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In the xy-plane, line segment PR intersects the x-axis at point Q and is parallel to the y-axis. If the legnth of PQ is twice the length of QR, what are the corrdinates of point R, in terms of a and b?
If $$1 \leq x \leq 4$$ and $$-3 \leq y \leq 2$$, what is the least possible value of $$x^{-2} +y^{-2}$$?
In a marketing survey of 600 consumers about two brands of coffee, A and B, the consumers responded that they had tried either Brand A only, Brand B only, both brands, or neither brand. In the survey, 130 consumers responded that they had tried neither brand.

Which of the following statements individually provide(s) sufficient additional information to determine the number of consumers who, based on their response, had not tried Brand A?

Indicate all such statements.
The average (arithmetic mean) of 3 integers, x, y, and z, equals the average of 12, 14, 21, and 45.

Quantity A

x+y+z

Quantity B

69

Quantity A

$$5(2^{x})$$

Quantity B

$$4(3^{x})$$


Quantity A

4

Quantity B

k
The dollar value of a certain carving in 1983 was 20 percent greater than its dollar value in 1978. The dollar value of the carving in 1988 was 70 percent greater than its dollar value in 1978.

Quantity A

The percent increase in the dollar value of the carving from 1983 to 1988

Quantity B

50%
x and y are integers, and 2x+3y=5

Quantity A

x+y

Quantity B

0
n > 1

Quantity A

The product of ($$\sqrt{n+1}-\sqrt{n-1}$$) and ($$\sqrt{n+1}+\sqrt{n-1}$$)

Quantity B

2
List R contains 30 values, and the average (arithmetic mean) of the values in R is m. List S contains 20 values, and the average of the values in S is m+40. List T consists of the vaues in R followed by the values in S.

Quantity A

The average of the values in T

Quantity B

m+16


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.
The line with equation $$y=3x-2$$ will be translated $$4$$ units to the right and $$5$$ units up in the xy-plane. Which of the following is the equation of the resulting line?
Machines A and B each assembled 3,000 metal clips in 15 hours and 12 hours, respectively, working alone at their constant rates. On Monday, working simultaneously at their respective constant rates, the two machines assembled a total of n clips in x hours. The next day, machine A was modified so that its constant rate decreased by 25 percent. If the two machines worked simultaneously at their respective constant rates for x hours after the modification of machine A, then the total number of clips that they assembled in x hours was approximately what percent less than it was the day before?


In the figure, line AP and PC are tangent to the circle at points A and C, respectively. Point O is the center of the circle, and the length of the line segment PO is 4. If the measure of angle APC is 60 degrees, what is the length of arc ABC?
If 20 percent of the amount budgeted for vacation had instead been added to the amount budgeted for entertainment, which of the following is closest to the percent by which the amount budgeted for entertainment would have increased?
The three children in the Alden family contributed 30 percent of the amount budgeted for savings. The oldest child contributed $150 more than the youngest child, and the middle child contributed $60 more than the youngest child. What was the median of the amounts that the children contributed to savings ?
In each of the years after year X, the Alden family budgeted $200 more for savings than it budgeted for savings the previous year. What is the total amount that the Alden family budgeted for savings over the 10 years beginning with year X?
If a, b, and c are positive integers such that $$\frac{a}{c}$$=0.075 and $$\frac{b}{c}$$=0.09, what is the least possible value of c?
Line k lies in the xy-plane. The x-intercept and the y-intercept of line k are a and b, respectively, where a≠0 and b≠0.

Which of the following statements individually provide(s) sufficient additional information to conclude that the slope of line k is positive?

Indicate all such statements.

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