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138
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The sequence $${a}_{1}$$, $${a}_{2}$$, $${a}_{n}$$, such that $${a}_{n}={2a}_{n-1}-{x}$$ for all positive integers $$n \ge 2$$ and for certain number x. If $${a}_{5}={99}$$ and $${a}_{3}={27}$$, what is the value of x?
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138
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The sequence $$a_1$$, $$a_2$$, ... $$a_n$$, ... is such that $$a_n= 2a_{n-1} - x$$ for all positive integers $$ n\geq 2$$ and for a certain number x. If $$a_5 = 99$$ and $$a_3 = 27$$, what is the value of x?
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139
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A window is in the shape of a regular hexagon with each side of length 80 centimeters. If a diagonal through the center of the hexagon is w centimeters long, then w =
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140
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In the figure shown, PQRSTU is a regular polygon with sides of length x. What is the perimeter of triangle PRT in terms of x ?
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141
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In a certain medical survey, 45 percent of the people surveyed had the type A antigen in their blood and 3 percent had both the type A antigen and the type B antigen. Which of the following is closest to the percent of those with the type A antigen who also had the type B antigen?
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142
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On a certain transatlantic crossing, 20 percent of
80
a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did $$\underline {not}$$ take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
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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 Sis between which of the following two fractions?
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145
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For every even positive integer m, f(m) represents the product of all even integers from 2 tom, inclusive. For example, $$f(12) = 2 \times 4 \times 6 \times 8 \times 10 \times 12$$. What is the greatest prime factor of f(24) ?
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146
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In pentagon PQRST, $$PQ = 3$$, $$QR= 2$$, $$RS= 4$$, and $$ST= 5$$. Which of the lengths 5, 10, and 15 could be the value of PT ?
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147
|
3, k, 2, 8, m, 3
The 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
|
$$2x+ y = 12$$
$$|y| \le 12$$
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 $$\frac{4\pi}{3}$$ , what is the length of line segment RU?
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152
|
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 candidate.s 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 fringebenefit 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
|
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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