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Positive integers m and k are to be chosen such that $$\frac{m}{5} < k < \frac{m}{3}$$

Quantity A

The least possible value of k

Quantity B

1


List A consists of 25 positive integers $$a_1$$, $$a_2$$, $$a_3$$,...,$$a_{25}$$ that are ordered from least to greatest. The median and the mode of the integers in A are both equal to 10. List B consists of 25 positive integers $$b_1$$, $$b_2$$, $$b_3$$,...,$$b_{25}$$ that are ordered from least to greatest. The median and the mode of the integers in B are both equal to 15. List C consists of the 25 sums $$a_i$$ +$$b_i$$, for all integers $$i$$ such that 1 ≤ $$i$$ ≤ 25. The mode of the integers in C is $$m$$.

Quantity A

The median of the integers in C

Quantity B

$$m$$


(六选二) An abundance of nutrient-rich pollution in estuaries causes algae to _____________, much as houseplants grow better when their soil contains added fertilizer.
The function $$f$$ is defined for all numbers $$x$$ by $$f(x) = 2+ 3x$$.

Quantity A

$$f(x+4)-f(x)$$

Quantity B

12




In the figure shown, O is the center of the circle and $$x$$ and $$y$$ are the lengths of two line segments.

Quantity A

The radius of the circle

Quantity B

$$\frac{x+y}{2}$$


On a scaled map, the point for the geographical center of City A is 4 inches from the point for the geographical center of City B, and the point for the geographical center of City B is 2 inches from the point for the geographical center of City C. The actual distance from the geographical center of City A to the geographical center of City B is 500 miles. Which of the following values could be the actual distance, in miles, from the geographical center of City A to the geographical center of City C?

Indicate all such values.
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%




The table above shows the values of f(x) for selected values of x, where f(x) is a linear function. What is the value of f(-10)?
Machines A, B, and C produce widgets at their respective constant rates. Machine A produces $$n$$ widgets in $$x$$ hours, machine B produces $$n$$ widgets in $$2x$$ hours, and machine C produces $$n$$ widgets in $$3x$$ hours. In terms of $$x$$, how many hours does it take the three machines, working simultaneously at their respective constant rates to produce $$n$$ widgets?
In the xy-plane, circle C is centered at (0, 3) and passes through the point (2, 0).

Quantity A

The area of circle C

Quantity B

13π


When 9 gallons of a solution that is 30 percent alcohol are mixed with 18 gallons of a solution that is x percent alcohol, the resulting mixture is 25 percent alcohol. Which of the following is closest to the value of x?
A manufacturer is designing a closed box in the shape of a rectangular solid where the ratio of the width to the height to the length of the box is 1 to 3 to 5. If the volume of the box is 405 cubic inches, what is the total surface area of the closed box, in square inches?
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

$$5$$




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.
For all integers $$k \gt 1$$, $$P_{k}=\frac{k+1}{k}$$. For all integers $$k \gt 2$$, $$b_{k}=P_{k}-P_{k-1}$$. The integer $$n$$ is greater than $$2$$.

Quantity A

$$b_{n}$$

Quantity B

$$\frac{-1}{n^2-n}$$


Which statement best expresses the author' s main conclusion in the passage?

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