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OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If [x] denotes the least integer greater than or equal to x, is [x] = 0 ?(1) -1 < x< 1(2) x < 0
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If x and y are integers, is x > y?(1) x+y >0(2) $${y}^{x}$$ < 0
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If r and s are the roots of the equation $${x}^{2}+{b}{x}+{c}={0}$$, where b and c are constants, is rs < 0 ?(1) b < 0(2) c < 0
OG16 OG17 OG18 OG19 OG20 OG20 OG2022	The figure above represents an L-shaped garden. What is the value of k?(1) The area of the garden is 189 square feet.(2) The perimeter of the garden is 60 feet
OG17 OG18 OG19 OG20 OG2022	The only articles of clothing in a certain closet are shirts, dresses, and jacket. The ratio of the number of shirts to the number of dresses to jackets in the closet is 9:4:5, respectively. If there are more than 7 dresses in the closet, what is the total number of articles of clothing in the closet?(1) The total number of shirts and jackets inthe closet is less than 30.(2) The total number of shirts and dresses in the closet is 26.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	The figure above represents a circle graph of Company H's total expenses broken down by the expenses for each of its five divisions. If O is the center of the circle and if Company H's total expenses are $5,400,000, what are the expenses for Division R ?(1)x = 94(2)The total expenses for Divisions S and T are twice as much as the expenses for Division R.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If x is negative, is $$x < -3$$?(1)$${x}^{2} >{9}$$(2)$${x}^{3}<-{9}$$
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	What is the number of cans that can be packed in a certain carton?(1) The interior volume of this carton is 2,304 cubic inches.(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each row and exactly once in each column. What is the value of r?(1)v + z = 6(2)s + t + u + x = 6
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Material A costs $3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x > y?(1)y > 4(2)The cost of the 10 kilograms of material K is less than $40.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	At what speed was a train traveling on a trip when it had completed half of the total distance of the trip?(1)The trip was 460 miles long and took 4 hours to complete.(2)The train traveled at an average rate of 115 miles per hour on the trip.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?(1)The price of Tom's house was $110,000.(2)The price of Jane's house was $120,000.
OG18 OG19 OG20 OG2022	What is the value of x if $$x^{3} < x^{2}$$? (1) -2 < x < 2 (2) x is an integer greater than -2.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ?(1)w = max(20, z) for some integer z.(2)w = max(10, w)
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	A certain bookcase has 2 shelves of books. On the upper shelf, the book with the greatest number of pages has 400 pages. On the lower shelf, the book with the least number of pages has 475 pages. What is the median number of pages for all of the books on the 2 shelves?(1)There are 25 books on the upper shelf.(2)There are 24 books on the lower shelf.
OG12 OG15 OG16 OG17 OG18 OG19 OG20	In the figure, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?(1)AB = 3 and BC =2(2)CD =1 and DE = 4
OG16 OG17 OG18 OG19 OG20 OG2022	In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hour of the actual time that the trip took?(1) Joan`s estimate for the distance was within 5 miles of the actual distance.(2) Joan`s estimate for her average speed was within 10 miles per hour of her actual average speed.
OG16 OG17 OG18 OG19 OG20 OG2022	A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?(1)The range of the 3 numbers is equal to twice the difference between the greatest number and the median.(2)The sum of the 3 numbers is equal to 3 times one of the numbers.
OG18 OG19 OG20 OG2022	Line $$\ell$$ lies in the xy-plane and does not pass through the origin. What is the slope of line $$\ell$$ ? (1) The x - intercept of line $$\ell$$ is twice the y-intercept of line $$\ell$$. (2) The x-and y-intercepts of line $$\ell$$ are both positive.
OG16 OG17 OG18 OG19 OG20 OG2022	y = ax - 5y = x + 6y = 3x + bIn the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?(1) a = 2(2) r = 17