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OG19-定量推理
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Half of a large pizza is cut into 4 equal-sized pieces, and
the other half is cut into 6 equal-sized pieces. If a person
were to eat 1 of the larger pieces and 2 of the smaller
pieces, what fraction of the pizza would remain $$\underline{uneaten}$$?
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OG19-定量推理
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David used part of $100,000 to purchase a house. Of the remaining portion, he invested $$\frac{1}{3}$$ of it at 4 percent simple annual interest and $$\frac{2}{3}$$ of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?
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OG19-定量推理
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For every even positive integer m, f(m) represents the product of all even integers from 2 tom, inclusive. For example, $$f(12) = 2 \times 4 \times 6 \times 8 \times 10 \times 12$$. What is the greatest prime factor of f(24) ?
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OG12 OG15 OG16 OG17 OG18
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A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?(1)The average (arithmetic mean) number of eggs for the 10 nests was 4.(2)Each of the 10 nests contained the same number of eggs.
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OG15 OG16 OG17 OG18
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In Mr, Smith's class, what is the ratio of the number of boys to the number of girls?(1) There are 3 times as many girls as boys in Mr. Smith's class.(2) The number of boys is 1/4 of the total number of boys and girls in Mr. Smith's class
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OG12 OG15 OG16 OG17 OG18
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A taxi company charges f cents for the first mile of the taxi ride and m cents for each additional mile. How much does the company charge for a 10-mile taxi ride?(1)The company charges $0.90 for a 2-mile ride.(2)The company charges $1.20 for a 4-mile ride.
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OG12 OG15 OG16 OG17
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It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
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OG12
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A total of n trucks and cars are parked in a lot. If the number of cars is $$\frac1 4$$ the number of trucks,and $$\frac2 3$$ of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?
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OG12 OG15 OG16 OG17
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A clothing store acquired an item at a cost of x dollars and sold the item for y dollars. The store`s gross profit from the item was what percent of its cost for the item?(1)$$y - x = 20$$(2)$$\frac y x=\frac5 4$$
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OG12 OG15 OG16 OG17 OG18
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The profit from the sale of a certain appliance increases, though not proportionally, with the number of units sold. Did the profit exceed $4 million on sales of 380,000 units?(1)The profit exceeded $2 million on sales of 200,000 units.(2)The profit exceeded $5 million on sales of 350,000 units.
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OG12 OG15
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Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio $$\frac r s $$ is expressed as a decimal, is $$\frac r s$$ a terminating decimal?(1)$$90 < r < 100$$(2)$$s = 4$$
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OG12 OG15 OG16 OG17 OG18
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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.
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OG12 OG15 OG16
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Every member of a certain club volunteers to contribute equally to the purchase of a $60 gift certificate. How many members does the club have?(1)Each member's contribution is to be $4.(2)If 5 club members fail to contribute, the share of each contributing member will increase by $2.
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OG12
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If k, m, and t are positive integers and $$\frac k 6+\frac m 4=\frac t {12}$$, do t and 12 have a common factor greater than 1 ?(1)k is a multiple of 3.(2)m is a multiple of 3.
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OG17
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Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?
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OG15
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In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was $$\frac{3}{5}$$.After 600 additional Republicans and 500 additional Democrats registered, the ratio was $$\frac{4}{5}$$.After these registrations, there were how many more voters in the district registered as Democrats than as Republicans?
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OG12 OG15 OG16
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Of the final grades received by the students in acertain math course, $$\frac{1}{5}$$ are A's, $$\frac{1}{4}$$ are B's,$$\frac{1}{2}$$ are C's,and the remaining 10 grades are D's. What is the number of students in the course?
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OG12 OG15 OG16 OG17 OG18
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The average distance between the Sun and a certain planet is approximately 2.3 x $${10}^{14}$$ inches. Which of the following is closest to the average distance between the Sun and the planet, in kilometers? (1 kilometer is approximately 3.9 x $${10}^{4}$$ inches.)
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OG18
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The symbol $$\Delta$$denotes one of the four arithmetic operations: addition, subtraction, multiplication, or division. If 6$$\Delta3\le3$$, which of the following must be true? I. 2$$\Delta$$2=0II.2$$\Delta$$2=1III. 4$$\Delta$$2=2
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OG18 OG19 OG20 OG2022
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Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?
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