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OG17 OG18 OG19 OG20 OG2022	If the positive integer n is added to each of the integers 69,94, and 121, what is the value of n?(1) 69 + n and 94 + n are the squares of two consecutive integers.(2) 94 + n and 121 + n are the squares of two consecutive integers.
OG12 OG15 OG16 OG17 OG18	Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on January 1, 1989, when both his gross income and his deductions increased?(1)Guy`s gross income increased by 4 percent on January 1, 1989.(2)Guy`s deductions increased by 15 percent on January 1, 1989.
OG12 OG15 OG16 OG17 OG18	If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P ?(1)There are 10,000 more students in School District M than there are in School District P.(2)The ratio of the number of teachers to the number of students in School District M is 1 to 20.
OG18 OG19 OG20 OG2022	For a certain city's library, the average cost of purchasing each new book is $28. The library receives $15,000 from the city each year; the library also receives a bonus of $2,000 if the total number of items checked out over the course of the year exceeds 5,000. Did the library receive the bonus last year?(1) The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost. (2) The lowest number of items checked out in one month was 459.
OG15 OG16 OG17 OG18 OG19	Each gift certificate sold yesterday by a certain bookstore cost either $10 or $50. If yesterday the bookstore sold more than 5 gift certificates that cost $50 each, what was the total number of gift certificates sold yesterday by the bookstore?(1) Yesterday the bookstore sold fewer than 10 gift certificates that cost $10 each.(2) The total cost of gift certificates sold yesterday by the bookstore was $460.
OG12 OG15 OG16 OG17 OG18	What is the tens digit of positive integer x ?(1)x divided by 100 has a remainder of 30.(2)x divided by 110 has a remainder of 30.
OG17 OG18 OG19 OG20 OG2022	Three dice, each of which has its 6 sides numbered 1 though 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?(1) None of the 3 numbers that are facing up is divisible by 3.(2) Of the numbers that are facing up, 2, but not all 3. are equal.
OG17 OG18 OG19 OG20 OG2022	On the number line, point R has coordinate r and point T has coordinate t. Is $$t<0$$?(1) $$-1<{r}<0$$(2) The distance between R and T is equal to $${r}^{2}$$.
OG16 OG17 OG18 OG19 OG20 OG2022	S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?(1) The number of distinct points in S is 5.(2) No three of the points in S are collinear.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Stores L and M each sell a certain product at a different regular price. If both stores discount their regular price of the product, is the discount price at Store M less than the discount price at Store L ?(1)At Store L the discount price is 10 percent less than the regular price; at Store M the discount price is 15 percent less than the regular price.(2)At Store L the discount price is $5 less than the regular store price; at Store M the discount price is $6 less than the regular price.
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If d denotes a decimal, is $$d \ge 0.5$$?(1)When d is rounded to the nearest tenth, the result is 0.5.(2)When d is rounded to the nearest integer, the result is 1.
OG18 OG19 OG20 OG2022	In the two-digit integers $$3■$$ and $$ 2▲$$, the symbols $$■$$ and $$▲$$ represent different digits, and the product ( $$3■$$) ($$2▲$$) is equal to 864. What digit does $$■$$ represent? (1) The sum of $$■$$ and $$▲$$ is 10. (2) The product of $$■$$ of $$▲$$ is 24.
OG16 OG17 OG18 OG19 OG20 OG2022	Two points, N and Q (not shown), lie to the right of point M on line ℓ. What is the ratio of the length of QN to the length of MQ?(1) Twice the length of MN is 3 times the length of MQ.(2) Point Q is between points M and N.
OG16 OG17 OG18 OG19 OG20 OG2022	Did the sum of the prices of three shirts exceed $60?(1) The price of the most expensive of the shirts exceeded $30.(2) The price of the least expensive of the shirts exceeded $20.
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	What is the total number of coins that Bert and Claire have?(1) Bert has 50 percent more coins than Claire.(2) The total number of coins that Bert and Claire have is between 21 and 28.
OG16 OG17 OG18 OG19 OG20 OG2022	A telephone station has x processors, each of which can process a maximum of y calls at any particular time, where x and y are positive integers. If 500 calls are sent to the station at a particular time, can the station process all of the calls?(1) x = 600(2) 100 < y < 200
OG18 OG19 OG20 OG2022	Kim and Sue each bought some roses and some daisies at the prices shown above. If Kim bought the same total number of roses and daisies as Sue, was the price of Kim's purchase of roses and daisies higher than the price of Sue's purchase of roses and daisies?(1) Kim bought twice as many daisies as roses.(2) Kim bought 4 more roses than Sue bought.
OG18 OG19 OG20 OG2022	Jazz and blues recordings accounted for 6 percent of the $840 million revenue from the sales of recordings in Country Y in 2000. What was the revenue from the sales of jazz and blues recordings in Country Y in 1998?(1) Jazz and blues recordings accounted for 5 percent of the revenue from the sales of recordings in Country Y in 1998.(2) The revenue from the sales of jazz and blues recordings in Country Y increased by 40 percent from 1998 to 2000.
OG16 OG17 OG18 OG19 OG20 OG2022	On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?(1) 2x + 3y = 280(2) y = x + 10
OG17 OG18 OG19 OG20 OG2022	If x is a positive integer, what is the value of $$\sqrt{x+24}$$ - $$\sqrt{x}$$ ?(1) $$\sqrt{x}$$ is an integer.(2) $$\sqrt{x+24}$$ is an integer.