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OG12 OG15 OG16 OG17
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A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
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OG15 OG16 OG17
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For the positive integers a, b, and k, $${a}^{k}$$ || b means that $${a}^{k}$$ is a divisor of b, but $${a}^{k+1}$$ is not a divisor of b. If k is a positive integer and $${2}^{k}$$ || 72, then k is equal to
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OG12
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If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x =$${2}^{i}{3}^{k}{5}^{m}{7}^{p}$$, then i + k + m + p =
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OG12 OG15 OG16
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A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?
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OG12 OG15 OG16
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What is the 25th digit to the right of the decimal point in the decimal form of $$\frac{6}{11}$$
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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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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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OG18 OG19 OG20
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A worker carries jugs of liquid soap from a production line to a packing area, carrying 4 jugs per trip. If the jugs are packed into cartons that hold 7 jugs each, how many jugs are needed to fill the last partially filled carton after the worker has made 17 trips?
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OG17 OG18 OG19 OG20 OG2022
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Last year Joe grew 1 inch and Sally grew 200 percent more than Joe grew. How many inches did Sally grow last year?
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OG21 OG2022
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3P5
$$\frac{+4QR}{8S4}$$
In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S?
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OG18 OG19 OG20 OG2022
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If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths digit in the decimal 0.02Y, where X and Y are nonzero digits, which of the following is closest to the greatest possible value of $$\frac{0.1X}{0.02Y}$$?
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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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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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OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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If [x] is the greatest integer less than or equal to x, what is the value of [-1.6] +[3.4]+[2.7]?
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OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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In a certain sequence, the term $${x}_{n}$$, is given by the formula $${x}_{n}={2}{x}_{n-1}-\frac{1}{2}({x}_{n-2})$$ for all $${n}\geq{2}$$. If $${x}_{0}=3$$ and $${x}_{1}=2$$, what is the value of $${x}_{3}$$
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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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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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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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KMFPS
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If x and y are positive integers such that the remainder when x is divided by 5 is 2 and the remainder when y is divided by 5 is 3, what is the remainder when xy is divided by 5?
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