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OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Each year for 4 years, a farmer increased the number of trees in a certain orchard by $$\frac{1}{4}$$ of the number of trees in the orchard the preceding year. If all of the trees thrived and there were 6,250 trees in the orchard at the end of the 4-year period, how many trees were in the orchard at the beginning of the 4-year period?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	According to the chart shown, which of the following is closest to the median annual number of shipments of manufactured homes in the United States for the years from 1990 to 2000,inclusive?
OG18 OG19 OG20 OG2022	For the positive integers a, b, and k, $$a^{k}$$ \|\| b means that $$a^{k}$$ is a divisor of b, but $$a^{k +1}$$ is not a divisor of b. If k is a positive integer and $$2^{k}$$ \|\| 72, then k is equal to
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
OG16 OG17 OG18 OG19 OG20 OG2022	Four extra-large sandwiches of exactly the same size were ordered for m students, where m>4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
OG17 OG18 OG19 OG20 OG2022	Which of the following equations has 1 + $$\sqrt{2}$$ as one of its roots?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	In Country C, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
OG16 OG17 OG18 OG19 OG20 OG2022	In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
OG16 OG18 OG19 OG20 OG2022	At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	A pharmaceutical company received $3 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
OG18 OG19 OG20 OG2022	The light in a restroom operates with a 15-minute timer that is reset every time the door opens as a person goes in or out of the room. Thus, after someone enters or exits the room, the light remains on for only 15 minutes unless the door opens again and resets the timer for another 15 minutes. If the times listed above are the times at which the door opened from 8:00 to 10:00, approximately how many minutes during this two-hour period was the light off?
OG16 OG17 OG18 OG19 OG20 OG2022	The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which $$3^k$$ is a factor of p?
OG18 OG19 OG20 OG2022	If $$n = 3^{8} - 2^{8}$$, which of the following is NOT a factor of n ?
OG16 OG17 OG18 OG19 OG20 OG2022	In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Club X has more than 10 but fewer than 40 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	if $$s >0$$ and $$\sqrt{\frac{r}S}=s$$,what is r in terms of s ?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If 3 < x < 100, for how many values of x is $$\frac{x}{3}$$the square of a prime number?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?