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$$S_1$$, $$S_2$$, $$S_3$$,....., .$$S_k$$,......

The sequence shown is defined by $$S_1$$=5, and $$S_{k+1}$$=2$$S_k$$, for each positive integer k.

Quantity A

$$S_8$$

Quantity B

$${\frac{1}{2^{13}}}S_{21}$$
Each player in a certain chess tournament is categorized as either amateur or expert, and each player is given a rating as a number of points. The average (arithmetic mean) rating of the expert players is 2,050 points, and the average rating of all the players is 1,900 points. If $$\frac{3}{5}$$ of the players are expert players, what is the average rating of the amateur players?
If $$y=(x-2)(x-1)(x+1)$$, which of the following graphs indicates all of the values of $$x$$ for which $$y$$ is positive?
On the first day of work for a certain task, $$\frac{1}{3}$$ of the work was completed. On the second day of work for the task, $$\frac{1}{4}$$ of the work that remained was completed. What fraction of all the work for the task remained to be completed after the second day?
In the xy-plane, a triangle has vertices $$(0, 3)$$, $$(b, 3)$$, and $$(0, 3b)$$, where $$b$$ is a constant. If the area of the triangle is $$18$$. which of the following is a possible value of $$b$$?


Which of the following is closest to the median length of the time periods, in months, during which trees produced pollen in the six regions?


For approximately what fraction of Year X was pollen produced by both grasses and weeds in the Southwest?


For Year X, which of the following is closest to the total length, in months, of the time period during which no pollen was produced by trees or grasses in any of the six regions?


The table shows values of the fucntion f for selected values of x. The graph of y=f(x) is a line in the xy-plane. What is the value of f(1)?

Give your answer as a fraction.


The table above shows the times, in seconds, that it took each of 5 mechanics to perform a simple task. For the 5 times shown, if the median is greater than the average (arithmetic mean), which of the following could be the value of x?

Indicate all such values.

Quantity A

$$89!-88!$$

Quantity B

$$(87!)(88)^{2}$$

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