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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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 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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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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If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
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OG12
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Drum X is $$\frac{1}{2}$$ full of oil and Drum Y, which has twice the capacity of Drum X, is $$\frac{2}{3}$$ full of oil. If all of the oil in Drum X is poured into Drum Y, then Drum Y will be filled to what fraction of its capacity?
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Which of the following ratios is most nearly equal to the ratio $$1 +\sqrt{5}$$ to 2?
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OG16 OG17 OG18 OG19 OG20 OG2022
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In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
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A gumball dispenser has 24 gumballs, 12 white and 12 black, which are dispensed at random. If the first 3 gumballs dispensed are black, what is the probability that the next gumball dispensed will be black?
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A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?
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On the first day of the climb, mountaineers covered $$\frac{5}{7}$$ of the distance to the top, on the second day of the climb, they covered $$\frac{1}{5}$$ of the remaining distance. What fraction of the total climb do the mountaineers have to cover to reach the top on the third day?
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PREP07 Test 2
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If two of the four expressions x + y, x + 5y, x - y, and 5x - y are chosen at random, what is the probability that their product will be of the form of $$x^2 - (by)^2$$, where b is an integer?
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PREP07 Test 2
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If $$(7^\frac{3}{4})^n=7$$, what is the value of n ?
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Manhattan
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What is$$\frac{3}{5} of \frac{5}{8} of \frac{2}{3}?$$
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Magoosh
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0.25% =
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Magoosh
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A division of a company consists of seven men and five women. If three of these twelve employees are randomly selected as representatives of the division, what is the probability that the representatives will consist of two females and one male?
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Magoosh
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x is betweenNote: Figure not drawn to scale
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Magoosh
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Which of the following sets of numbers has the greatest standard deviation?
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Manhattan
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Two buses and a van were employed to transport a class of students on a field trip. $$\frac{3}{5}$$ of the class boarded the first bus. $$\frac{2}{3}$$ of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down,$$\frac{ 1}{2}$$ of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?
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Magoosh
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In the coordinate plane, rectangular region R has vertices at (0,0), (0,3), (4,3), and (4,0). If a point in region R is randomly selected, what is the probability that the point's y-coordinate will be greater than its x-coordinate?
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