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PREP07 Test 1
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A construction company was paid a total of $500,000 for a construction project. The company's only costs for the project were for labor and materials. Was the company's profit for the project greater than $150,000?(1)The company's total cost was three times its cost for materials.(2)The company's profit was greater than its cost for labor.
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OG18-数学分册
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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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OG17 OG18 OG19 OG20 OG2022
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When n liters of fuel was added to a tank that was already $$\frac1 3$$ full, the tank was filled to $$\frac7 9$$ of its capacity. In terms of n, what is the capacity of the tank, in liters?
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OG18-数学分册
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Of all the students in a certain dormitory, $$\frac1 2$$ are first-year students and the rest are second-year students. If $$\frac4 5$$ of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
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OG12 OG15 OG16 OG17 OG18
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At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders?
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OG16 OG17 OG18
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If n is a positive integer and the product of all the integers from 1 to n, inclusive, is divisible by 990, what is the least possible value of n?
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Last year, 36 houses in a certain development had roof repairs and 48 houses were repainted. If 20 houses in the development had roof repairs but were not repainted last year, how many houses were repainted but did not have roof repairs?
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 The figure shown represents a board with 4 rows of pegs, and at the bottom of the board are 4 cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has the probability $$\frac1 2$$ of passing through the opening immediately to the left of that peg and probability $$\frac1 2$$ of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end in Cell 2?
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The function f is defined by $${f}({x})=-\frac{1} x$$ for all nonzero numbers x. If $${f}({a})=-\frac1 2$$ and $${f}({a}{b})=\frac1 6$$, then b =
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OG16 OG17 OG18 OG19 OG20 OG2022
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If $${x}{y}≠{0}$$ and $${x}^{2}{y}^{2}-{x}{y}={6}$$, which of the following could be y in terms of x?I.$$\frac1 {2x}$$II.$$-\frac2 x$$III $$\frac3 x$$
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A certain computer program generates a sequence of numbers $${a}_{1}$$, $${a}_{2}$$, ... , $${a}_{n}$$ such that $${a}_{1}={a}_{2}={1}$$ and $${a}_{k}={a}_{k-1}+{2a}_{k-2}$$ for all integers k such that $$3 \le k\le n$$. If $$n > 6$$, then $${a}_{7}=$$ ?
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If $$5x = 2y$$ and $${x}{y}≠{0}$$, then x is what percent of y?
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OG17
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The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?
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During a spring season, a certain glacier surged at the rate of 1 mile per 100 days. What was its rate in feet per hour? (1 mile = 5,280 feet)
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If $${2}{x}^{2}-{y}^{2}={2}{x}{y}$$, then $$({x}+{y})^{2}=$$
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PREP07 Test 2
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For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 - n points whenever one of its members finished in nth place, where $$1\le n \le 5$$. There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?
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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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If |d - 9| = 2d, then d =
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排列组合
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When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?
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In a certain English class, $$\frac1 4$$ of the number of girls is equal to $$\frac1 6$$ of the total number of students. What is the ratio of the number of boys to the number of girls in the class?
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