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If x + y + z = 0, x + 2y + 3z = 0, and $$y \neq 0$$, then $$\frac{x}{y}$$ =
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Last month, a certain manufacturer sold a total of 1,000 unites of its two products, A and B. The selling price of each unit of product A was $1,500, and the selling price of each unit of product B was $2,000. How many units of product A did the manufacturer sell last month?(1) Last month, the manufacturer's total revenue from the sale of units of products A and B was $1,600,000.(2) Last month, the manufacturer's revenue from the sale of units of products A was 3 times the manufacturer's revenue from the sale of units of product B.
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If r > 0, is rs < 0 ?(1) s < 0(2) s < r
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For each positive integer n, the integer n* is defined by $$ n^* = {n}^{2}$$ + 1. What is the value of the positive integer k ?(1) When k is divided by 4, the remainder is 1.(2) $$18 \leq k^* \leq 36$$
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When the positive integer n is divided by 13, the remainder is 4. What is the remainder when 2n – 3 is divided by 13 ?
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 The figure shows two squares, and the points W, X, Y, and Z lie on a line. If the distance between W and X is equal to the distance between X and Y and to the distance between Y and Z, then the area of the smaller square is what fraction of the area of the larger square?
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A certain database charges users a registration fee of x dollars, and if charges registered users y dollars per file downloaded. If there are no other charges for users of this database, what is the amount of the registration fee?(1) The total charge to download 50 files is $150, including the registration fee.(2) The total charge to download 100 files is $225, including the registration fee.
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If k is a two-digit positive integer with tens digit x and units digit y, then $${k}^{2}$$ =
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The total number of printers and computers at a certain company is 36. How many printers does the company have?(1) The ratio of the number of the company's printers to the number of its computers is 5 to 7.(2) The company has 6 more computers than printers.
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OG16 OG17 OG18 OG19 OG20 OG2022
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In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hour of the actual time that the trip took?(1) Joan's estimate for the distance was within 5 miles of the actual distance.(2) Joan's estimate for her average speed was within 10 miles per hour of her actual average speed.
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Working at their respective constant rates, machine A makes 100 copies in 12 minutes and machine B makes 150 copies in 10 minutes. If these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce?
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The average (arithmetic mean) of a list of numbers is what percent of the sum of the numbers?(1) There are 8 numbers in the list.(2) The sum of the numbers in the list is 100.
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If x and y are positive integers, what is the value of $$({x}+{y})^{2}$$?(1) x = y - 3(2) x and y are prime numbers.
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OG16 OG17 OG18 OG19 OG20 OG2022
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Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
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All 48 seniors in a certain high school take one of two English classes. What is the average (arithmetic mean) height of the seniors in this school?(1)In the school, the average height of the seniors in the English class with the larger number of students is 70 inches.(2) In the school, the average height of the seniors in the English class with the smaller number of students is $$\frac4 5$$ of the average height of the seniors in the other English class.
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If S is the sum of all the integers from 1 to 30, inclusive, what is the greatest prime factor of S ?
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The average (arithmetic mean) cost per book for the 12 books on a certain table is k dollars. If a book that costs 18 dollars is removed from the table and replaced by a book that costs 42 dollars, then in terms of k, what will be the average cost per book, in dollars, for the books on the table?
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$${10},{000}^{100}$$ is equivalent to which of the following?I. $$({100}^{2})({100}^{100})$$II. $${100}^{200}$$III. $${10}^{400}$$
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Chris mixed 3 pounds of raisins with 4 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?
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Of the high school students who participated in a recent survey, 110 had taken a course in biology and 230 had taken a course in history. How many students participated in the survey?(1) Of the students who participated in the survey, 120 had taken neither a course in biology nor a course in history.(2) Of the students who participated in the survey, 60 had taken both a course in biology and a course in history.
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