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题目内容
A large pump and a small pump are available to fill a public fountain with 7,500 gallons of water. The pumps can be used alone or simultaneously. Working alone at their respective constant rates, the small pump would take 1.6 times as long as the large pump to fill the fountain. Working simultaneously at their respective constant rates, the two pumps would take 3 hours to fill the fountain. How long would the small pump take to fill the fountain, working alone at its constant rate?
A survey of voters who were either supporters of Candidate A or supporters of Candidate B showed that 64 percent of the supporters of Candidate A and 50 percent of the supporters of Candidate B were in favor of a progressive income tax.

Quantity A

The percent of the voters surveyed who were in favor of a progressive

Quantity B

57%
A tour group in an art museum consisted of 40 people, some of whom were art students. Of the art students who were in the tour group, 5 were studying sculpting and the rest were studying painting.

Which of the following statements individually provide(s) sufficient additional information to determine the number of art students who were in the tour group?

Indicate all such statements.
Five gift cards will be distributed among 10 people so that no person receives more than one gift card. The gift cards consist of one $100 gift card, one $50 gift card, one $25 gift card and two $10 gift cards. How many different distributions of the five gift cards among the 10 people are possible if the two $10 gift cards are considered to be identical?
In the $$xy$$-plane, line $$n$$ has $$x$$-intercept $$h$$ and $$y$$-intercept $$t$$, where $$h$$ and $$t$$ are positive numbers. Which of the following points must lie on line $$n$$?

Indicate all such points.
The function $$f$$ is defined by $$f(n)=3n^2+2n+5$$ for all integers $$n$$.

Quantity A

The least value of $$f(n)$$ for all integers $$n$$

Quantity B

$$5$$
Cylindrical can A contains five servings of soup when full. How many servings of the soup are contained in a full cylindrical can with 2 times the diameter and 3 times the height of can A?


In the figure above, the line segments represent paths in a garden and the dots represent benches. All of the paths allow two-way traffic except the path between the waterfall bench and the roses bench, which can be traveled only in the direction of the arrow. What is the greatest possible number of different routes from the entrance bench to the fountain bench along these paths that a visitor can travel without passing the same bench more than once?


In the figure shown, a square is inscribed in a circle, which is inscribed in a square.

Quantity A

The total area of the regions shaded black

Quantity B

The total area of the regions shaded gray
$$0 < x < y$$

$$Rx+y < 0$$

Quantity A

$$x-y$$

Quantity B

$$R$$
Calvin drives east along a straight road from point A to point B. His speed is never more than 60 miles per hour. Which of the following graphs could represent Calvin's distance from point A as a function of time?

Indicate all such graphs.
Machine A and machine B, working simultaneously and independently at their respective constant rates, processed $$\frac{3}{4}$$ of the shipment of a certain product in 4.5 hours. Then machine A, working alone at its constant rate, processed the rest of the shipment in 6 hours. How many hours would it have taken machine B, working alone at its constant rate, to process the entire shipment of the product?
The width and the length of a rectangular piece of plywood are 4 feet and 8 feet, respectively. Along one edge of the plywood, a strip $$x$$ inches wide and 8 feet long is removed. Then, along an edge perpendicular to the 8-foot edge, a strip $$x$$ inches wide is removed. For what value of $$x$$ will the remaining rectangular piece have width and length in the ratio of 2 to 5? (1 foot = 12 inches)
A furniture store purchased sofas for a wholesale price of $400 each and sold most of them for a retail price of $560 each. In a summer sale, the retail price of the last few sofas was reduced by $$x$$ dollars, and they were sold at this reduced price. The store's profit from selling the last sofa was more than 15 percent of its wholesale price. Which of the following could be the value of $$ x$$ ?

Indicate all such values.
A survey was given to a sample of residents in a certain town to determine the level of interest in creating a new park. Of those residents in the sample, 50 percent responded they were in favor of the park and 30 percent responded they were not in favor of the park. The remaining 20 percent of the sample did not respond to the survey. Which of the following statements individually provide(s) sufficient additional information to determine the number of residents in the sample? Indicate all such statements
A survey was given to a sample of residents in a certain town to determine the level of interest in creating a new park. Of those residents in the sample, 50 percent responded they were in favor of the park and 30 percent responded they were not in favor of the park. The remaining 20 percent of the sample did not respond to the survey.

Which of the following statements individually provide(s) sufficient additional information to determine the number of residents in the sample?

Indicate all such statements
Marina's total monthly salary consists of a base monthly salary of $400 plus a commission equal to 10 percent of her sales up to a certain amount and a commission of 20 percent on any additional sales in excess of that amount. Last month Marina's sales were $12,000, and her total monthly salary was $2,000. What is the amount of sales at which the commission rate changes from 10 percent to 20 percent?
The median salary for assistant professors lies in which of the following intervals?
Approximately what percent of the full professors had a salary of $110,000 or greater?
If the average (arithmetic mean) salary of the full professors whose salaries were in the interval $50,000-$120,000 was $$x$$, and if the average salary of the full professors whose salaries were $120,000 and above was $$y$$, what was the average salary of all the full professors, in terms of $$x$$ and $$y$$?

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