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OG18 OG19 OG20 OG2022	The figure shown above consists of a shaded 9-sided polygon 9 unshaded isosceles triangles. For each isosceles triangle, the longest side is a side of the shaded polygon and the two sides of equal length are extensions of the two adjacent sides of the shaded polygon. What is the value of a?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	List T consists of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, £, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If $$\frac{1}{3}$$ of the decimals in T have a tenths digit that is even, which of the following is a possible value of E - S ?I.-16II.6III.10
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If $$5-\frac{6}{x}=x$$ then x has how many possible values?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ?
OG21 OG2022	In the figure above, ABCD is a parallelogram and E is the midpoint of side AD. The area of triangular region ABE is what fraction of the area of quadrilateral region BCDE?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	How many of the integers that satisfy the inequality $${\frac{(x+2)(x+3)}{x-2}}\ge{0}$$ are less than 5 ?
OG18 OG19 OG20 OG2022	Of the 150 houses in a certain development, 60 percent have air - conditioning, 50 percent have a sunporch, and 30 percent have a swimming pool. If 5 of the houses have all three of these amenities and 5 have none of them, how many of the houses have exactly two of these amenities?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	The value of $$\frac{({2}^{-14}+{2}^{-15}+{2}^{-16}+{2}^{-17})}{5}$$ is how many times the value of$${2}^{-17}$$?
OG19 OG20 OG2022	What is the number of pages of a certain journal article? (1)The size of each page is $$5\frac{1}{2}$$ inches by 8 inches. (2)The average(arit metic mean)number of words per page is 250.
OG19 OG20 OG2022	if a certain vase contains only roses and tulips, how many tulips are there in the vase? (1 )The number of roses in the vase is 4 times the number of tulips in the vase . (2)There is a total of 20 flowers in the vase.
OG21 OG2022	In the xy-coordinate plane above, what are the coordinates of point N? (1) Triangle MNP is equilateral. (2) Point M has coordinates（-4,0）.
OG19 OG20 OG2022	The cost of 10 pounds of apples and 2 pounds of grapes was $12. What was the cost per pound of apples? (1)The cost per pound of grapes was $2 (2)The cost of 2 pounds of apples was less than the cost of 1 pound of grapes.
OG19 OG20 OG2022	What was the median annual salary for the employees at Company X last year? (1)Last year there were 29 employees at Company X (2)Last year 12 employees at Company X had an annual salary of $24,000
OG19 OG20 OG2022	How many basic units of currency X are equivalent to 250 basic units of currency Y? (1)100 basic units of currency X are equivalent to 625 basic units of currency Y. (2)2,000 basic units of currency X are equivalent to 12, 500 basic units of currency Y
OG21 OG2022	In the xy-coordinate plane, what are the x-coordinates of the four vertices of square JKMN? (1) J and M are on the x-axis, and l < k and N are on the y-axis. (2) The center of the square is at the origin.
OG19 OG20 OG2022	A company bought 3 printers and 1 scanner. What was the price of the scanner? (1)The total price of the printers and the scanner was $1, 300. (2)The price of each printer was 4 times the price of the scanner.
OG17 OG18 OG19 OG20 OG2022	In the figure above, point D is on $$\overline {AC}$$. What is the degree measure of $$\angle BAC$$?(1)The measure of $$\angle BDC$$ is 60°.(2)The degree measure of $$\angle BAC$$ is less than the degree measure of $$\angle BDC$$.
OG19 OG20 OG2022	Each of the 256 solid-colored marbles in a box is either blue, green, or purple What is the ratio of the number of blue marbles to the number of purple marbles in the box? (1)The number of green marbles in the box is 4 times the number of blue marbles in the box. (2)There are 192 green marbles in the box.
OG18 OG19 OG20 OG2022	A certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients. If there are ample quantities of the blue and red paints available, is there enough of the yellow paint available to make the desired amount of the mixture? (1) Exactly 20 quarts of the mixture are needed. (2) Exactly 10 quarts of the yellow paint are available.
OG21 OG20 OG2022	There are 2 groups of students who took a history test. Was the average (arithmetic mean) score of the students in Group A higher than the average score of the students in Group B who took the test? (1) Of the students who took the test, 10 were in Group A and 12 were in Group B. (2) On the test, the highest score achieved was achieved by a Group B student and the lowest score achieved was achieved by a Group A student.