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OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If x and y are integers, what is the value of x + y ?(1) $$3<{\frac{x+y}{2}}<4$$(2) $$2<{x}<{y}<5$$
OG12 OG15 OG16 OG17	Is the number of seconds required to travel $${d}_{1}$$ feet at $${r}_{1}$$ feet per second greater than the number of seconds required to travel $${d}_{2}$$ feet at $${r}_{2}$$ feet per second?(1)$${d}_{1}$$ is 30 greater than $${d}_{2}$$.(2)$${r}_{1}$$ is 30 greater than $${r}_{2}$$.
OG12 OG15 OG17 OG16 OG18 OG19 OG20 OG2022	Last year, if Arturo spent a total of $12,000 on his mortgage payments, real estate taxes, and home insurance, how much did he spend on his real estate taxes?(1)Last year, the total amount that Arturo spent on his real estate taxes and home insurance was $$33\frac{1}{3}$$ percent of the amount that he spent on his mortgage payments.(2)Last year, the amount that Arturo spent on his real estate taxes was 20 percent of the total amount he spent on his mortgage payments and home insurance.
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If a, b, c, and d are positive numbers, is $$\frac a b < \frac c d$$ ?(1) $$0<\frac{(c-a)}{(d-b)}$$(2)$$(\frac{ad}{bc})^{2}<{\frac{ad}{bc}}$$
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Is the number of members of Club X greater than the number of members of Club Y ?(1)Of the members of Club X, 20 percent are also members of Club Y.(2)Of the members of Club Y, 30 percent are also members of Club X.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	On the number line above, p, q, r, s, and t are five consecutive even integers in increasing order. What is the average (arithmetic mean) of these five integers?(1)q + s = 24(2)The average (arithmetic mean) of q and r is 11.
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
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.
OG16 OG17	For any positive integer x, the 2-height of x is defined to be the greatest nonnegative integer n such that $${2}^{n}$$ is a factor of x. If k and m are positive integers, is the 2-height of k greater than the 2-height of m ? (1) $$k>{m}$$ (2)$$\frac{K}{M}$$ is an even integer.
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.
OG15 OG16 OG17	4, 6, 8, 10, 12, 14, 16, 18, 20, 22List M (not shown) consists of 8 different integers each of which is in the list shown. What is the standard deviation of the numbers in list M ?(1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown.(2) List M does not contain 22.
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.
OG12 OG15 OG16 OG17	If x and y are integers, is xy even?(1)$$x = y+1$$(2)$$\frac{x}{y}$$ is an even integer.