PS-OG20：第141-160题 练习册详情

1

If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n ?

• 10
• 11
• 12
• 13
• 14

2332人做过此题 平均耗时为16min34s 平均正确率为 40%

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2

The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?

• $$\frac{1}{5}$$
• $$\frac{2}{5}$$
• $$\frac{3}{5}$$
• $$\frac{4}{5}$$
• $$\frac{12}{25}$$

3541人做过此题 平均耗时为20min46s 平均正确率为 63%

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3

The total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool. Each tool sells for $8. The gross profit earned from producing and selling these tools is the total income from sales minus the total production cost. If a batch of 20,000 tools is produced and sold, then Company X's gross profit per tool is

• $3.00
• $3.75
• $4.50
• $5.00
• $5.50

6297人做过此题 平均耗时为29min18s 平均正确率为 53%

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4

If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

• $$\frac{Q-1}{2}+{120}$$
• $$\frac{Q}{2}+{119}$$
• $$\frac{Q}{2}+{120}$$
• $$\frac{Q+119}{2}$$
• $$\frac{Q+120}{2}$$

8675人做过此题 平均耗时为35min32s 平均正确率为 57%

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5

A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?

• 35
• 42
• $${35}\sqrt{3}$$
• $$7+{35}\sqrt{3}$$
• $$7+{42}\sqrt{3}$$

8775人做过此题 平均耗时为31min20s 平均正确率为 54%

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6

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

• 40 + 8π
• 40 + 2π
• 32 + 8π
• 32 + 4π
• 32 + 2π

2743人做过此题 平均耗时为7min53s 平均正确率为 64%

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7

If there are fewer than 8 zeros between the decimal point and the first nonzero digit in the decimal expansion of $$(\frac{t}{1000})^{4}$$, which of the following numbers could be the value of t?

I. 3

II. 5

III. 9

• None
• I only
• II only
• III only
• II and III

2767人做过此题 平均耗时为22min32s 平均正确率为 70%

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8

A three-digit code for certain logs uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?

• 144
• 152
• 160
• 168
• 176

7863人做过此题 平均耗时为25min32s 平均正确率为 41%

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9

Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?

• 18
• 20
• 24
• 36
• 42

1335人做过此题 平均耗时为14min16s 平均正确率为 48%

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10

If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake's present weight, in pounds?

• 131
• 135
• 139
• 147
• 188

6013人做过此题 平均耗时为21min31s 平均正确率为 57%

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11

For each student in a certain class, a teacher adjusted the student's test score using the formula y = 0.8x + 20, where x is the student's original test score and y is the student's adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class?

• 12
• 16
• 28
• 36
• 40

556人做过此题 平均耗时为5min55s 平均正确率为 49%

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12

Last year 26 members of certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?

• 52
• 67
• 71
• 73
• 79

2100人做过此题 平均耗时为17min15s 平均正确率为 46%

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13

A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?

• 2%
• 17%
• 20%
• 65%
• 83%

4418人做过此题 平均耗时为15min56s 平均正确率为 56%

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14

When positive integer x is divided by positive integer y, the remainder is 9. If $$\frac x y=96.12$$, what is the value of y?

• 96
• 75
• 48
• 25
• 12

9965人做过此题 平均耗时为10min31s 平均正确率为 61%

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15

If x (2x + 1) = 0 and (x + $$\frac{1}{2}$$)(2x - 3) = 0, then x =

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

442人做过此题 平均耗时为1min44s 平均正确率为 54%

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16

Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?

• 2:3
• $$\sqrt{2}:{2}$$
• $${2}\sqrt{2}:{3}$$
• 1:1
• $$\sqrt{2}:{1}$$

1368人做过此题 平均耗时为9min26s 平均正确率为 47%

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17

A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are

• 0 and 13
• 0 and 14
• 1 and 10
• 1 and 9
• 2 and 8

1099人做过此题 平均耗时为13min57s 平均正确率为 43%

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18

For the positive numbers, n, n + 1, n + 2, n + 4, and n + 8, the mean is how much greater than the median

• 0
• 1
• n+1
• n+2
• n+3

4489人做过此题 平均耗时为12min27s 平均正确率为 50%

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19

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

• $$\sqrt[3]{x}$$
• $$\sqrt[3]{\frac{2x}{3}}$$
• $$\sqrt[3]{\frac{3x}{2}}$$
• $$(\frac{2}{3})\sqrt[3]{x}$$
• $$(\frac{3}{2})\sqrt[3]{x}$$

8337人做过此题 平均耗时为29min49s 平均正确率为 40%

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20

The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

• 5
• 8
• 10
• 12
• 15

5147人做过此题 平均耗时为23min37s 平均正确率为 48%

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