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The function f is defined by f(x) =$$x^{2}$$-18x+56 for all numbers x. If r and t are two different numbers such that f(r) = f(t) = 0. What is the value of $$\frac{r+t}{2}$$?
In the distribution of heights in a group of a thousand people, height $$p$$ is at the 42nd percentile, height $$r$$ is at the 48th percentile, height $$s$$ is at the 54th percentile, and height $$t$$ is at the 60th percentile.

Quantity A

$$r-p$$

Quantity B

$$t-s$$




For the programming languages shown, the ratio of the greatest number of job postings in 2018 to the least number of job postings in 2018 was closest to which of the following?
For 2017, let M be the median number of job postings for the programming languages shown and let P be the median number of job postings for the programming languages shown except for PHP. What is the value of P-M?
If the numbers of job postings for each language and year except Java in 2018 were as shown, and if the range of the numbers of job postings for 2018 had been equal to that for 2017 instead of what it actually was, what would have been the number of job postings for Java in 2018?

_____thousand


Quantity A

RS

Quantity B

3


x ≤ 5

y ≤ 40

Quantity A

xy

Quantity B

300


Of the 72 fish in a certain aquarium, $$\frac{1}{3}$$ are brown and the remaining $$\frac{2}{3}$$ are white. Among the 72 fish, $$\frac{1}{2}$$ have orange fins and $$\frac{1}{2}$$ have black fins. If $$\frac{2}{3}$$ of the white fish have orange fins, how many of the brown fish have black fins?
For how many of the years shown was Company B's monthly rate at least 10 percent greater than Company A's monthly rate?
Which of the following is closest to the percent increase in the monthly rate for Company A from 1996 to 1997?
For which of the following years was the amouont by which the monthly rate for Company C exceeded that for Company A closest to the amount by which the monthly rate for Company B exceeded that for Company C?
For all integers $$x$$ and $$y$$, the operation $$▽$$ is defined as $$x▽y=x$$ if $$xy$$ is even, and $$x▽y=-y$$ if $$xy$$ is odd. What is the value of $$(-57▽68)▽(-81)$$?
A box contains 100 purple balls, 100 red balls, and 100 white balls. What is the minimum number of balls that must be chosen to ensure that at least 4 of the balls chosen have the same color?
Whether the film is ____________ adaptation of the legend is debatable: the author of the screenplay claims that it was based on the original tale, but admits taking some interpretive license with the story.
That the announcement of the new treatment was greeted with ___________ is hardly surprising given the claims made for it, but attitudes were markedly tempered once the paucity of supporting data became apparent.
According to the passage, which of the following statements about the sculptures produced by nineteenth-century women sculptors is true?
The author would most likely agree with which of the following assertions about the environmental impact of hydroelectric power?
The phone extensions of a certain company run consecutively from 3000 to 3799. The phone extensions that began with the digits 33 or 34 belong to Division 1 of the company. The phone extensions that end with the digit 0 or 1 belong to managers. What percent of the phone extensions of the company belong to managers in Division 1?


In a survey, 100 people were asked how many meals they ate at restaurants in the previous year. The table above shows a frequency distribution of their response. Which of the following values could be the median of the numbers of meals eaten at restaurants for the 100 people surveyed?

Indicate all such values.
For many who are not philosophers, the word “metaphysics” still retains connotations of (i)____________, so that many hard scientists still use the term as a byword for (ii)____________ thinking.

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