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OG15 OG16 OG17 OG18 OG19 OG20 OG2022	A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If $${d}=\frac{1}{{2}^{3}\times{5}^{7}}$$ is expressed as a terminating decimal, how many nonzero digits will d have?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	For any positive integer n, the sum of the first n positive integers equals $$\frac{n(n+1)} 2$$. What is the sum of all the even integers between 99 and 301?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	How many prime numbers between 1 and 100 are factors of 7,150 ?
OG17 OG18 OG19 OG20 OG2022	A sequence of numbers $${a}_{1}$$, $${a}_{2}$$, $${a}_{3}$$, ... is defined as follows:$${a}_{1}$$ = 3, $${a}_{2}$$ = 5, and every term in the sequence after $${a}_{2}$$ is the product of all terms in the sequence preceding it, e.g., $${a}_{3}$$ = ($${a}_{1}$$)($${a}_{2}$$) and $${a}_{4}$$ =($${a}_{1}$$)($${a}_{2}$$)($${a}_{3}$$). If $${a}_{n}$$ = t and n > 2, what is the value of $${a}_{n+2}$$ in terms of t?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	if $${m}^{-1}=-\frac{1}{3}$$,then $${m}^{-2}$$ is equal to
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer`s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer`s initial cost for the 60 cameras?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Seven pieces of rope have an average (arithmetic mean) length of 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	What is the difference between the sixth and the fifth terms of the sequence 2,4, 7,... whose $$n^{th}$$ term is $$n + {2}^{n-1}$$?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	From the consecutive integers -10 to 10, inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers?
OG17 OG18 OG19 OG20 OG2022	The letters D, G, I, I, and T can be used to form 5-letter strings such as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by least one other letter?
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	$${\frac{0.99999999}{1.0001}}-{\frac{0.99999991}{1.0003}}=$$
OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store`s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 55 units per day, what is the value of n ?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	In the coordinate system above, which of the following is the equation of line ￡ ?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	In an electric circuit, two resistors with resistances x and y are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y ?
OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022	Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are $$\frac{1}{4}$$, $$\frac{1}{2}$$ and $$\frac{5}{8}$$ respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?