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In a group of 13 students, 9 are English majors and 9 are physics minors. Which of the following could be the number of students in the group who are both English majors and physics minors?


A town library held a reading drive, in which 20 elementary school students were asked to record the number of books they read over the summer. Only whole numbers of books were recorded. The table above shows the results of the reading drive. The average (arithmetic mean) number of books read by the students was 2 books per student.

Which of the following statements individually provide(s) sufficient additional information to conclude that only one student read only 5 books?

Indicate all such statements.
All members of a university debate club are either undergraduate students or graduate students. At the beginning of a semester, the club had more undergraduate students than graduate students and the number of undergraduate students was $$p$$ percent of the number of members of the club. At the end of the semester, the club had $$n$$ more undergraduate students and $$n$$ more graduate students than at the beginning and the number of undergraduate students was $$r$$ percent of the number of members of the club.

Quantity A

$$p$$

Quantity B

$$r$$


$$N$$ is a two-digit integer. The units digit of $$N^2$$ is 9.

Quantity A

The units digit of N

Quantity B

6


Four locations on a map are labeled A, B, C, and D. Location B is directly north of location A, location C is directly east of location B. and location D is directly north of location C. As represented on the map, the distances between locations A and B, locations B and C, and locations C and D are 3 kilometers, 7kilometers, and 12 kilometers, respectively. Which of the following is closest ot the distance, in kilometers, as represented on the map between locations A and D?
Last year 40 percent of the students at College X took Biology I. If all of the science majors and 10 percent of the nonscience majors took Biology I, approximately what percent of the students at College X last year were science majors?
The students in an elementary school were asked to choose their favorite color from a list of colors. Of all the students, $$\frac{1}{2}$$ chose red. Of the students who did not choose red, $$\frac{1}{4}$$ chose blue. Of the students who did not choose red or blue, $$\frac{1}{5}$$ chose green. What fraction of the students did not choose red, blue, or green?
At Central High School, 25 percent of the male students and 30 percent of the female students are on sports teams. Of all Central High School students, 60 percent are male.

Quantity A

The fraction of the Central High School students on sports teams that are female

Quantity B

$$\frac{4}{9}$$


In January a company purchased 5,000 gallons of fuel at an average price of $0.96 per gallon. In February the company purchased 6,000 gallons at an average price of $0.90 per gallon.

Quantity A

The amount by which the February fuel cost exceeded the January fuel cost

Quantity B

$600


The lengths of two of the sides of a certain isosceles triangle are 5 and 9.

Quantity A

The perimeter of the triangle

Quantity B

20


$$x^{4}=y^{4}$$

Quantity A

x

Quantity B

y


The operation ● is defined for all numbers a and b by the equation a●b=3a+2b.

Quantity A

(0●1)●2

Quantity B

0●(1●2)




ABCD is a rectangle. E and F are the midpoints of sides BC and CD, respectively.

Quantity A

The area of quadrilateral region AECF

Quantity B

$$\frac{1}{2}$$ the area of rectangular region ABCD


List P consists of all prime numbers between 30 and 100. List S consists of all odd integers between 30 and 100 that are not prime numbers.

Quantity A

The range of the numbers in P

Quantity B

The range of the numbers in S


N is the number of ordered pairs (x, y) such that 4y < 12-3x and each of x and y is a positive integer.

Quantity A

N

Quantity B

3


A={1, 4, 7, 9, 11}

B={3, 4, 5, 6, 7, 8, 9}

For sets A and B above, which of the following sets is a subset of A but not a subset of B?

Indicate all such sets.
A continuous random variable R has a mean of 77 and a standard deviation of 8. What is the value of R that is 2.5 standard deviation above the mean?
A ball is to be selected at random from a bag containing red balls, green balls, and blue balls. The probability of selecting a red ball is equal to x. If the probability of selecting a green ball equals the probability of selecting a blue ball, what is the probability of selecting a green ball, in terms of x ?


A simple sailboat often has two sails, the mainsail and the headsail, as shown in the figure above.A recreational sailor is building a simple sailboat and is designing each sail to be in the shape of a right triangle. The mainsail will have a height of 12 feet and a hypotenuse of length 15 feet.The headsail will have a height of 15 feet and a hypotenuse of length 16.25 feet. Based on the design, the area of the mainsail will be how much greater than the area of the headsail?

Give your answer to the nearest square foot.

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