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When randomly selecting an integer from 11 to 50, inclusive, what is the probability that the selected number is a multiple of both 2 and 3?
w, x, y, and z are consecutive positive multiples of 6.

Quantity A

$$\frac{w+z}{2}$$

Quantity B

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


x is even, y is odd, which of the following could be even?

Indicate all such statements.
x, y, z are consecutive positive integers and x < y < z.

Quantity A

$$(\frac{1}{x}-\frac{1}{y})^{-1}$$

Quantity B

$$(\frac{1}{y}-\frac{1}{z})^{-1}$$


Gramwell claims that questions such as "What are the core assumptions of astronarmy" are ____________ the field of astronomical science; if someone is discussing the nature of astronomy, that individual is engaged in the philosophy of science rather than astronomy itself.
Orchestra players are not always the best judges of conduction. Not surprisingly, when evaluating conductors they put a high premium on musicianship and (i)____________ and therefore typically gravitate toward conductors who are both technically competent and (ii)____________. But the ability to galvanize a hundred musicians into giving a great performance requires more than proficiency and affability.
Some renewable energy technologies are quite ____________: for example, hydro power from dams and rivers has been a source of power generation since the early 1900s, and today it supplies sixteen percent of electricity worldwide.
The prime minister's reputation for ____________ was sullied when it was revealed that he had known of fraudulent activities taking place in the country's banking system but failed to report them.
Because her poetry can be so (i)____________, Sylvia Plath's continued popularity with readers may seem surprising, but perhaps it is precisely that (ii)____________ quality that accounts for Plath's persistence: her poetry satisfies a hunger for subjective intuitions.
By the end of the 1970s, the postmodern novel had degenerated from a bold attempt to (i)____________ the conventions of traditional narrative into a literary style as (ii)____________ as any other. There are, it seems, (iii)____________ number of ways to avoid telling a straightforward story.
Although legislators on both sides of issues have repeatedly (i)____________ a desire to find a middle ground, until now their actions disclose an unwillingness to (ii)____________ any compromise. The script followed by the latest statements has therefore become a familiar one: (iii)____________ posturing of questionable sincerity accompanied by an hint of real concessions.
Though the art of writing was well established in Egypt and Mesopotama long before Shang period, the Chinese writing that appeared then seems to have been an entirely ______________ development.
Neuroscientists are discovering that our sensory systems are much more interconnected than previously thought: even in ordinary circumstances, our senses can ____________ one another in extraordinary ways.
x ≠ 0

Quantity A

The average (arithmetic mean) of the numbers x, -x, and |x|

Quantity B

x





According to a survey of 300 college students, 40 percent had students loans and 25 percent had scholarships. If 55 percent of the students surveyed had neither student loans nor scholarships, how many of the students had both student loans and scholarships?
In a barrel, there are in ping-pong balls labeled with consecutive integers from $$1$$ to $$n$$, where $$n$$ is an odd integer greater than $$50$$. If a ball is to be randomly selected from the barrel, what is the probability that the ball selected will be a ball that is labeled with an odd integer?


What is the perimeter of the shaded region of the rectangle shown above if each of the unshaded regions is a 90-degree sector of a circle with radius r?
A rectangular garden has a diagonal that is 26 feet long. If one side of the garden is between 8 feet and 12 feet long, which of the following values could be the area, in square feet, of the garden?

Indicate all such values.


If $$\frac{1}{2}$$ of the revenue from the sale of jazz recordings was from the sale of vocal jazz recordings, then revenue from vocal jazz recordings was approximately what fraction of revenue from all vocal recordings?


The graphs shown are drawn to scale. Which of the following is closest to the degree measure of the central angle of the sector that represents the category labeled "Other"?

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