Arithmetic | 9 897 0 0096 198 76 is approximately |

58 | PS | Easy | Geometry | If a square region has area n what is the length of the dia |

59 | PS | Easy | Number Properties | The prime sum of an integer n greater than 1 is the sum of |

60 | PS | Medium | Percents and Interest Problems/Word | A machine at a toy factory assembles a certain kind of toy at a co |

61 | PS | Easy | Percents and Interest Problems | When a subscription to a new magazine was purchased for m months the |

62 | PS | Easy | Word Problems | At a garage sale all of the prices of the items sold were d |

63 | PS | Medium | Word Problems | Half of a large pizza is cut into 4 equal sized pieces and the other |

64 | PS | Medium | Algebra/Arithmetic | If a 1 1 4 1 16 1 64 and b 1 1 4a then what is the value |

65 | PS | Medium | Arithmetic/Word Problems | In a certain learning experiment each participant had three trials an |

66 | PS | Easy | Remainders/Functions and Custom Cha | Or all positive integers m and v the expression m v represents the |

67 | PS | Medium | Graphs and Illustrations/Word Probl | The chart above shows year end values for darnella s investments for |

68 | PS | Easy | Fractions/Ratios/Decimals | If the sum of the reciprocals of two consecutive odd integers |

69 | PS | Easy | Number Properties/Arithmetic | What is the sum of odd integers from 35 to 85 inclusive |

70 | PS | Medium | Fractions/Ratios/Decimals/Inequalit | In a certain sequence each term after the first term is one half the |

71 | PS | Medium | Word Problems/Statistics and Sets P | A certain drive in movie theater has total of 17 rows of parking space |

72 | PS | Medium | Statistics and Sets Problems | Ada and paul received their scores on three tests on the fi |

73 | PS | Easy | Fractions/Ratios/Decimals | The price of a certain stock increased by 0 25 of 1 percent on a |

74 | PS | Hard | Word Problems | For each trip a taxicab company charges 4 25 for the first mile and |

75 | PS | Hard | Divisibility/Multiples/Factors/Numb | When 24 is divided by the positive integer n the remainder is 4 whic |

76 | PS | Easy | Fractions/Ratios/Decimals | What is the thousandths digit in the decimal equivalent of |

77 | PS | Easy | Algebra | If 1 2 the result obtained when 2 is subtracted from 5x is equal to th |

78 | PS | Easy | Coordinate Geometery | In a rectangular coordinate system straight line k passes through poi |

79 | PS | Medium | Distance/Rate Problems | If car a took n hours to travel 2 miles and car b took m hours to trav |

80 | PS | Medium | Algebra/Arithmetic | If x y and k are positive and x is less than y then x k y k |

81 | PS | Easy | Algebra/Inequalities | Consider the following set of inequalities p q s r q t s p |

82 | PS | Easy | Distance/Rate Problems | Carl averaged 2m miles per hour on a trip that took him h hours if ru |

83 | PS | Very Hard | Overlapping Sets | Of three persons two take relish two take pepper and two take salt |

84 | PS | Medium | Geometry | If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap |

85 | PS | Medium | Geometry | In the figure above the area of the parallelogram is 294399.ht |

86 | PS | Hard | Divisibility/Multiple/Factors | If the smaller of 2 consecutive odd integers is a multiple of 5 which |

87 | PS | Medium | Geometry | In the figure above if triangles abc acd and ade are isosceles righ |

88 | PS | Very Hard | Geometry | Each of 27 white 1 centimeter cubes will have exactly one face painted |

89 | PS | Medium | Geometry | The figure above is constructed by separating a circular region into |

90 | PS | Medium | Geometry | On a scale drawing of a triangular piece of land the sides of the tri |

91 | PS | Easy | Geometry | Which of the following gives all possible values of x in the figure ab |

92 | PS | Easy | Geometry | In the figure above lines are drawn at the vertices of the quadrilate |

93 | PS | Hard | Geometry | The dimensions of a ream of paper are 8 1 2 inches by 11 inches by |

94 | PS | Medium | Geometry | In the racetrack shown above regions i and iii are semicircular with |

95 | PS | Hard | Geometry | The figure above which is divided into 6 sectors of equal area conta |

