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题目内容
The number of points of intersection between an equilateral triangle and a square could be (such that none of the sides would be overlapping)?
Indicate all that is/are true.
The diagonal of square A and B is 10 and 20, respectively.
What is the ratio of the area of square A to the area of square B?
Give your answer as a fraction.

Quantity A

Area of a rectangle with perimeter 20

Quantity B

Area of a triangle with base 5 and height 10
Set A={2, 4, 6}

Set B={2, 4, 6, 8, 10, 12}

If Set A is a subset of Set M, while Set M is subset of Set B, then how many ways can Set M be constructed?
Set A consists of 40 integers, and set B consists of 150 integers. The number of integers that are in both set A and set B is 20.

Quantity A

The total number of integers that are in set A or set B, or both

Quantity B

170
Set A has 50 members and set B has 53 members. At least 2 of the members in set A are not in set B. Which of the following could be the number of members in set B that are not in set A?
Indicate all such numbers.
Among 66 students, 40 like dancing, 25 like swimming, while 6 like neither dancing nor swimming. How many of them like only dancing?
Of the students in a school, 20 percent are in the science club and 30 percent are in the band. If 25 percent of the students in the school are in the band but are not in the science club, what percent of the students who are in the science club are not in the band?
Of the people surveyed about the effectiveness of various treatments for insomnia, 65 percent reported that prescription drugs were effective and 48 percent reported that exercise was effective. If 22 percent of those surveyed reported that prescription drugs were effective but did not report that exercise was effective,what percent of those surveyed reported that exercise was effective but did not report that prescription drugs were effective?

_____%
A group of students could attend choir and orchestra hobby group as they wish. Among 110 female students, 35 only attend the choir, 26 only attend the orchestra, 9 attend both, while the rest 40 attend neither. Among 120 male students, 49 only attend the choir, 14 only attend the orchestra, 12 attend both, while the rest 45 attend neither. Which of the following statements must be true?
Indicate all such is/are true.
A group of people attend an activity. 40 per cent of them are teachers, while 80 per cent of all teachers have master`s degree.

Quantity A

The proportion of teachers who don`t have master`s degree among all teachers

Quantity B

$$\frac{1}{5}$$
52% of the bottled drinks in a shop contains A, 18% of the bottled drinks in the shop contains B, while 10% of the bottled drinks contains both A and B.

Quantity A

The percent of the bottled drinks in the shop that contains neither A nor B

Quantity B

34%
In a class of 80 students, 40 took biology, 30 took chemistry. Which of the following statements can individually help determine the number of students who took both courses?
Indicate all such statements.
The 50 students in an art class were given an assignment to visit two museums,A and B.During the week after the assignment was given, 25 of the students visited Museum A and 10 of those 25 students also visited Museum B.

Which of the following statements individually provide(s) sufficient additional information to determine how many of the students visited Museum B during that week?

Indicate all such statements.
In a group of people, the proportion of math major students and male students are the same. 35 per cent of all students are male and major in math, while 15 per cent of all students are female and don`t major in math. What`s the proportion of students who major in math?
______%
In transit, the probability that plates crack is $$\frac{1}{2}$$, the probability that plates break is $$\frac{2}{3}$$, while the probability that plates crack and break is $$\frac{1}{3}$$. If 80 plates neither crack nor break when a batch of plates arrive, then how many plates arrive in total?
At a certain university, 60% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?
Of the 120 first-semester students entering a certain college, $$\frac{3}{5}$$ registered for a statistics class and $$\frac{1}{2}$$ registered for a calculus class. Which of the following could be the number of first-semester students entering the college who registered for a statistics class but did not register for a calculus class?
Indicate all such possible numbers.
18 students can choose from snack, staple food, vegetables or none for lunch. Each student can choose whatever types of food as they want. Among 12 students who choose vegetables, 3 also choose snack but not staple food, 2 also choose staple food but not snack, while 4 also choose snack and staple food. What's the ratio of students who only choose vegetables to all students?
Give your answer as a fraction.

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