Problem Solving |

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

1 | PS | Easy | Geometry | In the figure the 6 small squares are identical each with sides of l |

2 | PS | Easy | Arithmetic/Graphs and Illustrations | The table shows a summary of the ticket sales from four performances o |

3 | PS | Easy | Statistics and Sets Problems | During a trip that they took together carmen juan maria a |

4 | PS | Easy | Word Problems | Each week a clothing salesperson receives a commission equal |

5 | PS | Easy | Arithmetic/Word Problems | A certain restaurant that regularly advertises through the mail has |

6 | PS | Easy | Geometry | In the figure above what are the coordinates of point r |

7 | PS | Easy | Percents and Interest Problems | The price of a coat in a certain store is 500 if the price of the co |

8 | PS | Easy | Arithmetic | (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) = |

9 | PS | Easy | Word Problems | While a family was away on vacation they paid a neighborhood boy |

10 | PS | Easy | Word Problems | Last year 48 000 of a certain store s profit was shared by its 2 owne |

11 | PS | Easy | Fractions/Ratios/Decimals | On a vacation rose exchanged 500 00 for euros at an exchange rate of |

12 | PS | Easy | Fractions/Ratios/Decimals | Each of the 12 squares shown is labeled x y v or w what is the ratio |

13 | PS | Easy | Coordinate Geometry | In the xy coordinate plane if the point 0 2 lies on the graph of th |

14 | PS | Easy | Number Properties/Word Problems | Bouquets are to be made using white tulips and red tulips and the rat |

15 | PS | Easy | Word Problems | Over the past 7 weeks the smith family had weekly grocery bills of |

16 | PS | Easy | Arithmetic/Percents and Interest Pr | 125% of 5 = |

17 | PS | Easy | Statistics and Sets Problems | During a recent storm 9 neighborhoods experienced power failures of |

18 | PS | Easy | Distance/Rate Problems/Word Problem | When traveling at a constant speed of 32 miles per hour a certain mot |

19 | PS | Easy | Percents and Interest Problems/Word | A technician makes a round trip to and from a certain service center b |

20 | PS | Medium | Word Problems | From 2000 to 2003 the number of employees at a certain company increa |

21 | PS | Easy | Statistics and Sets Problems | Which of the following statements must be true about the average arit |

22 | PS | Easy | Algebra | A collection of 16 coins each with a face value of either 10 cents or |

23 | PS | Easy | Word Problems | A retailer purchased eggs at 2 80 per dozen and sold the eggs at 3 eg |

24 | PS | Easy | Probability | In a set of 24 cards each card is numbered with a different positive |

25 | PS | Easy | Geometry | If the circumference of a circle inscribed in a square is 25 what is |

26 | PS | Easy | Inequalities | If 1 x y z which of the following has the greatest value |

27 | PS | Medium | Number Properties/Statistics and Se | Set x consists of eight consecutive integers set y consists of all th |

28 | PS | Easy | Arithmetic | Of the following which is the closest to |

29 | PS | Easy | Algebra | Thabo owns exactly 140 books and each book is either paperback fictio |

30 | PS | Easy | Arithmetic | If the average arithmetic mean of the four numbers 3 15 32 and n |

31 | PS | Easy | Word Problems/Geometry | Abdul barb and carlos all live on the same straight road on which |

32 | PS | Easy | Geometry | In the figure shown what is the value of x |

33 | PS | Easy | Word Problems/Work/Rate Problems | During a certain time period car x traveled north along a straight ro |

34 | PS | Easy | Fractions/Ratios/Decimals/Word Prob | Cheryl purchased 5 identical hollow pine doors and 6 identical solid o |

35 | PS | Easy | Min/Max Problems/Word Problems | A certain store will order 25 crates of apples the apples will be of |

36 | PS | Easy | Word Problems | A bicycle store purchased two bicycles one for 250 and the other for |

37 | PS | Easy | Geometry | In the figure shown ac 2 and bd dc 1 what is the measure of |

38 | PS | Easy | Absolute Values/Modulus/ | If k 2 m 2 which of the following must be true |

39 | PS | Easy | Algebra | Makoto nishi and ozuro were paid a total of 780 for waxing the floo |

