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OG19 OG20 OG2022	If a and b are positive integers, is $\frac{a}{b} < \frac{9}{11}$ ? (1) $\frac{ a}{b} < 0.818$ (2) $\frac{ b}{a} > 1.223$
OG18 OG19 OG20 OG2022	Every object in a box is either a sphere or a cube,and every object in the box is either red or green. How many objects are in the box? (1) There are six cubes and five green objects in the box. (2) There are two red spheres in the box.
OG18 OG19 OG20 OG2022	If x and y are positive integers, is xy even? (1) $x^{2} + y^{2} - 1$ is divisible by 4. (2) x+y is odd.
OG18 OG19 OG20 OG2022	If a and b are integers, is a+b+3 an odd integer? (1) ab is an odd integer.(2) a-b is an even integer.
OG16 OG17 OG18 OG19 OG20 OG2022	If x and y are positive integers, what is the value of $\sqrt{x}+\sqrt{y}$ ?(1) x + y = 15(2) $\sqrt{xy}= 6$
OG16 OG17 OG18 OG19 OG20 OG2022	A certain truck uses $\frac{1}{12}$ + ${k}{v}^{2}$ gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses $\frac{5}{12}$ gallon of fuel per mile?(1) The value of k is $\frac{1}{10800}$ (2) When the truck travels at 30 miles per hour, it uses $\frac{1}{6}$ gallon of fuel per mile.
OG19 OG20 OG2022	On June 1, Mary paid Omar $360 for rent and utilities for the month of June. Mary moved out early, and Omar refunded the money she paid for utilities, but not for rent, for the days in June after she moved out. How many dollars did Omar refund to Mary? (1)Mary moved out on June 24 (2)The amount Mary paid for utilities was less than 1/5 the amount Mary paid for rent
OG16 OG17 OG18 OG19 OG20 OG2022	If x = 2t and ${y}=\frac{t}{3}$ , what is the value of ${x}^{2}-{y}^{2}$ ?(1) ${t}^{2}$ − 3 = 6(2) ${t}^{3}$ = −27
OG19 OG20 OG2022	The 10 students in a history class recently took an examination. What was the maximum score on the examination? (1)The mean of the scores was 75, (2)The standard deviation of the scores was 5.
OG18 OG19 OG20 OG2022	Last school year, each of the 200 students at a certain high school attended the school for the entire year. If there were 8 cultural performances at the school during the last school year, what was the average (arithmetic mean) number of students attending each cultural performance? (1) Last school year, each students attended at least one cultural performance.(2) Last school year, the average number of cultural performances attended per student was 4.
OG17 OG18 OG19 OG20 OG2022	A clothing manufacturer makes jackets that are wool or cotton or a combination of wool and cotton. The manufacturer has 3,000 pounds of wool and 2,000 pounds of cotton on hand. Is this enough wool and cotton to make at least 1,000 jackets?(1) Each wool jacket requires 4 pounds of wool, and no cotton.(2) Each cotton jacket requires 6 pounds of cotton, and no wool.
OG19 OG20 OG2022	If n is an integer, what is the greatest common divisor of 12 and n? (1)The product of 12 and n is 432 (2)The greatest common divisor of 24 and n is 12
OG18 OG19 OG20 OG2022	Each month, Jim receives a base salary plus a 10 percent commission on the price of each car he sells that month. If Jim sold 15 cars last month, what was the total amount of base salary and commissions that Jim received that month?(1) Last month, Jim's base salary was $3,000.(2) Last month, Jim sold 3 cars whose prices totaled $60,000 and 5 cars whose prices totaled $120,000.
OG17 OG18 OG19 OG20 OG2022	If x is a positive integer greater than 1, what is the value of x ?(1) 2x is a common factor of 18 and 24.(2) x is a factor of 6.
OG16 OG17 OG18 OG19 OG20 OG2022	By what percent was the price of a certain television set discounted for a sale?(1) The price of the television set before it was discounted for the sale was 25 percent greater than the discounted price.(2) The price of the television set was discounted by $60 for the sale.
OG18 OG19 OG20 OG2022	Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than $\frac{π}{100}$ square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains?(1) Jack's rug covers an area of 9π square feet.(2) The centers of the stains are less than 4 feet apart.
OG18 OG19 OG20 OG2022	In the multiplication table above, each letter represents an integer. What is the value of c?(1) c=f(2) $h\neq0$
OG16 OG17 OG18 OG19 OG20 OG2022	If n is an integer, is $({0.1})^{n}$ greater than $({10})^{n}$ ?(1) n > −10(2) n < 10
OG17 OG18 OG19 OG20 OG2022	For a basic monthly fee of F yen ($F), Naoko's first cell phone plan allowed him to use a maximum of 420 minutes on calls during the month. Then, for each of x additional minutes he used on calls, he was charged $M, making his total charge for the month $T, where T = F + xM. What is the value of F?(1) Naoko used 450 minutes on calls the first month an the total charge for the month was $13,755.(2) Naoko used 400 minutes on calls the second month and the total charge for the month was $13,125.
OG19 OG20 OG2022	Is the sum of the prices of the 3 books that Shana bought less than $48? (1)The price of the most expensive of the 3 books that Shana bought is less than $17. (2)The price of the least expensive of the 3 books that Shana bought is exactly $3 less than the price of the second most expensive book.