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KMFPS
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If n is a positive integer, what is the remainder when $${3}^{8n+3}+2$$ is divided by 5?
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If n is a positive integer, what is the remainder when $$7^{4n+3}6^n$$ is divided by 10 ?
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If $${n}={8}^{11}-{8}$$, what is the units digit of n?
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If n is the greatest positive integer for which $${2}^{n}$$ is a factor of $$10!$$, then n =
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OG12 OG15 OG16 OG17
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In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
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OG12 OG15 OG16 OG17 OG18
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If y is an integer, then the least possible value of |23 - 5y| is
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OG12 OG15 OG16
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There are 4 more women than men on Centerville's board of education. If there are 10 members on the board, how many are women?
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OG12 OG15 OG16
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if $$\frac{(4-x)}{(2+x)}= x$$, what is the value of $${x}^{2} + 3x - 4$$?
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OG12 OG15
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A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?
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OG12
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The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has maximum volume?
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OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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Club X has more than 10 but fewer than 40 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
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OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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If $${n}={33}^{43}+{43}^{33}$$, what is the units digit of n?
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OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?
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OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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How many of the integers that satisfy the inequality $${\frac{(x+2)(x+3)}{x-2}}\ge{0}$$ are less than 5 ?
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A closed cylindrical tank contains 36π cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?
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If $$\mathbf{y}={4}+({x}-{3})^{2}$$, then y is least when x =
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PREP07 Test 1
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3 teaspoons = 1 tablespoon4 tablespoons = $$\frac{1}{4}$$ cupAccording to the information above, how many teaspoons are equal to $$\frac{3}{8}$$ cup?
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What is the 99th digit after the decimal point in the decimal expansion of$$\frac{2}{9}+\frac{3}{11}$$ ?
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Three stacks containing equal numbers of chips are to be made from 9 red chips, 7 blue chips and 5 green chips are used and each stack contains at least 1chip of each color. What is the maximum number of red chips in one stack?
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OG16 OG18 OG19 OG20 OG2022
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At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?
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