40 | PS | Easy | Geometry | The figure above shows a path around a triangular piece of land mary |

41 | PS | Easy | Algebra/Exponents/Powers | If x is a positive integer and 4 x 3 y which of the following can |

42 | PS | Easy | Algebra | If (1 – 1.25)N = 1, then N = |

43 | PS | Easy | Remainders | The quotient when a certain number is divided by 2 3 is 9 2 what is |

44 | PS | Easy | Geometry | If a sphere with radius r is inscribed in a cube with edges of length |

45 | PS | Medium | Word Problems | The price of gasoline at a service station increased from 1 65 per ga |

46 | PS | Easy | Word Problems | Based on the rates above how much would company x charge a customer |

47 | PS | Easy | Algebra | If 2x + y = 7 and x + 2y = 5, then (x + y)/3 = |

48 | PS | Easy | Fractions/Ratios/Decimals | City x has a population 4 times as great as the population of city y |

49 | PS | Easy | Graphs and Illustrations | The graph above shows the height of the tide in feet above or below |

50 | PS | Easy | Arithmetic | If S = 1 + 1/2^2 + 1/3^2 + 1/4^2 + 1/5^2 + 1/6^2 + 1/7^2 + 1/8^2 + 1/9 |

51 | PS | Easy | Percents and Interest Problems/Word | A manufacturer of a certain product can expect that between 0 3 percen |

52 | PS | Easy | Geometry | A flat patio was built alongside a house as shown in the figure above |

53 | PS | Easy | Arithmetic/Roots | Which of the following is closest to (4.2(1,590)/15.7)^(1/2) ? |

54 | PS | Easy | Percents and Interest Problems/Stat | The sum of the weekly salaries of 5 employees is 3 250 if each of th |

55 | PS | Easy | Word Problems | Last week chris earned x dollars per hour for the first 40 hours worke |

56 | PS | Easy | Geometry | In the figure above what is the ratio of the measure of angle b to |

57 | PS | Easy | Arithmetic | The value of 7 8 1 9 1 2 is closest to which of the following |

58 | PS | Easy | Divisibility/Multiples/Factors | The positive two digit integers x and y have the same digits but in |

59 | PS | Easy | Sequences | In a certain sequence of 8 numbers each number after the first is |

60 | PS | Medium | Algebra/Word Problems | A total of s oranges are to be packaged in boxes that will hold r oran |

61 | PS | Easy | Arithmetic/Inequalities | If 0 a b c which of the following statements must be true |

62 | PS | Easy | Coordinate Geometry | In the xy plane the origin o is the midpoint of line segment pq if t |

63 | PS | Medium | Statistics and Sets Problems | The table above shows the number of packages shipped daily by each of |

64 | PS | Easy | Percents and Interest Problems/Word | Company q plans to make a new product next year and sell each unit of |

65 | PS | Easy | Word Problems | A small business invests 9 900 in equipment to produce a |

66 | PS | Medium | Remainders | The dial shown above is divided into equal sized intervals at which |

67 | PS | Medium | Percents and Interest Problems | According to the table shown the estimated number of home schooled |

68 | PS | Easy | Coordinate Geometry | The graph of the equation xy k where k 0 lies in which two of th |

69 | PS | Easy | Fractions/Ratios/Decimals | When n liters of fuel was added to a tank that was already |

70 | PS | Medium | Geometry | The smaller rectangle in the figure above represents the original size |

71 | PS | Medium | Percents and Interest Problems | Kevin invested 8 000 for one year at a simple annual interest rate of |

72 | PS | Easy | Geometry | The figure above represents a semicircular archway over a flat street |

73 | PS | Easy | Fractions/Ratios/Decimals | The harvest yield from a certain apple orchard was 350 bushels of appl |

74 | PS | Medium | Fractions/Ratios/Decimals/Percents | In a certain fraction the denominator is 16 greater than the numerato |

75 | PS | Hard | Word Problems | Greg assembles units of a certain product at a factory each day he is |

76 | PS | Medium | Arithmetic/Roots | Which of the following is greatest |

77 | PS | Hard | Distance/Rate Problems | Al and ben are drivers for sd trucking company one snowy day ben lef |

