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In a certain sequence, each term after the first is equal to the preceding term multiplied by -$$\frac{1}{2}$$. If the 200th term is positive, which of the following statements must be true?

Indicate all such statements.
During a certain month, 20 percent of all the electricity used by a household was used by the water heater. The cost per kilowatt-hour of the electricity used by the water heater was half the cost per kilowatt-hour of the rest of the electricity used. For that month, the cost of the electricity used by the water heater was what fraction of the cost of the electricity used by the household?
Let x and y be positive integers such that when y is divided by x, the remainder is 4, and when y+10 is divided by x, the remainder is 2. Which of the following must be an integer?
The average (arithmetic mean) of the values of the homes in Town A is $100,000. The average of the values of the homes in Town B is $150,000. The number of homes in Town A is between 2 times and 3 times the number of homes in Town B. Which of the following values could be the average of the values of the homes in Town A and Town B combined?

Indicate all such values.
How many x-intercepts, and y-intercepts does the graph of the equation 4$$x^{2}$$-9$$y^{2}$$=1 have?
A hexagon with sides of equal length and interior angles of equal measure is inscribed in a circle. If the perimeter of the hexagon is 12, what is the perimeter of an equilateral triangle inscribed in the same circle?
From 1989 to 1992, there was a 10 percent increase in the percent of families that owned directly held stocks. Which of the following is closest to the percent of families who owned directly held stocks in 1989?
If 38.7 percent of the families who owned a home owed money on a home mortgage loan or home equity loan, or both, approximately what percent of United States families owned homes free of both home mortgage and home equity loans?
In 1992, if 7.9 percent of the families in the survey owned both savings bonds and mutual funds, what percent owned neither savings bonds nor mutual funds?
The top surface of a certain 1-inch-thick oak board is 8 inches wide and has an area of 960 square inches. What is the price of this board? (1 foot=12 inches)
For the 6-inch-wide boards listed, which of the following is closest to the ratio of the price per linear foot of the least expensive type of board to the price per linear foot of the most expensive type of board?
The price of one maple board that is 8 inches wide and n feet long is $1.50 less than the price of 2 maple boards that are each 4 inches wide and n feet long. What is the value of n?
An urn contains 4 red balls, 8 green balls and 2 yellow balls. Five balls are randomly selected WITH replacement from the urn. What is the probability that 1 red ball, 2 green balls, and 2 yellow balls will be selected?

Give your answer as a fraction.


The table above consists of 10 rows and 10 columns. Each entry in the table is either a zero or a one. A zero is to be selected at random from the table. What is the probability that the zero selected will be in a row with an odd number of zeros and in a column with an odd number of zeros?

Give your answer as a fraction.
The reciprocal of x-2 is x+3. What is the product of all the possible values of x?
$$x < x^{3} < x^{2}$$

Quantity A

$$x^{5}$$

Quantity B

$$x^{7}$$


In triangle ABC, the length of side AB is 13, the length of side AC is 15, and the length of side BC is 14. What is the length of the height that corresponds to the base BC?
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?
In 1990 in neighborhood V, $$\frac{1}{3}$$ of the foreign-born population whose region of origin was Asia came from China. Approximately what fraction of the entire foreign-born population in neighborhood V came from China?
A list of the names of the people of the entire 1990 foreign-born population in neighborhood V was generated, with each person's name appearing once.The names of 2 different people will be randomly selected from the list. Which of the following is closest to the probability that both names selected will be names of people whose region of origin was "Other"?

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