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OG18-数学分册
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Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?
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$$(1 + \sqrt{5})(1 - \sqrt{5}) = $$
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OG18-数学分册
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$$(1 + \sqrt{5})(1 - \sqrt{5}) = $$
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OG18-数学分册
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Stephan has $$2\frac{1}{4} $$ cups of milk on hand and makes 2 batches of cookies, using $$\frac{2}{3}$$ cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?
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OG18-数学分册
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The price of a certain stock increased by 0.25 of 1 percent on a certain day. By what fraction did the price of the stock increase that day?
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OG18-数学分册
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There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?
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OG18-数学分册
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Last week Jack worked 70 hours and earned $1,260. If he earned his regular hourly wage for the first 40 hours worked, $$1\frac{1}{2}$$ times his regular hourly wage for the next 20 hours worked, and 2 times his regular hourly wage for the remaining 10 hours worked, what was his regular hourly wage?
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OG18-数学分册
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 In the rectangular coordinate system above, the area of triangular region RST is
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OG18-数学分册
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Three business partners, Q, R, and S, agree to divide their total profit for a certain year in the ratios 2:5:8, respectively. If Q's share was $4,000, what was the total profit of the business partners for the year?
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OG18-数学分册
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If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2, and 5j – 1 is 8, what is the value of j ?
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OG18-数学分册
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After 4,000 gallons of water were added to a large water tank that was already filled to $$\frac{3}{4}$$ of its capacity, the tank was then at $$\frac{4}{5}$$ of its capacity. How many gallons of water does the tank hold when filled to capacity?
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OG18 OG19 OG20 OG2022
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Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than $$\frac{π}{100} $$square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains?(1) Jack's rug covers an area of 9π square feet.(2) The centers of the stains are less than 4 feet apart.
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OG18 OG19 OG20 OG2022
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For a certain city's library, the average cost of purchasing each new book is $28. The library receives $15,000 from the city each year; the library also receives a bonus of $2,000 if the total number of items checked out over the course of the year exceeds 5,000. Did the library receive the bonus last year?(1) The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost. (2) The lowest number of items checked out in one month was 459.
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OG18 OG19 OG20 OG2022
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Is x<5?(1) $$x^{2}$$>5 (2)$$ x^{2}+x<5$$
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OG18 OG19 OG20 OG2022
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If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z?(1) x-y=y-z(2) $$x^{2}-y^{2}=z$$
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OG18 OG19 OG20 OG2022
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If r and t are three-digit positive integers, is r greater than t?(1) The tens digit of r is greater than each of the three digits of t.(2) The tens digit of r is less than either of the other two digits of r.
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OG18 OG19 OG20 OG2022
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Each month, Jim receives a base salary plus a 10 percent commission on the price of each car he sells that month. If Jim sold 15 cars last month, what was the total amount of base salary and commissions that Jim received that month?(1) Last month, Jim's base salary was $3,000.(2) Last month, Jim sold 3 cars whose prices totaled $60,000 and 5 cars whose prices totaled $120,000.
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OG18 OG19 OG20 OG2022
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At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year? (1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.(2) At the end of the year, 21 members remained on the Planning Committee.
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Researchers recently examined the initial public offering (IPO) - a private firm's first sale of stock shares to the public- of firms listed on Kenya's Nairobi Stock Exchange (NSE) between 1994 and 2008. During this time, the number of IPOS listed per year varied to examine the extent to which four different variables-investor sentiment, firm size. board prestige, and firm age- affected the IPO stock share price, which is set by the firm.They hypothesized that all four variavles would show a strong positive correlation with this IPO asking price. However, after examining the firms listed, they were surprised to find that none of the variables showed a strong positive correlation with IPO pricing, and in fact investor sentiment and board prestige both showed a strong negative correlation.The researchers also discovered that nearly all of these IPOs were underpriced by an average of 50 percent, which is to say the IPO share prices were about half of what the share prices were at the close of that first day of trading. Such underpricing constitutes a loss to the listed firm because teh firm could have immediately raised more money with a higher price. The researchers noted that firms should take care to set an IPO price low enough to capture investor interest but high enough to generate sufficient capital for the firm.
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In their study of whether offering a guarantee of service quality will encourage customers to visit a particular restaurant, Tucci and Talaga have found that the effect of such guarantees is mixed. For higher-priced restaurants, there is some evidence that offering a guarantee increases the likelihood of customer selection, probably reflecting the greater financial commitment involved in choosing an expensive restaurant. For lower-priced restaurants, where one expects less assiduous service, Tucci and Talaga found that a guarantee could actually have a negative effect: a potential customer might think that a restaurant offering a guarantee is worried about its service. Moreover, since customers understand a restaurant's product and know what to anticipate in terms of service, they are empowered to question its quality. This is not generally true in the case of skilled activities such as electrical work, where, consequently, a guarantee might have greater customer appeal. For restaurants generally, the main benefit of a service guarantee probably lies not so much in customer appeal as in managing and motivating staff. Staff members would know what service standards are expected of them and also know that the success of the business relies on their adhering to those standards. Additionally, guarantees provide some basis for defining the skills needed for successful service in areas traditionally regarded as unskilled, such as waiting tables.
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