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OG20 OG2022	If a and b are integers, is $$a^{5}$$ < $$4^{b}$$ ? 1.$$a^{3}= –27$$ 2.$$b^{2} = 16$$
OG20 OG2022	If each side of parallelogram P has length 1, what is the area of P ? 1.One angle of P measures 45 degrees. 2.The altitude of P is $$\frac{\sqrt{2}}{2}$$
OG20 OG2022	If x is an integer greater than 0, what is the remainder when x is divided by 4 ? 1.The remainder is 3 when x + 1 is divided by 4. 2.The remainder is 0 when 2x is divided by 4.
OG20 OG2022	A certain painting job requires a mixture of yellow, green, and white paint. If 12 quarts of paint are needed for the job, how many quarts of green paint are needed? 1.The ratio of the amount of green paint to the amount of yellow and white paint combined needs to be 1 to 3. 2.The ratio of the amount of yellow paint to the amount of green paint needs to be 3 to 2.
OG20 OG2022	Is the average (arithmetic mean) of the numbers x, y, and z greater than z ? 1.z – x < y – z 2.x < z < y
OG20 OG2022	Is the point Q on the circle with center C ? 1.R is a point on the circle and the distance from Q to R is equal to the distance from Q to C. 2.S is a point on the circle and the distance from Q to S is equal to the distance from S to C.
OG20 OG2022	In the figure above, if A, B, and C are the areas, respectively, of the three nonoverlapping regions formed by the intersection of two circles of equal area, what is the value of B + C ? 1.$$A + 2B + C = 24$$ 2.$$A + C = 18$$ and $$B = 3$$
OG20 OG2022	A company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green. If, for each size, there are equal numbers of red and green toys in a certain production lot, what fraction of the total number of green toys is large? 1.In the production lot, 400 of the small toys are green. 2.In the production lot, $$\frac{2}{3}$$ of the toys produced are small.
OG20 OG2022	Is quadrilateral PQRS a parallelogram? 1.Adjacent sides PQ and QR have the same length. 2.Adjacent sides RS and SP have the same length.
OG20 OG2022	In the figure above, the vertices of ∆OPQ and ∆QRS have coordinates as indicated. Do ∆OPQ and ∆QRS have equal areas? 1.b = 2a 2.d = 2c
OG20 OG2022	After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence? 1.The sum of the first 3 terms in the sequence is 6. 2.The fourth term in the sequence is 6.
OG20 OG2022	Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith. How many years has Green worked at Firm X ? 1.Jones has worked at Firm X 9 years longer than Smith. 2.Green has worked at Firm X 5 years less than Jones.
OG20 OG2022	In ∆JKL shown above, what is the length of segment JL ? 1. $$JK = 10$$ 2. $$KL = 5$$
OG20 OG2022	br/] A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic? 1.Each side of each triangular piece of tile is 9 centimeters long. The mosaic can be put inside a rectangular frame that is 40 centimeters wide.
OG20 OG2022	If, in the figure above, ABCD is a rectangular region, what is the value of the ratio $$\frac{area of Δ EDA}{area of Δ EBC}$$ ? 1.AD = 4 2.AE = 2 and EB = 4
OG20 OG2022	A noncompressible ball in the shape of a sphere is to be passed through a square opening in a board. What is the perimeter of the opening? 1.The radius of the ball is equal to 2 inches. 2.The square opening is the smallest square opening through which the ball will fit.
OG20 OG2022	In the figure above, what is the area of region PQRST ? 1.PQ = RS 2.PT = QT
OG20 OG2022	The figure above represents a box that has the shape of a cube. What is the volume of the box? 1.PR = 10 cm 2.$$QT = 5 \sqrt{6}cm$$
OG20 OG2022	If x and y are the lengths of the legs of a right triangle, what is the value of xy ? 1.The hypotenuse of the triangle is $$10\sqrt{2}$$ 2.The area of the triangular region is 50.
OG20 OG2022	In the figure above, PQRT is a rectangle. What is the length of segment PQ ? 1.The area of region PQRS is 39 and TS = 6. 2.The area of region PQRT is 30 and QR = 10.