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Each time a certain coin is tossed, it lands either heads up or tails up. The coin has the property that the probability that it will land heads up when tossed 1 time is 0.6. If the coin is to be tossed 3 times, what is the probability that it will land heads up at least 2 times?


The circle on the left has radius r and center O, and the circle on the right has radius s and center P. The lengths of arcs ABC and DEF are both equal to 3, and r < s < 3.

Quantity A

x

Quantity B

y


A plot of land used to display flowers in a botanical garden was designed in the shape of a trapezoid in which the lengths of the two sides that are not parallel are equal. The length of the longer parallel side is 5 times the length of the shorter parallel side, and the distance between the two parallel sides is 3 times the length of the shorter parallel side. The perimeter of the plot is 135 meters. Approximately what is the length, in meters, of the shorter parallel side?


What's the height of the unknown altitude?

Give your answer as a fraction.


The cube shown above has edges of length x, where x is an integer. The length of diagonal AG (not shown) is 10.39, to the nearest 0.01. What is the value of the integer x?

x=_____


PQST is a parallelogram and R is the midpoint of side PT.

Quantity A

The area of triangular region PQR

Quantity B

The area of triangular region RST




Of the 72 fish in a certain aquarium, $$\frac{1}{3}$$ are brown and the remaining $$\frac{2}{3}$$ are white. Among the 72 fish, $$\frac{1}{2}$$ have orange fins and $$\frac{1}{2}$$ have black fins. If $$\frac{2}{3}$$ of the white fish have orange fins, how many of the brown fish have black fins?
What percent of all the presidents and vice presidents are less than 50 years old?
For how many of the organizations does the age of the president exceed the age of the corresponding vice president by 15 years?
A committee of 4 people consisting of 2 men and 2 women is to be selected from 5 sets of fraternal twins, where each set consists of one man and one woman. If only 1 person from each set of twins may be selected for the committee, what is the total number of distinct committees that can be formed?
a+b=5

Quantity A

$$(a+\frac{b}{4})+(\frac{a}{4}+b)$$

Quantity B

6


When the positive number k is multiplied by itself, the result is $$\frac{1}{2}$$ of k.

Quantity A

k

Quantity B

$$\frac{1}{4}$$


The set S consists of all of the different ordered pairs (x, y) for which x is a positive integer less than 50 and $$y=\frac{1}{2}x+10$$.

Quantity A

The number of ordered pairs in S for which y is not an integer

Quantity B

25


Michael ate $$\frac{1}{6}$$ of the cookies in a full jar of cookies, and Tess ate $$\frac{1}{7}$$ of the remaining cookies in the jar.

Quantity A

The fraction of the cookies in the full jar that were not eaten by either Michael or Tess

Quantity B

$$\frac{5}{7}$$


Triangle ABC is equilateral. Vertices P, Q, and R of triangle PQR lie on sides AB, AC, and BC, respectively.

Quantity A

The sum of the measures of two of the interior angles of triangle ABC

Quantity B

The sum of the measures of two of the interior angles of triangle PQR


Which of the following indicates all values of b such $$(x-b)^{2}+1$$ is positive?
A demographic study describes a group of corporation executives and non executives having an average (arithmetic mean) age of 42 years. If the executives in the group average 40 years of age and the nonexecutives average 45 years of age, what is the ratio of the number of executives to the number of non executives in the group?
It cost a certain company a total of $4,200.00 to make and sell 3,000 widgets. If the company sold each of the 3,000 widgets for $2.10, what was the company`s profit per widget? (Profit is equal to the selling price minus the cost)

$_____
If the population of the United Kingdom was 60 million in year X, which of the following is closest to the total number of Internet users in the United Kingdom in year X?
In year X, for how many of the countries shown was the number of Internet users greater than 15 percent of the population of that country?

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