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Theo owns $$\frac{1}{3}$$ of the number of pairs of shoes that Samantha owns, and Richard owns twice as many pairs as Samantha. If Richard owns fewer than 30 pairs of shoes, which of the following could be the number of pairs he owns?

Indicate all such numbers.
Sequence $$S$$ is generated by repeating the 11-term sequence 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5 indefinitely. What is the 1,999th term of sequence $$S$$?


The graph of which of the following functions is shown in the xy-plane?
A scientist conducted an experiment and collected three measurements. Each measurement was an integer. The range of the three measurements was 2 and the least value was 1. Which of the following values could be the average (arithmetic mean) of the measurements collected for the experiment? Indicate all such values.
Printer $$P$$ prints at the constant rate of $$x$$ seconds per page, and printer $$O$$ prints at the constant rate of y seconds per page. If both printers print at their respective rates, then, in terms of x and y, what is the total number of pages the two printers print in 1 hour?
Last month 200 students, including Jim and Joseph, took a certain test. Jim' s score on the test was 96, which was at the 86th percentile of the 200 scores on the test. Joseph' score on the test was 89, which was at the nth percentile of the 200 scores on the test.

Quantity A

$$n$$

Quantity B

$$79$$


If the surface area of a cube is 96, what is its volume?
In a poll, 50 percent of those polled said they would vote for Candidate M, and 80 percent said they were in favor of proposition 3.

Quantity A

The percent of those polled who said they would not vote for Candidate M and were not in favor of proposition 3

Quantity B

$$25%$$


The first and last terms in a certain sequence are -8 and 184, respectively. Each term in the sequence after the first term is 3 greater than the immediately preceding term.

Quantity A

The number of terms in the sequence

Quantity B

$$65$$


A list of data values was divided into three smaller lists, where list A contains one-half of the data values, list B contains one-fifth of the data values, and list C contains the rest. The average (arithmetic mean) of the data values in list A is 12, the average of the data values in list B is 15, and the average of the data values in list $$C$$ is 6. What is the average of all of the data values in the original list?
When the positive integer n is divided by 5, the remainder is 3. Which of the following could be the units digit of n?

Indicate all such digits.
The graph above shows the annual sales, in thousands of dollars, for a certain product sold at three different stores for the years 2011 to 2015. Of the following sales, which had the greatest percent increase?
If $$x+y=1$$ and $$xy \neq 0$$, then $$\frac{1}{x}$$+ $$\frac{1}{y}$$=


Three machines, A, B, and C, will work on three different kinds of tasks, respectively, over an 8-hour period. Each machine will work continuously for a constant time per task, as shown in the table, without stopping between consecutive tasks. If the three machines start working on their tasks simultaneously at the beginning of the 8-hour period, how many times during the 8-hour period will all three machines complete a task simultaneously?
In a certain homeowners' association, $$\frac{2}{3}$$ of the members in the association must vote in favor of a proposed change in the bylaws in order for the change to pass. At the last meeting, in which voting for a certain proposed change in the bylaws took place, $$\frac{1}{4}$$ of the members did not vote. If the proposed change was passed, at least what fraction of the members who voted must have voted in favor of the proposed change?
Michael, Kim, Glenda, and Ian all own DVDs, and no DVD is owned by two or more of them. Michael owns $$\frac{1}{2}$$ of the number of DVDs that Kim owns. Glenda owns $$\frac{1}{3}$$ of the number of DVDs that Ian owns. If Kim and Ian own the same number of DVDs, what is the ratio of the total number of DVDs that Michael and Glenda own to the total number of DVDs that Kim and lan own?

Give your answer as a fraction.
A certain machine that produces copies of pictures has settings of 60 percent, 80 percent, 100 percent, 150 percent, and 200 percent, where each setting indicates the dimensions of the copy as a percent of the corresponding dimensions of the original picture. Which of the following combinations of settings could be used to make a second copy of a first copy of an original picture for which the dimensions of the second copy are 120 percent of the corresponding dimensions of the original picture?

Indicate all such combinations.
The closing price of a stock on a certain day was p dollars. For the next 8 consecutive trading days, the closing price changed as follows. For the 1st, 3rd, 5th, and 7th days, the closing price of the stock was 10 percent less than its closing price on the preceding day. For the 2nd, 4th, 6th, and 8th days, the closing price of the stock was 10 percent greater than its closing price on the preceding day. Which of the following represents the closing price, in dollars, of the stock on the 8th day?
A large pump and a small pump deliver water into a tank at their respective constant rates. Working simultaneously, the two pumps take 6 hours to fill the empty tank. If each pump worked alone, then the amount of time that it takes the large pump to fill the empty tank is $$\frac{2}{3}$$ of the amount of time that it takes the small pump to fill the empty tank. How many hours does it take the large pump, working alone, to fill the empty tank?

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