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Square ABCD has sides of length 1. Arc AC is an arc of the circle of radius 1 centered at B. Arc BD is an arc of the circle of radius 1 centered at A. These arcs divide the square into four regions, $$S_1, S_2, S_3$$, and $$S_4$$.

Quantity A

The area of region $$S_1$$ minus the area of region $$S_3$$

Quantity B

$$\frac{π}{2}$$ -1




The circle shown has center O, and arc EPF is a semicircle. Quadrilateral EAOD, ABCD, and OBFC are squares, and the length of each side of ABCD is 1. What is the perimeter of region EPFCD?


For each of 20 brands of protein bars, the number of grams of protein per bar was rounded to the nearest gram and recorded. The histogram shows the frequency distribution of the recorded numbers of grams of protein per bar for the 20 brands, where each interval shown includes its left endpoint and excludes its right endpoint. Based on the histogram, which of the following could be the average (arithmetic mean) and the median, respectively, of the recorded numbers of grams of protein per bar for the 20 brands?

Quantity A

The average (arithmetic mean) of x and y

Quantity B

The average (arithmetic mean of 2x and $$\frac{y}{2}$$


0 < a < b < c < d < e

List X: a, b, c, d, e

List Y: -2a, -2b, -2c, -2d, -2e

Quantity A

The standard deviation of the numbers in list X

Quantity B

The standard deviation of the numbers in list Y


$$B_n=\frac{n}{n+1}$$ for all integers n > 1.

$$C_n=B_n + B_{n-1}$$ for all integers n > 2.

The integer k is greater than 2.

Quantity A

$$C_k$$

Quantity B

$$\frac{2k^2-1}{k+k}$$


Working continuously for a total of 120 hours, a machine first assembled x units of product A and then assembled y units of product B. where x and y are positive integers. It took the machine 3 hours to assemble each unit of product A and 5 hours to assemble each unit of product B. Which of the following could be the total number of units of product A and product B that the machine assembled in the 120 hours?

Indicate all such numbers.

Quantity A

The number of integers between 10,000 and 25,000 that are multiples of 14

Quantity B

The number of integers between 10,000 and 26,000 that are multiples of 15


In a probability experiment, R and S are independent events such that 0 < P(R) < $$\frac{1}{2}$$ and 0 < P(S) < 1.

Quantity A

The probability that S will occur given that R has occurred

Quantity B

P(R)


Of the 60 people in a room, \frac{2}{3} are women and \frac{2}{5} are vegetarian. What is the greatest possible number of people in the room who are women that are not vegetarian? [/blank]


If the perimeter of the isosceles right triangle is (1+$$\sqrt{2}$$), what is the area of the triangular region?
$$\frac{2}{\sqrt{3}+\sqrt{1}}$$, $$\frac{2}{\sqrt{5}+\sqrt{3}}$$, $$\frac{2}{\sqrt{7}+\sqrt{5}}$$, .............., $$\frac{2}{\sqrt{121}+\sqrt{119}}$$

Consider the sequence above, where the $$k$$th term is equal to $$\frac{2}{\sqrt{2k+1}+\sqrt{2k-1}}$$ for each integer $$k$$ from 1 to 60. What is the sum of the 60 terms of the sequence?
$$x$$ and $$y$$ are positive integers.

$$xy$$ is divisible by 24.

$$\frac{x}{2}$$ is an odd integer.

Quantity A

The remainder when y is divided by 4

Quantity B

1


A gardener is planning a vegetable garden that will be enclosed by a fence.The garden will be rectangular with an area of 24 square meters, and each side of the garden will be a whole number of meters in length. Fence posts will be placed so that there is a post at each corner, the centers of the posts are along the perimeter of the garden, and the distance between the centers of adjacent posts is 1 meter.Which of the following CANNOT be the total number of fence posts in the plan?
How many integers between 360 and 630 are there such that they have odd number of divisors?

Quantity A

The remainder when $$35^{12}+63^{17}$$ is divided by 14

Quantity B

3


What is the remainder when $$8^{43}$$ is divided by 7?

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