Problem Solving |

1 | PS | Easy | Operations with rational numbers | A project scheduled to be carried out over a single fiscal |

2 | PS | Easy | Arithmetic Properties of numbers | For which of the foleasying values of n is 100 n n not an |

3 | PS | Easy | Area | Rectangular floors x and y have equal area if floor x is |

4 | PS | Easy | Algebra Simplifying algebraic expre | A case contains c cartons each carton contains b boxes and |

5 | PS | Easy | Properties of numbers | The sum of prime numbers that are greater than 60 but less |

6 | PS | Medium | Applied problems | A rainstorm increased the amount of water stored in state j |

7 | PS | Medium | Interpretation of graphs | On the graph above when x 1 2 y 2 and when |

8 | PS | Easy | Percents | When 1 10 percent of 5 000 is subtracted from 1 10 of |

9 | PS | Easy | Operations on radical expressions | Which of the foleasying is the value of root 3rd rt |

10 | PS | Medium | Probability | Raffle tickets numbered consecutively from 101 through |

11 | PS | Easy | First-degree equations | When leo imported a certain item he paid a 7 percent import |

12* | PS | Easy | Statistics | The numbers of cars sold at a certain dealership on six of |

13* | PS | Easy | Quadrilaterals; Perimeter | A rectangular garden is to be twice as long as it is wide |

14* | PS | Easy | Inequalities; Absolute value | If y 1 2 11 2 which of the foleasying could be a value |

15* | PS | Easy | Fractions | At a supermarket john spent 1 2 of his money on fresh fruit |

16 | PS | Easy | Statistics | On monday a person mailed 8 packages weighing an average |

17 | PS | Easy | Operations on rational numbers | Topic |

18 | PS | Easy | Volume | A carpenter constructed a rectangular sandbox with a |

19 | PS | Easy | Operations on rational numbers; Per | A bakery opened yesterday with its daily supply of 40 dozen |

20 | PS | Easy | Properties of numbers | What is the 25th digit to the right of the decimal point in |

21 | PS | Easy | Percents | 150 is what percent of |

22 | PS | Easy | Operations on rational numbers | The ratio 2 to 1 3 is equal to the ratio |

23 | PS | Easy | Operations on rational numbers | Running at the same constant rate 6 identical machines can |

24 | PS | Easy | Properties of numbers | Of the five coordinates associated with points a b c d |

25 | PS | Easy | Percents | Of the 50 researchers in a workgroup 40 percent will be |

26 | PS | Easy | Properties of numbers | If n is a prime number greater than 3 what is the remainder |

27 | PS | Easy | Operations with rational numbers | 1 |

28 | PS | Easy | Coordinate geometry | In the figure above the coordinates of point v are |

29 | PS | Easy | First-degree equations | A rope 40 feet long is cut into two pieces if one piece is |

30 | PS | Easy | Statistics | A student s average arithmetic mean test score on 4 tests |

31 | PS | Easy | Percents | Lucy invested 10 000 in a new mutual fund account exactly |

32 | PS | Easy | Properties of numbers | If the quotient a b positive which of the foleasying must be |

33 | PS | Easy | Interpretation of graphs and tables | The dots on the graph above indicate the weights and fuel |

34 | PS | Easy | First-degree equations | How many minutes does it take john to type y words if he |

35 | PS | Easy | Operations on radical expressions | Root of |

36 | PS | Easy | Circles and area | If o is the center of the circle above what fraction of the |

37* | PS | Easy | Simplifying algebraic expressions | Which of the foleasying equations is not equivalent to 10y |

38 | PS | Easy | Applied problems | If juan takes 11 seconds to run y yards how many seconds |

39 | PS | Easy | Operations on rational numbers | John has 10 pairs of matched socks if he loses 7 individual |

40 | PS | Medium | Operations on rational numbers | What is the easyest positive integer that is divisible by |

41 | PS | Easy | Operations with rational numbers | 1 |

42 | PS | Easy | First-degree equations | If 1 5 0 2 x 5 then x |

43 | PS | Easy | Coordinate geometry | In the figure above the point on segment pq that is twice a |

44 | PS | Easy | Properties of integers | If n is an integer which of the foleasying must be even |

45 | PS | Medium | Second-degree equations | If 4 is one solution of the equation x2 3x k 10 where |

