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Each morning Betty walks from intersection P to intersection R, always walking along streets shown in the figure above and always going east or north. If she varies her walks as much as possible, taking every different path in turn before repeating the sequence of paths, on how many mornings in 48 consecutive mornings will Betty walk through intersection Q?
n is the least possible integer such that 108n is the square of an integer.

Quantity A

n

Quantity B

9


The positive numbers a, b, c, d, e, and f are different from each other.

Quantity A

The range of the numbers a, b, c, d, e, and f

Quantity B

The range of the numbers $$a^{2}$$, $$b^{2}$$, $$c^{2}$$, $$d^{2}$$, $$e^{2}$$ and $$f^{2}$$


Kim, Megan, Nina, and Paula are planning to go to a movie theater, where three different movies--A, B and C--are being shown simultaneously in different auditoriums. Each of them will see only one of the movies but not necessarily the same movie as any of the other three people. One possible outcome is that Kim and Megan will see C while Nina and Paula will see A. How many possible outcomes are there?
The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean x is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences, $$(x_{i}- x)^{2}$$ for 1 ≤ i ≤ n.

Data sets K and T have the same number of values.Each value in K is either 0 or 2, and both 0 and 2 occur in K at least once. Each value in T is either 0 or 1,and both 0 and 1 occur in T at least once.

Quantity A

The standard deviation of the values in K

Quantity B

The standard deviation of the values in T


A teacher will assign a group project to 2 or more of the 4 students James, Kalla, Lomi, and Michelle. To how many different groups of students can the teacher assign the project?

Quantity A

The ones digit of $$208^{208}$$

Quantity B

7


In a distribution of 1,300 different positive numbers, 65.1 is at the 54th percentile and 63.8 is at the 4th percentile. Approximately how many of the numbers in the distribution are greater than 65.1?


In the figure, line segment RM, SM, and TM bisect the angles of △RST.

Quantity A

$$\frac{x+y}{2}$$

Quantity B

33


The four-digit integer $$8,82X$$ is a multiple of 9, where $$X$$ is the units digit.

Quantity A

$$X$$

Quantity B

2




Quantity A

The standard deviation of data set Ⅰ

Quantity B

The standard deviation of data set Ⅱ




BC=DC

Quantity A

x

Quantity B

y




□, △, ▽, and ⬠ each represent a different digit from 1 to 9.

Quantity A

Quantity B

2


$$x^{4}-3x^{2}+2=0$$ and x > 1

Quantity A

x

Quantity B

$$\sqrt{2}$$


If 30 percent of the presidents and 80 percent of the vice presidents are serving their first terms, what is the least possible number of the organizations that have both their president and corresponding vice president serving their first term?


In the rectangular coordinate plane, (x, y) is a point on the circle with center O and radius 1, and xy ≠ 0.

Quantity A

|$$x^3 + y^3$$|

Quantity B

1


A dog show features four breeds consisting of 3 poodles, 3 German shepherds, 3 boxers, and 2 Irish setters. If the winning group will consist of one dog from each breed, how many different winning groups are possible?


The scores earned by 635 college students on an English test and a Spanish test are integers and are summarized in the boxplots shown above.For each student, the interaction score is defined to be the product of the scores that the student earned on the two tests. Which of the following statements must be true?
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?
A certain candle store has 1,000 unscented candles, 1,000 blue candles, and 2,000 white candles in stock. Of the blue candles, 75 percent are scented, and of the white candles, 85 percent are scented. If a customer buys all the unscented blue candles and all the unscented white candles, how many unscented candles will remain in stock?

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