96 | PS | Medium | Geometry | When a rectangular vat that is 3 feet deep is filled to 2 3 of its cap |

97 | PS | Easy | Geometry | The figure above represents an antenna tower with two guy wires that e |

98 | PS | Medium | Geometry | The figures above show a sealed container that is a right circular cyl |

99 | PS | Medium | Geometry | The figure above shows a drop leaf table with all four leaves down th |

100 | PS | Easy | Geometry | If the diameter of a circular skating rink is 60 meters the area of |

101 | PS | Easy | Geometry | What is the greatest number of blocks 8 centimeters by 6 centimeters |

102 | PS | Medium | Word Problems | Eight light bulbs numbered 1 through 8 are arranged in a circle as sho |

103 | PS | Medium | Min/Max Problems/Set and statistics | The average arithmetic mean of the positive integers x y and z is |

104 | PS | Hard | Number Properties | The product of 3 305 and the 1 digit integer x is a 5 digit integer th |

105 | PS | Medium | Algebra | If x and y are integers such that 2 x 8 and 2 y 9 what is the |

106 | PS | Medium | Word Problems | Items that are purchased together at a certain discount store are pric |

107 | PS | Medium | Exponents/Powers - Arithmetic | What is the least integer z for which |

108 | PS | Easy | Set and statistics problems | The average arithmetic mean length per film for a group of 21 films |

109 | PS | Hard | Geometry | An open box in the shape of a cube measuring 50 centimeters on each si |

110 | PS | Hard | Word Problems | A garden center sells a certain grass seed in 5 pound bags at |

111 | PS | Easy | Absolute Values/Modulus/Algebra | If x w which of the following must be true |

112 | PS | Hard | Percents and Interest Problems | A certain financial institution reported that its assets totaled |

113 | PS | Easy | Arithmetic | In the correctly worked addition problem shown where the |

114 | PS | Medium | Coordinate Geometry/Geometry | Planning is in progress for a fenced rectangular playground with an a |

115 | PS | Hard | Absolute Values/Modulus/Inequalitie | Given the inequalities above which of the following cannot be |

116 | PS | Medium | Number Properties | If m is an even integer v is an odd integer and m v 0 which of |

117 | PS | Medium | Divisibility/Multiples/Factors | A positive integer is divisible by 9 if and only if the sum of its |

118 | PS | Medium | Geometry | The perimeter of rectangle a is 200 meters the length of rectangle b |

119 | PS | Easy | Inequalities | In the number line the shaded interval is the graph of which of the |

120 | PS | Hard | Statistics and Sets Problems | Last year members of a certain professional organization for teachers |

121 | PS | Medium | Fractions/Ratios/Decimals | If all the students in a certain dormitory 1 2 are first year student |

122 | PS | Easy | Fractions/Ratios/Decimals | If the average arithmetic mean of x y and z is 7x and x |

123 | PS | Easy | Distance/Rate Problems | Jonah drove the first half of a 100 mile trip in x hours and the secon |

124 | PS | Medium | Coordinate Geometry | In the xy plane the points c d c d and c d |

125 | PS | Hard | Percents and Interest Problems | If the amount of federal estate tax due on an estate valued at |

126 | PS | Easy | Fractions/Ratios/Decimals | If 3 10 4 x then x |

127 | PS | Easy | Remainders | What is the remainder when 3 24 is divided by |

128 | PS | Hard | Geometry | In the figure shown a square grid is superimposed on the map of a par |

129 | PS | Medium | Arithmetic | If the volume of a ball is 32 490 cubic millimeters what is the volum |

130 | PS | Medium | Percents and Interest Problems/Word | David used part of 100 000 to purchase a house of the remaining port |

131 | PS | Medium | Word Problems | A certain manufacturer sells its products to stores in 113 different r |

132 | PS | Medium | Percents and Interest Problems | Andrew started saving at the beginning of the year and had saved |

133 | PS | Medium | Arithmetic | Two numbers differ by 2 and sum to s which of the following is the gr |

134 | PS | Medium | Geometry | The figure shown above consists of three identical circles t |

135 | PS | Medium | Arithmetic/Statistics and Sets Prob | In a numerical table with 10 rows and 10 columns each entry is either |

136 | PS | Medium | Arithmetic/Number Properties | A positive integer n is a perfect number provided that the sum of all |