46 | PS | Easy | Operations with rational numbers | The sum 7 8 1 9 is between |

47 | PS | Easy | Simultaneous equations | If x 1 3t and y 2t 1 then for what value of t does x |

48 | PS | Easy | Operations with rational numbers | 1 |

49* | PS | Medium | Applied problems | Car x averages 25 0 miles per gallon of gasoline and car y |

50 | PS | Medium | Inequalities | How many integers n are there such that 1 5n |

51 | PS | Easy | Absolute value; Operations with int | If y is an integer then the least possible value of |

52 | PS | Easy | Operations with radical expressions | Root 80 root |

53 | PS | Easy | Statistics | The average arithmetic mean of 10 30 and 50 is 5 more |

54 | PS | Easy | First-degree equations | In the equation above k is a constant if y 17 when x |

55 | PS | Easy | Interpretation of tables; Applied p | In the table above what is the number of green marbles in j |

56* | PS | Medium | Ratio and proportion | Four staff members at a certain company worked on a project |

57* | PS | Medium | Percents | Company p had 15 percent more employees in december than it |

58 | PS | Medium | Percents | A glass was filled with 10 ounces of water and 0 01 ounce |

59 | PS | Easy | Applied problems | A glucose solution contains 15 grams of glucose per |

60* | PS | Medium | Applied problems | On a certain day orangeade was made by mixing a certain |

61* | PS | Easy | Coordinate geometry | In the xy plane what is the slope of the line with equation |

62 | PS | Easy | Polygons | In the figure above if pqrs is a parallelogram then y x |

63 | PS | Easy | Arithmetic | If 1 kilometer is approximately 0 6 mile which of the |

64 | PS | Medium | First-degree equations; Operations | A certain fruit stand sold apples for 0 70 each and bananas |

65 | PS | Medium | Measurement conversion | The average distance between the sun and a certain planet is |

66 | PS | Medium | Ratio and proportion | At a certain school the ratio of the number of second grade |

67 | PS | Easy | Statistics | If m is the average arithmetic mean of the first |

68 | PS | Medium | Probability; Concepts of sets | Two integers will be randomly selected from the sets above |

69* | PS | Easy | Coordinate geometry; Circles; Area | In the coordinate plane a circle has center 2 3 an |

70 | PS | Medium | Simplifying algebraic expressions | At a certain instant in time the number of cars n |

71* | PS | Medium | Percents | Yesterday s closing prices of 2 420 different stocks listed |

72 | PS | Easy | First-degree equations | If y 3x 5 2 y and y 0 then x |

73 | PS | Easy | Algebra | If x 5 2 and x 3 7 the value of x must be between |

74 | PS | Easy | Properties of numbers | A gym class can be divided into 8 teams with an equal number |

75* | PS | Very Hard | Angles | In the figure above triangle abc is equilateral and point |

76 | PS | Easy | Operations on rational numbers | At least 2 3 of the 40 members of a committee must vote in |

77* | PS | Easy | Properties of numbers | If n 20 17 then n is divisible by which of the |

78* | PS | Medium | Volume | In the rectangular solid above the three sides shown have |

79* | PS | Medium | Applied problems | After driving to a riverfront parking lot bob plans to run |

80* | PS | Medium | Estimation | M is the sum of the reciprocals of the consecutive integers |

81* | PS | Medium | Applied problems | Working simultaneously at their respective constant rates m |

82 | PS | Easy | Applied problems | In the johnsons monthly budget the dollar amounts allocate |

83 | PS | Easy | Simultaneous equations; Applied pro | There are 4 more women than men on centerville s board of |

84 | PS | Easy | Operations with rational numbers | Leona bought a 1 year 10 000 certificate of deposit that |

85 | PS | Medium | Operations with rational numbers | Topic |

86 | PS | Easy | Applied problems | Machine a produces bolts at a uniform rate of 120 every |

87 | PS | Medium | Properties of numbers | If n is an integer greater than 6 which of the foleasying mu |

88 | PS | Easy | Applied problems | The total cost for company x to produce a batch of tools i |

89 | PS | Medium | Factoring and Simplifying algebraic | A dealer originally bought 100 identical batteries at a tota |

90 | PS | Easy | First-degree equations | In an increasing sequence of 10 consecutive integers the |

91* | PS | Medium | Statistics | If q is an odd number and the median of q consecutive |

92* | PS | Medium | Triangles | A ladder of a fire truck is elevated to an angle of 60 and |

