300难题-PS：第16-30题 练习册详情

1

A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?

• 14
• 16
• 21
• 22
• 27

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2

A certain manufacturer uses the function C (x) = 0.04$x^{2}$ - 8.5x + 25,000 to calculate the cost, in dollars, of producing x thousand units of its product. The table above gives values of this cost function for values of x between 0 and 50 in increments of 10. For which of the following intervals is the average rate of decrease in cost less than the average rate of decrease in cost for each of the other intervals?

• From x = 0 to x=10
• From x = 10 to x=20
• From x = 20 to x=30
• From x = 30 to x=40
• From x = 40 to x=50

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3

There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold, 9 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?

• 45,000
• 360,000
• 364,500
• 392,000
• 396,900

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4

If C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C =5(F - 32). On a day when the temperature extremes recorded at a certain weather station differed by 45 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?

• 65/9
• 13
• 25
• 45
• 81

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5

In the formula w=$\frac{P}{\sqrt[t]{v}}$, integers p and t are positive constants. If w = 2 when v = 1 and if w=1/2 when v = 64, then t =

• 1
• 2
• 3
• 4
• 16

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6

On the day of the performance of a certain play, each ticket that regularly sells for less than $10.00 is sold for half price plus $0.50, and each ticket that regularly sells for $10.00 or more is sold for half price plus $1.00. On the day of the performance, a person purchases a total of y tickets， of which x regularly sell for $9.00 each and the rest regularly sell for $12.00 each. What is the amount paid, in dollars, for the y tickets?

• 7y - 2x
• 12x - 7y
• $\frac{9x+12y}{2}$
• 7y+4x
• 7y+5x

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7

A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per hour, the truck gets only 3.5 miles per gallon. On a 500-mile trip, if the truck used a total of 120 gallons of diesel fuel and traveled part of the trip at 55 miles per hour and the rest at 60 miles per hour, how many miles did it travel at 55 miles per hour?

• 140
• 200
• 250
• 300
• 360

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8

If there is a least integer that satisfies the inequality$\frac{9}{x} \geq 2$,what is that least integer?

• 0
• 1
• 4
• 5
• There is not a least integer that satisfies the inequality.

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9

A merchant paid $300 for a shipment of x identical calculators. The merchant used two of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $ 120 more than the cost of the shipment, how many calculators were in the shipment?

• 24
• 25
• 26
• 28
• 30

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10

If N = $\frac{K}{T+ \frac{x}{y}}$ ,Where T= $\frac{K}{5}$ and X=5- T,which of the following expresses y in terms of N and T?

• $\frac{N(5-T)}{T(5-N)}$
• $\frac{N(T-5)}{T(5-N)}$
• $\frac{5-T}{T(5-N)}$
• $\frac{5N(5-T)}{T(1-5N)}$
• $\frac{N(5-T)}{5}$

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11

Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?

• 18
• $13\frac{1}{2}$
• $7\frac{1}{5}$
• $4\frac{1}{2}$
• $3\frac{2}{3}$

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12

If $k\neq 0$ and k- $\frac{3-2k^{2}}{k}$ =$\frac{x}{k}$ , then x=

• - 3 - $k^{2}$
• $k^{2}$ - 3
• 3$k^{2}$ - 3
• k - 3 - 2$k^{2}$
• k - 3 + 2$k^{2}$

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13

The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now,in terms of y ?

• y - 6
• 2y - 6
• $\frac{y}{2}$ - 6
• $\frac{3y}{2}$ - 6
• $\frac{5y}{2}$ - 6

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14

If $\frac{s}{t}$= 2, then the value of which of the following can be determined?

I $\frac{2t}{s}$

II $\frac{s-t}{t}$

Ill $\frac{t-1}{s-1}$

• I only
• Ill only
• I and II only
• II and III only
• I, II, and III

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15

If 2x+5y = 8 and 3x = 2y, what is the value of 2x + y ?

• 4
• 70/19
• 64/19
• 56/19
• 40/19

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