78 | PS | Easy | Percents and Interest Problems | Of the land owned by a farmer 90 percent was cleared for planting of |

79 | PS | Easy | Sequences | At the start of an experiment a certain population consisted of |

80 | PS | Easy | Algebra | If (1/3 + 1/4 + 1/5 + 1/6) = r(1/9 + 1/12 + 1/15 + 1/18), then r = |

81 | PS | Medium | Algebra/Arithmetic | If x and y are positive integers such that y is a multiple of 5 and 3x |

82 | PS | Easy | Algebra | Which of the following expressions can be written as an integer |

83 | PS | Easy | Work/Rate Problems | Pumping alone at their respective constant rates one inlet pipe fills |

84 | PS | Easy | Coordinate Geometry | In the xy coordinate plane which of the following points must lie on |

85 | PS | Easy | Inequalities | If x 2 2 0 which of the following specifies all the possible |

86 | PS | Medium | Algebra/Remainders | Shawana made a schedule for reading books during 4 weeks 28 days of |

87 | PS | Hard | Percents and Interest Problems | In western europe x bicycles were sold in each of the years 1990 and |

88 | PS | Easy | Algebra/Remainders | If k is a positive integer what is the remainder when k 2 k 3 k |

89 | PS | Hard | Arithmetic/Fractions/Ratios/Decimal | Which of the following fractions is closest to 1/2 |

90 | PS | Easy | Algebra/Fractions/Ratios/Decimals | If p ≠ 0 and p – (1 – p^2 )/p = r/p, then r = |

91 | PS | Easy | Statistics and Sets Problems | If the range of the six numbers 4 3 14 7 10 and x is 12 what is the |

92 | PS | Easy | Algebra | What number is 108 more than two thirds of itself a 72 b 144 c |

93 | PS | Medium | Percents and Interest Problems | Company p had 15 percent more employees in december than it |

94 | PS | Easy | Word Problems | A doctor prescribed 18 cubic centimeters of a certain drug to a patien |

95 | PS | Easy | Exponents/Powers/Roots | The function f is defined by f(x) = x^(1/2) - 10 for all positive numb |

96 | PS | Medium | Geometry | If rectangle abcd is inscribed in the circle above what is the area |

97 | PS | Easy | Geometry | In quadrilateral abcd above what is the length of ab |

98 | PS | Very Hard | Geometry | Three fourths of the area of a rectangular lawn 30 feet wide by 40 fee |

99 | PS | Hard | Geometry | In the floor plan of an executive s beach house above the north and |

100 | PS | Medium | Geometry | On a scale drawing a rectangle 1 inch by 1 1 3 inches represents the |

101 | PS | Medium | Algebra/Inequalities | If m and p are positive integers and m 2 p 2 100 what is the |

102 | PS | Medium | Algebra/Must or Could be True Quest | If x/y = c/d and d/c = b/a, which of the following must be true? |

103 | PS | Easy | Arithmetic | If k is an integer and (0.0025)(0.025)(0.00025) × 10^k is an integer, |

104 | PS | Easy | Algebra | If a(a + 2) = 24 and b(b + 2) = 24, where a ≠ b, then a + b = |

105 | PS | Medium | Percents and Interest Problems | In a recent election ms robbins received 8 000 votes cast by indepen |

106 | PS | Easy | Geometry | In the figure shown the triangle is inscribed in the semicircle if |

107 | PS | Medium | Arithmetic/Statistics and Sets Prob | A manufacturer makes and sells 2 products p and q the revenue from t |

108 | PS | Medium | Remainders | A worker carries jugs of liquid soap from a production line to a packi |

109 | PS | Easy | Geometry | The figure shown above represents a modern painting that consists of f |

110 | PS | Medium | Work/Rate Problems | Working simultaneously and independently at an identical constant rate |

111 | PS | Medium | Algebra/Functions and Custom Charac | The symbol denotes one of the four arithmetic operations addition su |

112 | PS | Easy | Algebra/Percents and Interest Probl | If mn 0 and 25 percent of n equals 37 1 2 percent of m what is the |

113 | PS | Easy | Percents and Interest Problems | Last year joe grew 1 inch and sally grew 200 percent more than joe gre |

