PS-OG20：第221-230题 练习册详情

1

Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are $$\frac{1}{4}$$, $$\frac{1}{2}$$ and $$\frac{5}{8}$$ respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

• $$\frac{11}{8}$$
• $$\frac{7}{8}$$
• $$\frac{9}{64}$$
• $$\frac{5}{64}$$
• $$\frac{3}{64}$$

9806人做过此题 平均耗时为21min35s 平均正确率为 40%

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2

if $$\frac{1}{x}-\frac{1}{x+1}=\frac{1}{x+4}$$ then x could be

• 0
• -1
• -2
• -3
• -4

4340人做过此题 平均耗时为14min57s 平均正确率为 64%

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3

$$(\frac{1}{2})^{-3}(\frac{1}{4})^{-2}(\frac{1}{16})^{-1}=$$

• $${(\frac{1}{2}})^{-48}$$
• $${(\frac{1}{2}})^{-11}$$
• $${(\frac{1}{2}})^{-6}$$
• $${(\frac{1}{8}})^{-11}$$
• $${(\frac{1}{8}})^{-6}$$

4167人做过此题 平均耗时为15min0s 平均正确率为 61%

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4

The figure shown above consists of a shaded 9-sided polygon 9 unshaded isosceles triangles. For each isosceles triangle, the longest side is a side of the shaded polygon and the two sides of equal length are extensions of the two adjacent sides of the shaded polygon. What is the value of a?

• 100
• 105
• 110
• 115
• 120

2513人做过此题 平均耗时为19min33s 平均正确率为 49%

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5

List T consists of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, £, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If $$\frac{1}{3}$$ of the decimals in T have a tenths digit that is even, which of the following is a possible value of E - S ?

I.-16

II.6

III.10

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

9983人做过此题 平均耗时为20min48s 平均正确率为 53%

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6

If $$5-\frac{6}{x}=x$$ then x has how many possible values?

• None
• One
• Two
• A finite number greater than two
• An infinite number

7437人做过此题 平均耗时为17min0s 平均正确率为 41%

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7

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ?

• 10%
• $${33}\frac{1}{3}\%$$
• 40%
• 50%
• $${66}\frac{2}{3}\%$$

7134人做过此题 平均耗时为36min34s 平均正确率为 43%

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8

How many of the integers that satisfy the inequality $${\frac{(x+2)(x+3)}{x-2}}\ge{0}$$ are less than 5 ?

• 1
• 2
• 3
• 4
• 5

7384人做过此题 平均耗时为33min26s 平均正确率为 55%

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9

Of the 150 houses in a certain development, 60 percent have air - conditioning, 50 percent have a sunporch, and 30 percent have a swimming pool. If 5 of the houses have all three of these amenities and 5 have none of them, how many of the houses have exactly two of these amenities?

• 10
• 45
• 50
• 55
• 65

2452人做过此题 平均耗时为20min42s 平均正确率为 48%

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10

The value of $$\frac{({2}^{-14}+{2}^{-15}+{2}^{-16}+{2}^{-17})}{5}$$ is how many times the value of$${2}^{-17}$$?

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

4035人做过此题 平均耗时为19min31s 平均正确率为 42%

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