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OG17
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At a certain food stand, the price of each apple is ￠ 40 and the price of each orange is ￠ 60. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is ￠ 56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is￠52?
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$${C}{n \choose m}=\frac{m!}{[(m-n)!n!]}$$ for nonnegative integers m and n, $$m \ge n$$. If $${C}{3 \choose 5}={C}{x \choose 5}$$ and $$x \neq 3$$, what is the value of x?
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Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
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OG12 OG15
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For which of the following values of n is $$\frac{(100+n)}{n}$$ NOT an integer?
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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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OG12 OG15
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John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left
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OG12 OG15
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If 4 is one solution of the equation $${x}^{2} + 3x + k = 10$$, where k is a constant, what is the other solution?
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OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
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OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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if $$\frac{1}{x}-\frac{1}{x+1}=\frac{1}{x+4}$$ then x could be
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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 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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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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How many different positive integers are factors of 441?
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if $$y= 4 + (x-3)^2$$, then y is lowest when x=
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PREP07 Test 1
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If a, b, c, and d are consecutive even integers and a < b < c < d, then a + b is how much less than c + d ?
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In the xy-plane, line n passes through the origin and has slope 4. If points (1, c) and (d, 2) are on line n, what is the value of $$\frac{c}{d}$$?
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How many different sets of positive square integers, each greater than 1, add up to 75?
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If$$2^{x}+2^{y}=x^{2}+y^{2}$$ , where x and y are nonnegative integers, what is the greatest possible value of |x-y|?
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Which of the following is not a divisor of 52?
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George baked a total of 125 pizzas for 7 straight days, beginning on Saturday.He baked $$\frac{3}{5}$$ of the pizzas the first day, and $$\frac{3}{5}$$ of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
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