114 | PS | Medium | Fractions/Ratios/Decimals/Percents | The table shows partial results of a survey in which consumers were as |

115 | PS | Medium | Percents and Interest Problems | The cost c in dollars to remove p percent of a certain pollutant fro |

116 | PS | Medium | Algebra | If xy ≠ 0 and x^2y^2 − xy = 6, which of the following could be y in te |

117 | PS | Easy | Arithmetic | (4.8*10^9)^(1/2) is closest in value to |

118 | PS | Easy | Work/Rate Problems | Three printing presses r s and t working together at the |

119 | PS | Medium | Geometry | For a party three solid cheese balls with diameters of 2 inches 4 in |

120 | PS | Medium | Arithmetic | The sum of all the integers k such that 26 k 24 is |

121 | PS | Easy | Statistics and Sets Problems/Absolu | The number line shown contains three points r s and t whose coordin |

122 | PS | Medium | Word Problems | Mark and ann together were allocated n boxes of cookies to sell for a |

123 | PS | Easy | Overlapping Sets | A certain high school has 5 000 students of these students x are |

124 | PS | Easy | Overlapping Sets | Each person who attended a company meeting was either a stockholder in |

125 | PS | Hard | Arithmetic/Percents and Interest Pr | The table shows the amount budgeted and the amount spent for each of |

126 | PS | Hard | Word Problems/Arithmetic/Percents a | The graph shows the number of computers assembled during each of 6 con |

127 | PS | Easy | Divisibility/Multiples/Factors | If n = 20! + 17, then n is divisible by which of the following? |

128 | PS | Hard | Algebra | The product of two negative numbers is 160 if the lesser of the two |

129 | PS | Easy | Arithmetic | According to a certain estimate the depth n t in centimeters of |

130 | PS | Hard | Distance/Rate Problems | After driving to a riverfront parking lot bob plans to run |

131 | PS | Medium | Percents and Interest Problems | Alex deposited x dollars into a new account |

132 | PS | Medium | Arithmetic | M is the sum of the reciprocals of the consecutive integers from |

133 | PS | Medium | Work/Rate Problems | Working simultaneously at their respective constant rates m |

134 | PS | Easy | Statistics and Sets Problems | What is the median of the numbers shown |

135 | PS | Very Hard | Word Problems | If 1 3 of the total number of marbles in the three bags listed in the |

136 | PS | Medium | Statistics and Sets Problems | The table above gives the age categories of the 161 employees at compa |

137 | PS | Easy | Statistics and Sets Problems | Ron is 4 inches taller than amy and barbara is 1 inch taller than ron |

138 | PS | Hard | Algebra/Inequalities/Number Propert | If x and y are positive numbers such that x y 1 which of the |

139 | PS | Hard | Fractions/Ratios/Decimals | If x is the hundredths digit in the decimal 0 1x and if y is the thous |

140 | PS | Medium | Combinations | Clarissa will create her summer reading list by randomly choosing 4 bo |

141 | PS | Easy | Number Properties/Divisibility/Mult | If n is a positive integer and the product of all integers |

142 | PS | Medium | Probability | The probability that event m will not occur is 0 8 and the probability |

143 | PS | Easy | Word Problems | The total cost for company x to produce a batch of tools is |

144 | PS | Medium | Arithmetic/Statistics and Sets Prob | If q is an odd number and the median of q consecutive |

145 | PS | Easy | Geometry | A ladder of a fire truck is elevated to an angle of 60 and |

146 | PS | Medium | Geometry | The window in the figure above consists of a rectangle and a semicircl |

147 | PS | Very Hard | Fractions/Ratios/Decimals | If there are fewer than 8 zeroes between the decimal point and the |

148 | PS | Hard | Combinations | A three digit code for certain locks uses the digits |

149 | PS | Medium | Algebra/Mixture Problems | Jackie has two solutions that are 2 percent sulfuric acid |

150 | PS | Easy | Word Problems | If jake loses 8 pounds he will weigh twice as much as his |

151 | PS | Medium | Statistics and Sets Problems | For each student in a certain class a teacher adjusted the student s |

152 | PS | Medium | Overlapping Sets | Last year 26 members of a certain club traveled to england 26 members |

