PS-Manhattan：第101-120题 练习册详情

1

Lindsay can paint $$\frac{1}{x}$$ of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in one hour, what fraction of the room can Joseph paint in 20 minutes?

• $$\frac{1}{3x}$$
• $$\frac{x}{x-3}$$
• $$\frac{x-1}{3x}$$
• $$\frac{x}{x-1}$$
• $$\frac{x-1}{x}$$

126人做过此题 平均耗时为2min5s 平均正确率为 68%

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2

If x + y = 3, and $$x^{2} – y^{2} = 12$$, what is the value of x – y?

• -1
• 0
• 2
• 4
• 5

118人做过此题 平均耗时为54s 平均正确率为 40%

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3

In the rectangular coordinate plane points X and Z lie on the same line through the origin and points W and Y lie on the same line through the origin. If$$ a^{2} + b^{2} = c^{2} + d^{2} and e^{2} + f^{2} = g^{2} + h^{2}$$, what is the value of length XZ – length WY?

• -2
• -1
• 0
• 1
• 2

58人做过此题 平均耗时为1min33s 平均正确率为 91%

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4

Which of the following is greater than $$\frac{3}{4} $$?

• $$(\frac{3}{4})^{2}$$
• $$(\frac{7}{9})^{2}$$
• $$\frac{31}{42}$$
• $$\frac{16}{21}$$
• $$\sqrt{\frac{1}{2}}$$

120人做过此题 平均耗时为1min50s 平均正确率为 43%

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5

$$10 ^{5} – 560 $$ is divisible by all of the following EXCEPT:

• 11
• 8
• 5
• 4
• 3

119人做过此题 平均耗时为1min40s 平均正确率为 96%

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6

Ben is driving on the highway at x miles per hour. (One mile equals 5,280 feet.) Ben's tires have a circumference of y feet. Which of the following expressions gives the number of revolutions each wheel turns in one hour?

• 5,280$$(\frac{x}{y})$$
• 5,280$$(\frac{y}{x})$$
• 5289(xy)
• $$5280\over({xy})$$
• $$(xy)\over({5280})$$

55人做过此题 平均耗时为1min20s 平均正确率为 80%

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7

How many units long is the straight line segment that connects the points (-1,1) and (2,6) on a rectangular coordinate plane?

• 4
• $$\sqrt{26}$$
• $$\sqrt{34}$$
• 7
• $$\sqrt{58}$$

54人做过此题 平均耗时为53s 平均正确率为 94%

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8

If the side length of Square B is twice that of Square A, the area of Square B is how many times the area of Square A?

• $$\frac{1}{2}$$
• 1
• 2
• 3
• 4

0人做过此题 平均耗时为0 平均正确率为 0%

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9

Which of the following is the second greatest?

• $$0.08$$
• $$8*10^{-3}$$
• $$\frac{0.8}{1000}$$
• $$8÷10$$
• $$88÷10^{2}$$

54人做过此题 平均耗时为50s 平均正确率为 78%

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10

Given the circle to the right, with center O, diameter AOB, a radius of 5, and the inscribed triangle ABC, what is the length of AC?

• 4.5
• 5
• 6
• 6.5
• 7

0人做过此题 平均耗时为0 平均正确率为 0%

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11

John was 27 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now $$\frac{7}{8}$$ of John's. How old is Betty?

• 24
• 26
• 28
• 30
• 32

0人做过此题 平均耗时为0 平均正确率为 0%

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12

There are X girls in a class, and their average height is M inches. In the same class, there are Y boys with an average height of N inches. What is the average height of all the students in the class?

• $${X+Y}\over{M+N}$$
• $${M+N}\over{X+Y}$$
• $${XM+YN}\over{M+N}$$
• $${XM+YN}\over{X+Y}$$
• $$\frac{MN}{XY}$$

56人做过此题 平均耗时为35s 平均正确率为 96%

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13

If $$x^{2} – 4x = 5$$, then one possible value of x – 4 =

• -9
• -5
• -3
• -1
• 5

56人做过此题 平均耗时为45s 平均正确率为 80%

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14

In the figure to the right, what is the value of x?

Note: Not drawn to scale.

• 90
• 100
• 110
• 120
• 130

0人做过此题 平均耗时为0 平均正确率为 0%

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15

What is the slope of the line represented by the equation x + 2y = 1?

• $$-\frac{3}{2}$$
• -1
• $$-\frac{1}{2}$$
• 0
• $$\frac{1}{2}$$

55人做过此题 平均耗时为27s 平均正确率为 89%

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16

Machine A, working alone at a constant rate, can complete a certain production lot in x hours. Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours. Machines A and B, working together, can complete$$ \frac{1}{2}$$ of the same production lot in z hours. What is the value of y in terms of x and z?

• $${5x-10z}\over{2xz}$$
• $${2xz}\over{5x-10z}$$
• $${5xz}\over{x+z}$$
• $${xz}\over{x+z}$$
• $${xz}\over{x+2z}$$

56人做过此题 平均耗时为2min17s 平均正确率为 71%

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17

Two circles share a center at point C, as shown to the right. Segment AC is broken up into two shorter segments, AB and BC, with dimensions shown. What is the ratio of the area of the large circle to the area of the small circle ?

• $$\frac{25}{4}$$
• $$\frac{5}{2}$$
• $$\frac{3}{2}$$
• $$\frac{2}{5}$$
• $$\frac{4}{25}$$

54人做过此题 平均耗时为47s 平均正确率为 78%

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18

If a, b, c, and d are integers and$$ ab^{2}c^{3}d^{4} > 0$$, which of the following must be positive?

I. $$a^{2}cd $$

II. $$bc^{4}d $$

III.$$ a^{3}c^{3}d^{2} $$

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

58人做过此题 平均耗时为1min0s 平均正确率为 93%

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19

Pablo plays 3 rounds of a game, in which his chances of winning each round are$$\frac{1}{3} ,\frac{1}{6} , and\frac{1}{n}$$ , respectively. If$$ n \neq 0$$, what is the probability that Pablo wins the first two rounds, but loses the third?

• $$\frac{1}{18n}$$
• $$\frac{n-1}{18n}$$
• $$\frac{1}{2n}$$
• $$\frac{n+2}{2n}$$
• $$\frac{3n-2}{2n}$$

56人做过此题 平均耗时为54s 平均正确率为 93%

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20

Two buses and a van were employed to transport a class of students on a field trip. $$\frac{3}{5}$$ of the class boarded the first bus. $$\frac{2}{3}$$ of the remaining students boarded the second bus, and the rest of the students boarded the van. When the second bus broke down,$$\frac{ 1}{2}$$ of the students on the second bus boarded the first bus. What fraction of the class was on board the first bus?

• $$\frac{1}{2}$$
• $$\frac{2}{3}$$
• $$\frac{11}{15}$$
• $$\frac{23}{30}$$
• $$\frac{4}{5}$$

0人做过此题 平均耗时为0 平均正确率为 0%

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