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Quantity A

The number of points in the plane that are equidistant from all the three lines k, m, and p

Quantity B

3






A coffee shop sells its own brand of ground coffee packaged in two sizes-small and large. The small size is priced at $$k$$ dollars per package, and the large size is priced at $$m$$ dollars per package. If the total price of $$4$$ packages of the coffee is $30, which of the following could be the values of $$k$$ and $$m$$?

Indicate all such values.
If $$-8 \leq h \leq 10$$ and $$h+m=-4$$, what is the least possible value of $$mh$$?
If 20 were to be added to only one of the five factors in the product (173) (113) (131) (293) (239), to which factor must it to be added so that the resulting product is as great as possible?
$$0 \lt x^{7} \lt 1$$

Quantity A

$$\sqrt{x}$$

Quantity B

$$x$$


A hexagon is inscribed in a circle with diameter $$d$$. Each of the six sides of the hexagon have the same length, and each of the six angles of the hexagon have the same measure. What is the perimeter of the hexagon in terms of $$d$$?

Quantity A

$$y$$

Quantity B

$$z$$


Let $$S_8$$ represents the set of integers from $$1$$ to $$8$$, and let $$S_9$$ represents the set of integers from $$1$$ to $$9$$.

Quantity A

The number of the subsets of $$S_8$$

Quantity B

The number of the subsets of $$S_9$$ that contain the integer $$9$$


In a group of 150 people, 40 percent are older than 60 years and 80 percent are employed.Which of the following could be the number of people who are both employed and older than 60 years?
Indicate all such numbers.
The operation @ is defined for all numbers $$x$$ and $$y$$ by the equation $$x@y=x^2+y$$.

Quantity A

($$\frac{2}{3}$$@$$\frac{2}{3}$$)@$$\frac{2}{3}$$

Quantity B

$$\frac{2}{3}$$@($$\frac{2}{3}$$@$$\frac{2}{3}$$)


The leg of isosceles triangle A is 8, while the leg of isosceles triangle B is 10.

Quantity A

The area of isosceles triangle A

Quantity B

The area of isosceles triangle B




The figure represents a 5-foot-wide circular walkway that is bounded by two concentric circles. The outer boundary of the walkway is approximately how many feet longer than the inner boundary of the walkway?


The figure above shows five congruent circles each with radius 2 such that each of the five circles is tangent to two other congruent circles and to a smaller inner circle. The perimeter of the figure is composed of 5 line segments of length x and 5 circular arcs of length y. What is the perimeter of the figure?
If $$a$$ and $$b$$ are integers satisfying the equation $$a^{2}+b^{2}=145$$, which of the following could be the value of $$a+b$$?

Indicate all such values.

$$x=y$$

BD∥AE

Quantity A

The area of △ACE

Quantity B

The area of △BDF



In the figure, the perimeter of quadrilateral RSTW is 34. What is the perimeter of triangle STW?
If 12 percent of the books in a library are reference books, then the ratio of the number of reference books to the number of nonreference books is closest to which of the following?

Triangle ABC is inscribed in the circle centered at O.

Quantity A

Five times the area of triangular region ABC

Quantity B

The area of the circular region


List R={x, y, z, 2.7, 3.8, 5.5}

List S={x, y, z, -2.7, -3.8, -5.5}

If the average (arithmetic mean) of the 6 numbers in list R is r and the average of the 6 numbers in list S is s, then r-s is the average of which of the following lists?
$$x \lt y$$

The median of $$x$$, $$y$$ and $$120$$ is $$100$$

Quantity A

$$x$$

Quantity B

$$90$$


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