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OG18-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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OG18-定量推理
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For every even positive intger m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12) = 2 x 4 x 6 x 8 x 10 x 12. What is the greatest prime factorof f(24)?
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OG18-定量推理
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A triangle has side lengths of a, b, and c centimeters. Does each angle in the triangle measure less than 90 degrees?(1) The 3 semicircles whose diameters are the sides of the triangle have areas that are equal to 3 $$cm^{2}$$, 4$$cm^{2}$$, and 6 $$cm^{2}$$, respectively.(2) c < a + b < c + 2
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OG18-定量推理
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Is the perimeter of square S greater than the perimeter of equilateral triangle T?(1) The ratio of the length of a side of S to the length of a side of T is 4:5.(2) The sum of the lengths of a side of S and a side of T is 18.
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OG18-定量推理
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In the equation $$x^{2} + bx + 12 = 0$$, x is a variable and b is a constant. What is the value of b?(1) x - 3 is a factor of $$x^{2} + bx +12.$$(2) 4 is a root of the equation $$x^{2} + bx + 12 = 0$$.
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OG18-定量推理
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The toll T, in dollars, for a truck using a certain bridge is given by the formula T = 1.50 + 0.50(x – 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles?
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OG18-定量推理
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When 24 is divided by the positive integer n, the remainder is 4. Which of the following statements about n must be true?I. n is even.II. n is a multiple of 5.III. n is a factor of 20.
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OG18-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 uneaten?
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OG18-定量推理
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A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold.(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold.
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OG18-定量推理
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A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, which of the following could be the width, in inches, of the wooden strip?I. 1II. 3III. 4
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排列组合
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A company has assigned a distinct 3-digit code number to each of its 330 employees. Each code number was formed from the digits 2, 3, 4, 5, 6, 7, 8, 9 and no digit appears more than once in any one code number. How many unassigned code numbers are there?
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排列组合
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An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
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In the sequence of nonzero numbers $${t}_{1}$$, $${t}_{2}$$, $${t}_{3}$$, ..., $${t}_{n}$$, ..., $${t}_{n+1}=\frac{{t}_{n}}{2}$$ for all positive integers n. What is the value of $${t}_{5}$$?(1) $${t}_{3}=\frac{1}{4}$$(2) $${t}_{1}-{t}_{5}=\frac{15}{16}$$
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应用题
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John deposited $10,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in John's account 6 months after the account was opened?
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OG19-定量推理
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In the equation $$x^{2} +bx+ 12 = 0$$, xis a variable and b is a constant. What is the value of b ?
(1) $$x - 3$$ is a factor of $$x^{2} + bx+ 12$$.
(2) 4 is a root of the equation $$x^{2} +bx+ 12 = 0$$.
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OG19-定量推理
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Is the perimeter of square S greater than the perimeter of equilateral triangle T?
(1) The ratio of the length of a side of S to the length of a side of T is 4:5.
(2) The sum of the lengths of a side of S and a side of T is 18.
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OG19-定量推理
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A triangle has side lengths of a, b, and c centimeters. Does each angle in the triangle measure less than 90 degrees?
( 1) The 3 semicircles whose diameters are the sides of the triangle have areas that are equal to 3 $$cm^{2}$$, 4 $$cm^{2}$$, and 6 $$cm^{2}$$, respectively.
(2) c< a + b < c+ 2
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OG19-定量推理
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When 24 is divided by the positive integer n, the
remainder is 4. Which of the following statements
about n must be true?
I. n is even.
II. n is a multiple of 5.
Ill. n is a factor of 20.
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OG19-定量推理
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The toll T, in dollars, for a truck using a certain bridge is given by the formula $$ T = 1.50 + 0.50(x - 2)$$ , where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles?
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OG19-定量推理
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A certain toll station on a highway has 7 tollbooths,
and each tollbooth collects $0. 75 from each vehicle
that passes it. From 6 o'clock yesterday morning
to 12 o'clock midnight, vehicles passed each of the
tollbooths at the average rate of 4 vehicles per minute.
Approximately how much money did the toll station
collect during that time period?
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