93 | PS | Easy | Systems of equations | If jake loses 8 pounds he will weigh twice as much as his |

94 | PS | Easy | Percents | A store reported total sales of 385 million for february of |

95 | PS | Medium | Properties of numbers | When positive integer x is divided by positive integer y |

96 | PS | Easy | Percents; Applied problems | In a certain city 60 percent of the registered voters are |

97 | PS | Easy | Operations on rational numbers | |

98 | PS | Easy | Applied problems | Water consists of hydrogen and oxygen and the approximate |

99 | PS | Easy | Second-degree equations; Simultaneo | If x 2x 1 0 and x 1 2 2x 3 0 then x |

100 | PS | Medium | Operations on rational numbers | On a scale that measures the intensity of a certain phenomen |

101 | PS | Easy | Statistics | For the positive numbers n n 1 n 2 n 4 and n |

102 | PS | Easy | First-degree equations | If t 5 9 k 32 and if t 290 then k 143763.h |

103 | PS | Easy | Operations on rational numbers | The water from one outlet feasying at a constant rate can |

104 | PS | Medium | Perimeter; Pythagorean theorem | If a square mirror has a 20 inch diagonal what is th |

105 | PS | Medium | Applied problems | The present ratio of students to teachers at a certain |

106 | PS | Easy | Operations with rational numbers | What is the smallest integer n for which 25 n |

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

108* | PS | Medium | Operations on rational numbers | Each year for 4 years a farmer increased the number of tree |

109 | PS | Medium | Interpretation of graphs and tables | According to the chart shown which of the foleasying is |

110* | PS | Medium | Property of numbers | For the positive integers a b and k a k b means that a k |

111 | PS | Medium | Exponents; Operations with rational | If t 1 2 9 5 3 is expressed as a terminating decimal |

112* | PS | Medium | Statistics | A certain characteristic in a large population has a |

113* | PS | Medium | Applied problems | In a certain district the ratio of the number of registered |

114* | PS | Medium | Percents | In country c the unemployment rate among construction worke |

115 | PS | Medium | Percents | A pharmaceutical company received 3 million in royalties |

116 | PS | Medium | Properties of numbers | If p is the product of integers from 1 to 30 inclusive |

117* | PS | Medium | Properties of numbers | If n 3 8 2 8 which of the foleasying is not a factor of |

118* | PS | Medium | Properties of numbers | Club x has more than 10 but fewer than 40 members sometimes |

119* | PS | Medium | Applied problems | In order to complete a reading assignment on time terry |

120 | PS | Easy | Equations | If s 0 and r s 1 2 s what what is r in terms of s |

121 | PS | Medium | Area | The front of a 6 foot by 8 foot rectangular door has brass |

122 | PS | Medium | Operations on rational numbers | If a 0 3 which of the foleasying is true |

123 | PS | Easy | Applied problems; Percents | Mary s income is 60 percent more than tim s income and tim |

124 | PS | Medium | Interpretation of tables | Each in the mileage table above represents an entry indic |

125 | PS | Easy | Applied problems | The ratio of the length to the width of a rectangular advert |

126 | PS | Medium | Concepts of sets; Functions | An arithmetic sequence is a sequence in which each ter |

127* | PS | Medium | Properties of numbers | If 3 x 100 for how many values of x is x 3 the square |

128* | PS | Medium | Elementary combinatorics | A researcher plans to identify each participant in a certain |

129* | PS | Medium | Applied problems | An object thrown directly upward is at a height of h feet |

130 | PS | Easy | Inequalities | Which of the foleasying is equivalent to the pair of |

131 | PS | Easy | Applied problems; Simultaneous equa | David has d books which is 3 times as many as jeff and |

132 | PS | Easy | Statistics | If the median of the numbers in list i above is equal to the |

133 | PS | Easy | Operations on rational numbers | There are 8 teams in a certain league and each team plays |

134 | PS | Easy | Simplifying algebraic expressions | An operation is defined by the equation a b a b a |

135 | PS | Medium | Statistics; Applied problems | The price of lunch for 15 people was 207 00 including a |

136 | PS | Medium | Percents | In town x 64 percent of the population are employed and |

137* | PS | Hard | Second-degree equations | At his regular hourly rate don had estimated the labour cos |

138 | PS | Easy | Properties of numbers | If p q 1 and p and q are positive integers which of the |

