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Quantity A

20!+19!+18!

Quantity B

400(18!)


Set K consists of 9 positive integers, 5 of which are prime numbers. How many subsets of K consist of 3 integers such that 2 integers are prime numbers and 1 integer is not a prime number?


The figure above represents a game board with a chip at staring point M. On successive plays, the chip may be moved along the lines from one labled point to an adjacent labled point, but may not be moved to the same point twice. Along how many different paths can the chip be moved from M to N in this game?
The vehicles of Company W are numbered consecutively from 1 to 650. The vehicles with a number that ends with one of the digits 1, 2, 3, 4, or 5 are used by Division 1. Vehicles with a number between 130 and 389, inclusive, are trucks. What percent of the company vehicles are trucks used by Division 1?
In a probability experiment, $$R$$, $$S$$, and $$T$$ are events such that $$P(S)=P(T)=x$$, $$P(R)=kx$$, and $$P(R$$ or $$S) \lt P(S$$ or $$T)$$, where $$k$$ and $$x$$ are positive numbers. Events $$R$$ and $$S$$ are mutually exclusive, and events $$S$$ and $$T$$ are independent.

Quantity A

$$k$$

Quantity B

$$1-x$$


The campaign official argued that the large swings in the candidate`s approval ratings were a result not of the ____________ of the electorate but rather of the polls` margins of error and divergent methodologies.
Japanese consumers -no matter what a brief stroll in Tokyo`s Ginza shopping district may suggest-are saving more and spending less. In March, for instance, sales at department stores fell by 21 percent compared with the previous year. (i)____________, in the previous March shoppers had been out in force to (ii)____________ the implementation of a new consumption tax. But even when that is (iii)____________, households are still spending less than they did a year ago.
Seemingly to compensate for the (i)____________ nature of her subject, in her review the theater critic (ii)____________ a casual chatty style.
Scientists could not build on each other's work if they could not trust the published work of their colleagues; thus progress in science depends on the ____________ of practicing scientists.
The photocopier, widely adopted in the 1960s, became not merely a vehicle for copying but one for publishing in ____________ manner, so that ideas could be circulated without interference from potential censors.
California's building codes are more _____________ than those elsewhere in the United States to ensure that structures are capable of protecting people from frequent seismic events.
Advertising's role in popular music culture has been redefined: instead of a last resort for the creation and distribution of popular music, advertising now functions as a ___________ of music that might otherwise go unheard.
In A World on Fire, Joe Jackson draws on the biographies of two eighteenth-century chemists to bring to light intriguing tensions within their careers. Priestley, the (i)____________ chemist, was a passionate radical in virtually all of his other activities and writings. By contrast, Lavoisier, the (ii)____________ scientist, was very much a member of the social and political establishment.
The television network seems to regard its longest-running comedy show as _____________, keeping it in the schedule even as the humor it churns out is notoriously hit-or-miss.
Although it is quite probable that many small asteroids in the solar system`s asteroid belt have (i) _____________, the total mass of these objects cannot be (ii) _____________, since the combined gravitational pull of all known asteroids is (iii) ______ to fully account for the asteroid belt's effect on the motion of nearby planets such as Mars.
Meteorology is one of the few fields of applied science that demands prediction; since prediction involves considerable uncertainty and uncertainty is _____________ scientists, meteorology will continue to exist in a fraught intellectual space.
The painter Fu Baoshi lived and worked through a tumultuous period in Chinese history, _________ by exceptional talent and a steely dedication to his art.
The fantastic conceit of the film's plot is that global warming (i) __________ global freezing. After a chunk of Antarctic ice the size of Rhode Island suddenly melts, most of what follows—an instant ice age, for example—is impossible as science but not as metaphor. The data from the Greenland ice sheet show that, over the past hundred thousand years, temperatures have often (ii) ___________—so often that it is our own relatively static experience of climate that should now be seen as (iii) ___________.
In a production process that is complex and often unpredictable, roles that start out discretely defined may become quite _____________.
The auditors are relying on the failing bank to make changes that it has steadfastly resisted for years and even now does not seem _____________ to carry out.

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