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OG12 OG15 OG16 OG17	In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangular region RCS ?(1)The area of triangular region ABX is 32.(2)The length of one of the altitudes of triangle ABC is 8.
OG12 OG15 OG16 OG17	A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?(1)The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.(2)The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
OG12 OG15 OG16 OG17	On a company-sponsored cruise, $$\frac2 3$$ of the passengers were company employees and the remaining passengers were their guests. If $$\frac3 4$$ of the company-employee passengers were managers, what was the number of company-employee passengers who were NOT managers?(1)There were 690 passengers on the cruise.(2)There were 230 passengers who were guests of the company employees.
OG12 OG15 OG16 OG17	The length of the edging that surrounds circular garden K is $$\frac12$$ the length of the edging that surrounds circular garden G. What is the area of garden K ? (Assume that the edging has negligible width.)(1)The area of G is 25π square meters.(2)The edging around G is l0π meters long.
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.
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
OG16 OG17 OG18 OG19 OG20 OG2022	In the figure above, PQR and STU are identical equilateral triangles, and PQ = 6. What is the perimeter of polygon PQWTUVR?(1) Triangle SWV has perimeter 9.(2) VW has length 3.5.
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	The range of the numbers in set S is x, and the range of the numbers in set Tis y. If all of the numbers in set Tare also in set S, is x greater than y ?(1) Set S consists of 7 numbers(2) Set T consists of 6 numbers
OG12 OG15 OG16 OG17	The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?(1)$$x > y$$(2)$$\frac{xy} {100}<{x}-{y}$$
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle?(1)The area of the triangle is 25 square centimeters.(2)The 2 legs of the triangle are of equal length.
OG12 OG16 OG17 OG15	In the xy-plane,region R consists of all the points (x, y) such that 2x + 3y ≤ 6. Is the point (r, s)in region R ?(1)3r +2s =6(2)r ≤ 3 and s ≤ 2
OG12 OG15 OG16 OG17	What is the volume of a certain rectangular solid?(1)Two adjacent faces of the solid have areas 15 and 24, respectively.(2)Each of two opposite faces of the solid has area 40.
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5 or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments, was S3 shipped on the first truck?(1) S2 and S4 were shipped on the first truck.(2) S1 and S6 were shipped on the second truck
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	lf x, y, and z are three-digit positive integers and if x = y+ z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?(1) The tens digit of x is equal to the sum of the tens digits of y and z.(2) The units digit of x is equal to the sum of the units digits of y and z.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	The table above shows the results of a survey of 100 voters who each responded "Favorable" or "Unfavorable" or "Not Sure" when asked about their impressions of Candidate M and of Candidate N. What was the number of voters who responded "Favorable" for both candidates?(1)The number of voters who did not respond "Favorable" for either candidate was 40.(2)The number of voters who responded "Unfavorable" for both candidates was 10.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?(1)It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.(2)It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.