139 | PS | Easy | Work/Rate Problems | It would take one machine 4 hours to complete a large produc |

140 | PS | Medium | Applied problems | To mail a package the rate is x cents for the first pound |

141 | PS | Medium | Applied problems | If money is invested at r percent interest compounded annua |

142 | PS | Medium | Estimation | On a recent trip cindy drove her car 290 miles rounded t |

143 | PS | Easy | Inequalities | Which of the foleasying inequalities is an algebraic expressi |

144 | PS | Easy | Percents; Applied problems | A factory has 500 workers 15 percent of whom are women if |

145 | PS | Easy | Statistics; Applied problems | In a small snack shop the average arithmetic mean revenue |

146 | PS | Easy | Operations on rational numbers | A certain country had a total annual expenditure of 1 2 x |

147 | PS | Easy | Perimeter | A certain rectangular window is twice as long as it is wide |

148 | PS | Easy | Elementary combinatorics | The diagram above shows the various paths along which a mous |

149 | PS | Easy | Operations on rational numbers | If the operation is defined by x y xy 1 2 for all |

150 | PS | Medium | Operations on rational numbers | A bar over a sequence of digits in a decimal indicates tha |

151 | PS | Medium | Word Problem | At a loading dock each worker on the night crew loaded |

152 | PS | Easy | Estimation and percent | A restaurant meal cost 35 50 and there was no tax if the |

153 | PS | Easy | Applied problems | In a weight lifting competition the total weight of joe s t |

154 | PS | Easy | Applied problems | A club collected exactly 599 from its members if each |

155 | PS | Medium | Properties of numbers | If y is the smallest positive integer such that 3 150 multip |

156 | PS | Medium | Computation with integers | If is the greatest integer less than or equal to x what |

157 | PS | Easy | Second-degree equations | If 4 x 2 x x what is the value of x 2 3x |

158* | PS | Medium | Operations on rational numbers | In the first week of the year nancy saved |

159 | PS | Easy | Triangles and the Pythagorean theor | The trapezoid shown in the figure above represents a cross |

160 | PS | Easy | Simplifying algebraic expressions | In a certain sequence the term xn is given by the formula |

161 | PS | Easy | Pythagorean theorem | In the figure above v represents an observation point at on |

162 | PS | Medium | Applied problems | During a trip francine traveled x percent of the tota |

163* | PS | Medium | Properties of numbers | If n 33 43 43 33 what is the units digit of n |

164 | PS | Easy | Operations on rational numbers | If x 1 then x 4 x 3 x 2 x |

165 | PS | Easy | Area and the Pythagorean theorem | The shaded portion of the rectangular lot shown above repres |

166* | PS | Hard | Second-degree equations | A border of uniform width is placed around a rectangular |

167 | PS | Medium | Applied problems | Jack is now 14 years older than bill if in 10 years jack |

168 | PS | Easy | Applied problems | An empty pool being filled with water at a constant rate |

169 | PS | Easy | Second-degree equations | A positive number x is multiplied by 2 and this product is |

170* | PS | Medium | Operations on rational numbers | If d 1 2 3 5 7 is expressed as a terminating decimal how |

171 | PS | Medium | Operations on rational numbers; Per | A tank contains 10 000 gallons of a solution that is |

172 | PS | Medium | Simplifying expressions; Computatio | For any positive integer n the sum of the first n positive |

173 | PS | Easy | Probability | A committee is composed of w women and m men if 3 women and |

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

175 | PS | Easy | Area (Circles) | The figure above shows a circular feasyer bed with its cente |

176 | PS | Easy | Operations on radical expressions | The positive integer n is divisible by 25 if n 1 2 is |

177* | PS | Medium | Percents | Last year the price per share of stock x increased by |

178* | PS | Hard | Applied problems | Of the 300 subjects who participated in an experiment using |

179 | PS | Easy | Applied problems | A fruit salad mixture consists of apples peaches and grape |

180 | PS | Easy | Negative exponents | If m 1 1 3 then m 2 is equal to |

181 | PS | Medium | Percents | If m 0 and x is m percent of y then in terms of m y is |

182* | PS | Hard | Percents | A photography dealer ordered 60 model x cameras to be sold |

183* | PS | Medium | Statistics | Seven pieces of rope have an average arithmetic mean lengt |

184 | PS | Easy | Simplifying algebraic expressions | Lois has x dollars more than jim has and together they have |

