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143
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If x and k are integers and $$({12}^{x})({4}^{2x+1})=({2}^{k})({3}^{2})$$, what is the value of k?
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144
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If S is the sum of the reciprocals of the 10 consecutive integers from 21 to 30, then S is between which of the following two fractions?
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145
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For every even positive intger m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factorof f(24)?
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146
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 In pentagon PQRST, PQ = 3, QR = 2, RS = 4 , and ST = 5. Which iof the lengths 5, 10, and 15 could be the value of PT?
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147
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3, k, 2, 8, m, 3The arithmetic mean of the list of numbers above is 4. If k and m are integers and k$$\neq m$$, what is the median of the list?
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148
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 If the variables X, Y, and Z take on only the values 10, 20, 30, 40, 50, 60, or 70 with frequencies indicated by the shaded regions above, for which of the frequency distributions is the mean equal to the median?
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149
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 When the figure above is cut along the solid lines, folded along the dashed lines, and taped along the solid lines, the result is a model of a geometric solid. This geometric solid consists of 2 pyramids, each with a square base that they share. What is the sum of the number of edges and the number of faces of this geometric solid?
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150
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2x + y = 12$$| y | \le 12$$For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
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151
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The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is $$\frac4 3\pi$$, what is the length of line segment RU?
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152
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A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
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153
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A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?
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154
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The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x, y}, {w, x, y}, and { } (the empty subset). How many subsets of the set {w, x, y, z} contain w ?
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155
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There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
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156
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The number $$\sqrt{63-36\sqrt{3}}$$ can be expressed as $$x + y \sqrt{3} $$ for some integers x and y. What is the value of xy
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157
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There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback?
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158
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If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?
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159
|
The function f is defined for each positive three-digit integer n by $${f}({n})={2}^{x}{3}^{y}{5}^{z}$$, where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m) = 9f(v), then m-v = ?
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160
|
If $${10}^{50}-{74}$$ is written as an integer in base 10 notation, what is the sum of the digits in that integer?
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161
|
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
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162
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Becky rented a power tool from a rental shop. The rent for the tool was $12 for the first hour and $3 for each additional hour. If Becky paid a total of $27, excluding sales tax, to rent the tool, for how many hours did she rent it?
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