153 | PS | Easy | Percents and Interest Problems | A store reported total sales of 385 million for february of |

154 | PS | Medium | Remainders | When positive integer x is divided by positive integer y |

155 | PS | Easy | Algebra | If x(2x + 1) = 0 and (x + 1/2)(2x - 3) = 0, then x = |

156 | PS | Hard | Geometry | Figures x and y above show how eight identical triangular pieces of ca |

157 | PS | Very Hard | Min/Max Problems/Word Problems | A certain experimental mathematics program was tried out in 2 classes |

158 | PS | Easy | Statistics and Sets Problems | For the positive numbers, n, n + 1, n + 2, n + 4, and n + 8 |

159 | PS | Hard | Geometry | The interior of a rectangular carton is designed by a certain |

160 | PS | Easy | Fractions/Ratios/Decimals/Mixture P | The present ratio of students to teachers at a certain |

161 | PS | Easy | Exponents/Powers/Inequalities | What is the smallest integer n for which 25 n |

162 | PS | Easy | Probability | Sixty percent of the members of a study group are women and |

163 | PS | Hard | Arithmetic/Word Problems | Each year for 4 years a farmer increased the number of trees in a |

164 | PS | Medium | Graphs and Illustrations/Statistics | According to the chart shown which of the following is |

165 | PS | Medium | Divisibility/Multiples/Factors/Expo | For the positive integers a b and k a k b means that a k |

166 | PS | Hard | Statistics and Sets Problems | A certain characteristic in a large population has a distribution that |

167 | PS | Hard | Word Problems | Four extra large sandwiches of exactly the same size were ordered for |

168 | PS | Hard | Algebra | Which of the following equations has 1 2 as one of its roots |

169 | PS | Hard | Percents and Interest Problems | In country c the unemployment rate among construction worke |

170 | PS | Medium | Probability | In a box of 12 pens a total of 3 are defective if a customer buys |

171 | PS | Very Hard | Statistics and Sets Problems | At a certain fruit stand the price of each apple is 40 cents and the |

172 | PS | Hard | Percents and Interest Problems | A pharmaceutical company received 3 million in royalties |

173 | PS | Very Hard | Word Problems | The light in a restroom operates with a 15 minute timer that is reset |

174 | PS | Hard | Geometry | The parallelogram shown has four sides of equal length what is the |

175 | PS | Easy | Exponents/Powers | If p is the product of the integers from 1 to 30 inclusive |

176 | PS | Hard | Divisibility/Multiples/Factors | If n 3 8 2 8 which of the following is not a factor of |

177 | PS | Hard | Algebra/Exponents/Powers/Geometry | In the figure shown if the area of the shaded region is 3 times |

178 | PS | Hard | Remainders/Word Problems | Club x has more than 10 but fewer than 40 members sometimes the membe |

179 | PS | Medium | Work/Rate Problems | In order to complete a reading assignment on time terry |

180 | PS | Easy | Algebra | If s > 0 and (r/s)^1/2=s, what what is r in terms of s ? |

181 | PS | Hard | Number Properties | If 3 < x < 100, for how many values of x is x/3 the square |

182 | PS | Hard | Combinations | A researcher plans to identify each participant in a certain medical |

183 | PS | Hard | Coordinate Geometry | The graph of which of the following equations is a straight line that |

184 | PS | Medium | Algebra/Min/Max Problems | An object thrown directly upward is at a height of h feet |

185 | PS | Easy | Inequalities | Which of the following is equivalent to the pair of |

186 | PS | Easy | Word Problems | David has d books which is 3 times as many as jeff and |

187 | PS | Easy | Combinations | There are 8 teams in a certain league and each team plays each of the |

188 | PS | Very Hard | Word Problems | At his regular hourly rate don had estimated the labor cost |

189 | PS | Easy | Inequalities/Must or Could be True | If p/q < 1 and p and q are positive integers which of the |

190 | PS | Medium | Word Problems | To mail a package the rate is x cents for the first pound |

191 | PS | Medium | Percents and Interest Problems | If money is invested at r percent interest compounded annua |

192 | PS | Medium | Word Problems/Distance/Rate Problem | On a recent trip cindy drove her car 290 miles rounded to |

