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In a certain apartment complex,the probability that a household selected at random will be one that subscribes to newspaper T is 0.5 and the probability that a household selected at random will be one that subscribes to newspaper W is 0.3. If the probability that the selected household will be one that subscribes to both newspaper T and newspaper W is 0.1, what is the probability that the selected household will be one that subscribes to neither newspaper T nor newspaper W?


Quantity A

$$x$$

Quantity B

$$90$$
Let $$k$$ be a positive integer, and let $$n$$ be a random variable whose values are the integers from 1 to $$k$$. The probability distribution of $$n$$ is defined by $$P(n)=\frac{2n-1}{d}$$, where $$d$$ is a constant.

Quantity A

$$d$$

Quantity B

$$k^2$$
$$j$$ and $$k$$ are integers such that $$51 \leq j \lt k \leq 99$$.

Quantity A

The number of combinations of $$100$$ objects taken $$j$$ at a time

Quantity B

The number of combinations of $$100$$ objects taken $$k$$ at a time
The four letters w, x, y, z are to be randomly sequenced.

Quantity A

The probability that w will precede x in the sequence

Quantity B

$$\frac{1}{2}$$
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, 7 kilometers, 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?

Quantity A

The number of different 2-member subsets of a set of 5 members

Quantity B

The number of different 3-member subsets of a set of 5 members
A survey of 300 travelers was taken at an airport. Of these travelers 90 percent were traveling on Airline A. Of those who were traveling on Airline A, 30 percent had first-class seats. Which of the following statements must be true about the 300 travelers?

Indicate all such statements.
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?
In an art history class, 70 percent of the students submitted their assignments on time, and of those who did not, 40 percent submitted their assignments one day late.

Quantity A

The percent of the class who neither submitted their assignments on time nor submitted them one day late

Quantity B

18%
Of 50 people surveyed, 32 people reported that they own a dog and the rest reported that they do not own a dog. Of the same group of people surveyed, 19 people reported that they own a cat and the rest reported that they do not own a cat. If 14 of the people who reported they own a dog also reported they own a cat, how many of the people surveyed reported that they do not own either a dog or a cat?
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

$$\frac{4}{9}$$
Of the 45 candidates for a certain job, 20 are married. Of the candidates who are married, 8 do not have a PhD. Of the candidates who are not married, 15 have a PhD.

Quantity A

The number of candidates who do not have a PhD

Quantity B

18
Of the applicants for a job, 6 percent had a degree in computer science and spoke Russian. If 90 percent of the applicants who had a degree in computer science did not speak Russian, what fraction of all the applicants had a degree in computer science?
At a medical clinic, there are exactly 20 medical personnel-8 doctors and 12 nurses. Of these medical personnel, 9 are men, and 3 of the 9 men are nurses. If a doctor is chosen at random, what is the probability that the doctor chosen will be a woman?

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