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OG20 OG2022	The 9 squares above are to be filled with x 's and o 's, with only one symbol in each square. How many of the squares will contain an x ? 1.More than $$\frac{1}{2}$$ of the number of squares will contain an o. 2.Each of the 4 corner squares will contain an x.
OG20 OG2022	Is the sum of two integers divisible by 10 ? 1.One of the integers is even. 2.One of the integers is a multiple of 5.
OG20 OG2022	Is x an integer? 1.$$x^{3} = 8$$ 2.$$x = \sqrt{4}$$
OG20 OG2022	If a building has 6,000 square meters of floor space, how many offices are in the building? 1.Exactly $$\frac{1}{4}$$ of the floor space is not used for offices. 2.There are exactly 20 executive offices and each of these occupies 3 times as much floor space as the average for all of the remaining offices.
OG20 OG2022	If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ? 1.Twice x is equal to the sum of p, r, and s. 2.The sum of p, r, and s is zero.
OG20 OG2022	If m and n are integers, what is the value of m + n ? 1.$$(x + m)(x + n) = x^{2} + 5x + mn\ and\ x ≠ 0.$$ 2.$$mn = 4$$
OG20 OG2022	In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y ? 1.s = 40 2.r = 70
OG20 OG2022	If R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S, how far is S from T ? 1.R is between S and T. 2.S is to the left of R, and T is to the right of R.
OG20 OG2022	Is n equal to zero? 1.The product of n and some nonzero number is 0. 2.The sum of n and 0 is 0.
OG20 OG2022	On a map,$$\frac{1}{2}$$ inch represents 100 miles. According to this map, how many miles is City X from City Y ? 1.City X is 3 inches from City Y on the map. 2.Cities X and Y are each 300 miles from City Z.
OG20 OG2022	What is the remainder when the positive integer n is divided by 5 ? 1.When n is divided by 3, the quotient is 4 and the remainder is 1. 2.When n is divided by 4, the remainder is 1.
OG20 OG2022	If r and s are positive numbers and θ is one of the operations, +, −, *, or ÷, which operation is θ? 1.If r = s, then r θ s = 0. 2.If r ≠ s, then r θ s ≠ s θ r.
OG20 OG2022	In any sequence of n nonzero numbers, a pair of consecutive terms with opposite signs represents a sign change. For example, the sequence –2, 3, –4, 5 has three sign changes. Does the sequence of nonzero numbers $$s_1$$, $$s_2$$, $$s_3$$, - , $$s_n$$ have an even number of sign changes? 1.$$s_k= (-1)^{k}$$ for all positive integers k from 1 to n. 2.n is odd.
OG20 OG2022	Jack picked 76 apples. Of these, he sold 4y apples to Juanita and 3t apples to Sylvia. If he kept the remaining apples, how many apples did he keep? (t and y are positive integers.) 1.y ≥ 15 and t = 2 2.y = 17
OG20 OG2022	What number is 6 more than x + y ? 1.y is 3 less than x. 2.y is twice x.
OG20 OG2022	The total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. What was the price of the 5 pounds of regular coffee? 1.If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18.45. 2.The price of the 5 pounds of regular coffee was $3.50 more than the price of the 3 pounds of decaffeinated coffee.
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.