137 | PS | Easy | Sequences | The infinite sequence a1 a2 an is such that a1 |

138 | PS | Easy | Sequences | The sequence a1 a2 a n is such that an 2an 1 x |

139 | PS | Easy | Geometry | A window is in the shape of a regular hexagon with each side of length |

140 | PS | Medium | Geometry | In the figure shown pqrstu is a regular polygon with sides of lenght x |

141 | PS | Medium | Percents and Interest Problems | In a certain medical survey 45 percent of the people surveyed had the |

142 | PS | Medium | Overlapping Sets | In a certain transatlantic crossing 20 percent of a ship s |

143 | PS | Medium | Algebra/Exponents/Powers | If x and k are integers and 12 x 4 2x 1 2 k 3 2 what |

144 | PS | Easy | Fractions/Ratios/Decimals | If s is the sum of the reciprocals of the 10 consecutive integers from |

145 | PS | Easy | Number Properties | For every even positive integer m f m represents the produ |

146 | PS | Hard | Geometry | In pentagon pqrst pq 3 qr 2 rs 4 and st 5 which |

147 | PS | Easy | Statistics and Sets Problems | The arithmetic mean of the list of numbers above is 4 if k |

148 | PS | Medium | Statistics and Sets Problems | If the variables x y and z take on only the values |

149 | PS | Very Hard | Geometry | When the figure above is cut along the solid lines folded along the |

150 | PS | Hard | Absolute Values/Modulus/Algebra | For how many ordered pairs x y that are solutions of the |

151 | PS | Medium | Geometry | The points r t and u lie on a circle that has radius 4 if |

152 | PS | Easy | Combinations | A certain university will select 1 of 7 candidates eligible |

153 | PS | Medium | Percents and Interest Problems | A survey of employers found that during 1993 employment cost |

154 | PS | Hard | Combinations | The subsets of the set w x y are w x y w x w y |

155 | PS | Easy | Combinations | There are 5 cars to be displayed in 5 parking spaces with all the cars |

156 | PS | Very Hard | Number Properties | The number can be expressed as 63 36 3 1 2 1 2 can be expresse |

157 | PS | Hard | Combinations | There are 10 books on a shelf of which 4 are paperbacks and 6 are har |

158 | PS | Medium | Probability/Remainders | If x is to be chosen at random from the set 1 2 3 4 and |

159 | PS | Hard | Exponents/Powers/Functions and Cust | The function f is defined for each positive three digit |

160 | PS | Hard | Arithmetic/Exponents/Powers | If 10 50 74 is written as an integer in base 10 notation |

161 | PS | Medium | Percents and Interest Problems | A certain company that sells only cars and trucks reported |

162 | PS | Easy | Fractions/Ratios/Decimals | Becky rented a power tool from a rental shop the rent for the tool wa |

163 | PS | Very Hard | Inequalities/Must or Could be True | If 4 7 x 3 which of the following must be true |

164 | PS | Very Hard | Inequalities/Geometry | A certain right triangle has sides of length x y and z where x y |

165 | PS | Hard | Word Problems | In a certain day a bakery produced a batch of rolls at a total produc |

166 | PS | Medium | Must or Could be True Questions | A set of numbers has the property that for any number t in t |

167 | PS | Very Hard | Probability/Combinations | A couple decides to have 4 children if they succeed in havi |

168 | PS | Very Hard | Percents and Interest Problems | The closing price of stock x changed on each trading day last month t |

169 | PS | Very Hard | Geometry | In the figure above point o is the center of the circle and |

170 | PS | Medium | Word Problems | In airline passenger is planning a trip that involves three |

171 | PS | Hard | Number Properties/Divisibility/Mult | If n is a positive integer and n 2 is divisible by 72 then |

172 | PS | Easy | Algebra | A certain grocery purchased x pounds of produce for p dollar |

173 | PS | Medium | Divisibility/Multiples/Factors | If x y and z are positive integers such that x is a factor |

174 | PS | Very Hard | Work/Rate Problems | Running at their respective constant rates machine x takes |

175 | PS | Very Hard | Geometry/Must or Could be True Ques | A square wooden plaque has a square brass inlay in the |

176 | PS | Easy | Arithmetic | |