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m and n are integers.

Quantity A

$$\sqrt{( 10^{2m} )( 10^{2n} )}$$

Quantity B

$$10^{mn}$$


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)
If x is a positive integer such that the units digit of $$x^{3}$$ is 3, what is the units digit of $$x^{15}$$?
Which of the following statements about the managers surveyed must be true?
The number of managers surveyed who identified work experience as an important characteristic to consider was approximately what percent greater than the number who identified appropriate attire and behavior as an important characteristic to consider?
If 48 percent of the managers surveyed identified both ability to follow directions and computer expertise as an important characteristics to consider, what percent of the managers surveyed identified neither of these characteristics as important to consider?

In square ABCD, point P is the midpoint of side BC and point Q is the midpoint of side AD. Point E (not shown) is located on line l and triangle BCE is equilateral.

Quantity A

The length of PQ

Quantity B

The length of PE





Data sets X and Y each consist of 4 values, as shown in the table. If the range of dataset X is 21, what is the range of dataset Y?
In the xy -plane, line l is parallel to the line y = 3x + 2. If line l passes through the point (1, -1), then line l passes through which of the following points?
Indicate all such points.
In the xy-plane, C and D are circles centered at the origin with radii $$\sqrt{17}$$ and $$\sqrt{5}$$, respectively.

Quantity A

The number of points (a, b) on circle C where both a and b are integers

Quantity B

The number of points (a, b) on circle D where both a and b are integers


If k is a positive integer and n is the ones digit of $$7^{k}$$, what is the greatest possible value of |n-7|?
n is a positive integer, x is the units digit of $$7^{n}$$, y is the units digit of $$3^{n}$$

Quantity A

|x-y|

Quantity B

3


Jim exercises every third day. For example, if he exercises on a Monday, the next day he will exercise is the following Thursday. If Jim exercised last Monday, how many weeks from last Monday will be the next Monday that he exercises?


Point $$Q$$ (not shown) is on the number line between $$-2$$ and $$-1$$. Point $$R$$ (not shown) is on the number line between $$0$$ and $$1$$. Point $$S$$ (not shown) is on the number line between $$3$$ and $$4$$

Quantity A

$$QR$$

Quantity B

$$RS$$




x > 0

y < 0

Quantity A

$$(x-y)^{2}$$

Quantity B

$$x^{2}+y^{2}$$


x, y and z are all positive numbers

Quantity A

The square of the average (arithmetic mean) of x, y and z

Quantity B

The average (arithmetic mean) of $$x^{2}$$,$$y^{2}$$and $$z^{2}$$


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.
A line in the xy-plane has the equation y=mx+6, where m is a constant and 3 ≤ m ≤ 4. Which of the following could be the x-intercept of the line?

Indicate all such values.


A sphere, as shown above with a radius of 1 meter is rotating 360 degrees per second about its vertical axis. The speed, in meters per second, of a point on the sphere due to this rotation is in the range from

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