193 | PS | Easy | Absolute Values/Modulus/Inequalitie | Which of the following inequalities is an algebraic expressi |

194 | PS | Easy | Statistics and Sets Problems/Word P | In a small snack shop the average arithmetic mean revenue |

195 | PS | Easy | Number Properties | If y is the smallest positive integer such that |

196 | PS | Medium | Arithmetic/Functions and Custom Cha | If is the greatest integer less than or equal to x what is the va |

197 | PS | Medium | Sequences/Statistics and Sets Probl | In the first week of the year nancy saved |

198 | PS | Easy | Sequences | In a certain sequence the term xn is given by the formula |

199 | PS | Medium | Distance/Rate Problems | During a trip francine traveled x percent of the total distance at an |

200 | PS | Medium | Exponents/Powers/Number Properties | If n = (33)^43 + (43)^33 what is the units digit of n? |

201 | PS | Medium | Combinations | Team a and team b are competing against each other in a game |

202 | PS | Very Hard | Geometry | A border of uniform width is placed around a rectangular |

203 | PS | Hard | Fractions/Ratios/Decimals/Exponents | If d=1/(2^3*5^7) is expressed as a terminating decimal, how many nonze |

204 | PS | Hard | Number Properties/Arithmetic | For any positive integer n the sum of the first n positive integers |

205 | PS | Medium | Number Properties | How many prime numbers between 1 and 100 are factors of |

206 | PS | Very Hard | Sequences | A sequence of numbers a1 a2 a3 is defined as follows a1 3 a2 |

207 | PS | Very Hard | Percents and Interest Problems | Last year the price per share of stock x increased by k percent and |

208 | PS | Very Hard | Overlapping Sets/Word Problems | Of the 300 subjects who participated in an experiment using virtual re |

209 | PS | Easy | Exponents/Powers | If m^(-1) = -1/3 then m^(-2) is equal to |

210 | PS | Very Hard | Percents and Interest Problems | A photography dealer ordered 60 model x cameras to be sold |

211 | PS | Hard | Min/Max Problems/Fractions/Ratios/D | Seven pieces of rope have an average arithmetic mean lengt |

212 | PS | Easy | Sequences | What is the difference between the sixth and the fifth terms |

213 | PS | Hard | Arithmetic/Min/Max Problems | From the consecutive integers 10 to 10 inclusive |

214 | PS | Hard | Combinations | The letters d g i i and t can be used to form 5 letter strings as |

215 | PS | Very Hard | Algebra/Arithmetic/Number Propertie | 0.99999999/1.0001 - 0.99999991/1.0003 = |

216 | PS | Very Hard | Arithmetic/Percents and Interest Pr | Last sunday a certain store sold copies of newspaper a for |

217 | PS | Easy | Statistics and Sets Problems | For the past n days the average arithmetic mean daily |

218 | PS | Medium | Coordinate Geometry | In the coordinate system above which of the following is the equation |

219 | PS | Easy | Arithmetic | If a two digit positive integer has its digits reversed the resulting |

220 | PS | Easy | Algebra | In an electric circuit two resistors with resistances x and |

221 | PS | Easy | Probability | Xavier yvonne and zelda each try independently to solve a |

222 | PS | Easy | Algebra/Must or Could be True Quest | If 1/x - 1/(x+1) = 1/(x+4), then x could be |

223 | PS | Easy | Arithmetic/Exponents/Powers | (1/2)^(-3)*(1/4)^(-2)*(1/16)^(-1) |

224 | PS | Hard | Geometry | The figure shown above consists of a shaded 9 sided polygon and 9 un |

225 | PS | Very Hard | Min/Max Problems | List t consist of 30 positive decimals none of which is an integer |

226 | PS | Easy | Algebra | If 5 6 x x then x has how many possible values |

227 | PS | Medium | Mixture Problems | Seed mixture x is 40 percent ryegrass and 60 percent |

228 | PS | Very Hard | Inequalities | How many of the integers that satisfy the inequality x 2 x |

229 | PS | Very Hard | Overlapping Sets | Of the 150 houses in a certain development 60 percent have |

230 | PS | Easy | Exponents/Powers/Algebra | The value of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 is |