185 | PS | Easy | Percents; Applied problems | During a certain season a team won 80 percent of its first |

186 | PS | Easy | Operations on rational numbers | Of 30 applicants for a job 14 had at least 4 years |

187 | PS | Easy | First-degree equations | If 1 1 x 2 2 x then x |

188 | PS | Easy | Operations on rational numbers | Last year for every 100 million vehicles that traveled on a |

189 | PS | Easy | Applied problems | Thirty percent of the members of a swim club have passed the |

190 | PS | Medium | Simplifying algebraic expressions | What is the difference between the sixth and the fifth terms |

191 | PS | Medium | Second-degree equations | If x 1 2 400 which of the foleasying could be the value |

192 | PS | Medium | Inequalities | Which of the foleasying describes all values of x for which |

193 | PS | Medium | Probability | The probability is 1 2 that a certain coin will turn up head |

194 | PS | Easy | Applied problems | Of the final grades received by the students in a certain |

195 | PS | Medium | Simplifying algebraic expressions | As x increases from 165 to 166 which of the foleasying must |

196* | PS | Medium | Properties of numbers | From the consecutive integers 10 to 10 inclusive |

197 | PS | Easy | Pythagorean theorem | A rectangular box is 10 inches wide 10 inches long and |

198* | PS | Hard | Simultaneous equations | Last sunday a certain store sold copies of newspaper a for |

199 | PS | Hard | Operations on rational numbers | Topic |

200 | PS | Medium | Operations on rational numbers | The ratio by volume of soap to alcohol to water in |

201 | PS | Easy | Percents | If 75 percent of a class answered the first question on a ce |

202 | PS | Medium | Simple coordinate geometry | In the rectangular coordinate system above the line y x |

203 | PS | Medium | Applied problems | A store currently charges the same price for each towel that |

204 | PS | Medium | Properties of numbers | If n 4p where p is a prime number greater than 2 how man |

205 | PS | Medium | Applied problems | John and mary were each paid x dollars in advance to do a |

206 | PS | Easy | Simple coordinate geometry; Area | In the rectangular coordinate system above if point r not |

207 | PS | Easy | Operations on rational numbers | Car a is 20 miles behind car b which is traveling in the |

208 | PS | Medium | Statistics; Applied problems; Simul | For the past n days the average arithmetic mean daily |

209 | PS | Medium | Simplifying algebraic expressions | If x 0 and x 1 and if x is replaced by 1 x everywhere in th |

210 | PS | Easy | Angles; Measures of angles | In the figure above if z 50 then x y |

211 | PS | Easy | Simple coordinate geometry | In the coordinate system above which of the foleasying is |

212 | PS | Easy | Applied problems | If a two digit positive integer has its digits reversed the |

213 | PS | Easy | Circles; Simple coordinate geometry | The circle with center c shown above is tangent to both axes |

214 | PS | Medium | Applied problems | In an electric circuit two resistors with resistances x and |

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

216 | PS | Easy | Second-degree equations | If 1 x 1 x 1 1 x 4 then x could be |

217 | PS | Easy | Operations on rational numbers | 1 |

218* | PS | Very Hard | Operations on rational numbers | List t consist of 30 positive decimals none of which is an |

219 | PS | Medium | Properties of numbers | In a certain game a large container is filled with red yel |

220 | PS | Easy | First-degree equations | If 2 1 2 y 1 then y |

221 | PS | Easy | Properties of numbers | If a b and c are consecutive positive integers and a b |

222 | PS | Medium | Operations on rational numbers | Of the 200 students at college t majoring in one or more of |

223 | PS | Easy | Second-degree equations | If 5 6 x x then x has how many possible values |

224 | PS | Easy | Applied problems | Seed mixture x is 40 percent ryegrass and 60 percen |

225 | PS | Easy | Properties of numbers | N is a positive integer |

226 | PS | Medium | Operations on rational numbers | A straight pipe 1 yard in length was marked off in fourths |

227 | PS | Medium | Operations on rational numbers | If 0 0015 10 m 0 03 10 k 5 10 7 then m k |

228 | PS | Medium | Simple coordinate geometry; Element | Right triangle pqr is to be constructed in the xy plane s |

229* | PS | Hard | Inequalities | How many of the integers that satisfy the inequality x 2 x |

230 | PS | Easy | Negative exponents | The value of 2 14 2 15 2 16 2 17 5 is |