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题目内容
$$x$$ and $$y$$ are positive integers. $$x+y=15$$ $$y^2-x^2=105$$

Quantity A

$$y$$

Quantity B

$$12$$
In the $$xy$$-plane, the lines with equations $$y= 3x-1$$ and $$y=mx+1$$, where m is a constant, intersect in quadrant I. Which of the following could be the value of $$m$$?
For how many pairs of numbers $$x$$ and $$y$$ does $$(x - 7)^2 + (y + 3) ^2 = 0$$?
In the $$xy$$-plane, the point $$(s, 2s-4)$$ lies on the line with equation $$y=(\frac{-5}{2})x+\frac{1}{3}$$. What is the value of s? Give your answer as a fraction.
In the $$xy$$-plane, the graph of $$y=x^3-4x$$ intersects the x-axis between $$x=-1$$ and $$x=5$$ at how many points?
Line k in the xy-plane has y-intercept 8 and a negative x-intercept. The area of the triangle bounded by line k and the coordinate axes is 20. What is the slope of $$k$$? Give your answer as a fraction.
In the rectangular coordinate system, point $$(5, 5)$$ is equidistant from points $$(x, 0)$$ and $$(0, y)$$.

Quantity A

$$x$$

Quantity B

$$y$$

Quantity A

The sum of the coordinates of point P

Quantity B

$$0$$
In the $$xy$$-plane, the points $$(-2, 1)$$ and $$(2, 3)$$ lie on line l. Which of the following points does NOT lie on line l?
Of the employees in the 2001 workforce who were hired in 1997, 40 percent were hired to fill positions in a new subdivision of Company I. Approximately how many of the employees in the 2001 workforce were hired in 1997 to fill positions in the new subdivision?
If the ratio of the number of employees in the 2001 workforce who were hired in 1996 to the total number of employees hired in 1996 was 2 to 3, approximately what was the total number of employees hired in 1996?
In the 2001 workforce, the average (arithmetic mean) salary of the employees hired prior to 1999 was $39,900, and the average salary of the employees hired in 1999 and 2000 was $30,100. Which of the following is closest to the average salary of all employees in the 2001 workforce?

Quantity A

The number of positive integers that are factors of both 24 and 30 but are not factors of 20

Quantity B

The number of positive integers that are factors of both 20 and 30 but are not factors of 24
If $$x > 0, y > 0$$, and $$z < 0$$, which of the following numbers must be negative?
Indicate ALL such numbers.
What is the probability that an integer to be chosen at random between 1 and 50, inclusive, will be divisible by 3 or 7?


In the figure shown, a circle is inscribed in a hexagon and $$L, M$$, and $$N$$ are points of tangency. In the hexagon, all sides have length 5 and all angles have the same measure.

Quantity A

The length of arc LMN

Quantity B

$$10$$


In the figure, if $$n-t=80$$, what is the value of $$n$$?

$$n=$$
The ratio of the amount spent on basic research in 1995 by the Department of Health and Human Services to the corresponding amount spent by the National Science Foundation was approximately

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