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300难题
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If x + y + z > 0, is z > 1 ?
1.z > x + y + 1
2.x + y + 1 < 0
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300难题
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Is x less than y ?
1.x - y+ 1 < 0
2.x - y - 1 < 0
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300难题 OG20
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If n > 4, what is the value of the integer n ?
1. $$\frac{n!}{(n-3)!}$$ =$$\frac{3!n!}{4!(n-4)!}$$
2. $$\frac{n!}{3!(n-3)!}$$ +$$\frac{n!}{4!(n-4)!}$$ =$$\frac{(n+1)!}{4!(n-3)!}$$
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300难题
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At a certain university recreation center, a member can receive a 30-minute massage, a 60-minute massage, or a 90-minute massage, and is charged $0.50 per minute for each massage. A member receiving a massage is charged the same fixed amount for each additional service, such as nutrition advice or a fitness evaluation. At this center, what is the total charge to a member for a 60-minute massage and 3 additional services?
1.At this recreation center, Jordan,a member ,had a massage and 3 additional services for a total charge of $37.50.
2.At this recreation center,Ryan,a member,had a massage and 2 additional services for a total charge of $60.00.
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300难题
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Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?
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300难题
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The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now,in terms of y ?
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300难题
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The figure above shows the dimensions of a rectangular board that is to be cut into four identical pieces by making cuts at points A, B, and C,as indicated. If x = 45, what is the length AB ?(1 foot = 12 inches)
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300难题
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The figure above shows some of the dimensions of a triangular plaza with an L-shaped walk along two of its edges. If the width of the walk is 4 feet and the total area of the plaza and walk together is 10,800 square feet, what is the value of x ?
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300难题
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The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the length and width of the frame, what is the length of the picture, in inches?
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300难题
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In the figure above, the area of the shaded region is
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300难题
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When a certain stretch of highway was rebuilt and straightened, the distance along the stretch was decreased by 20 percent and the speed limit was increased by 25 percent. By what percent was the driving time along this stretch reduced for a person who always drives at the speed limit?
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300难题
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Store N gives a 50 percent discount on the list price of all its items and Store W gives a 60 percent discount on the list price of all its items. If the list price of the same item is 20 percent higher in Store W, what percent (more or less) of the selling price in Store N is the selling price of the item in Store W ?
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300难题
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The difference 942 - 249 is a positive multiple of 7. If a,b, and c are nonzero digits, how many 3-digit numbers abc are possible such that the difference abc - cba is a positive multiple of 7?
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300难题
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Five integers between 10 and 99, inclusive, are to be formed by using each of the ten digits exactly once in such a way that the sum of the five integers is as small as possible. What is the greatest possible integer that could be among these five numbers?
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300难题
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Let S be the set of all positive integers having at most 4 digits and such that each of the digits is 0 or 1. What is the greatest prime factor of the sum of all the numbers in S ?
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300难题
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A computer can perform 1，000，000 calculations per second. At this rate, how many hours will it take this computer to perform the 3.6 * $$10^{11}$$ calculations required to solve a certain problem?
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300难题
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A certain online form requires a 2-digit code for the day of the month to be entered into one of its fields, such as 04 for the 4th day of the month. The code is valid if it is 01,02, 03,...,31 and not valid otherwise. The transpose of a code xy is yx. For example, 40 is the transpose of 04. If N is the number of valid codes having a transpose that is not valid, what is the value of N?
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300难题
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Recent observations suggest that small, earthlike worlds form a very low percentage of the planets orbiting stars in the galaxy other than the sun. Of over two hundred planets that astronomers have detected around other stars, almost all are hundreds of times larger and heavier than the earth and orbit stars much smaller than the sun.
Which of the following, if true, would most weaken the above justification of the claim that earthlike worlds form a low percentage of the total number of planets?
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300难题
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Scientist: In an experiment, dogs had access to a handle they could pull to release food into a nearby enclosure that contained a familiar dog and nothing else, contained an unfamiliar dog and nothing else, or was empty. The dogs typically released more food to the familiar dog than to the unfamiliar dog. This suggests that dogs are more motivated to help other dogs they know than to help unfamiliar dogs.
The scientist's argument would be most strengthened if it were true that, in the experiment, the dogs with access to the handle tended to release more food when
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300难题
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Sasha: It must be healthy to follow a diet high in animal proteins and fats. Human beings undoubtedly evolved to thrive on such a diet, since our prehistoric ancestors ate large amounts of meat.
Jamal: But our ancestors also exerted themselves intensely in order to obtain this food, whereas most human beings today are much less physically active.
Jamal responds to Sasha by doing which of the following?
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