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Quantity A

The number of real roots of $$2x- \frac{4}{7}$$=0

Quantity B

The number of real roots of $$2x^2 + \frac{4}{7}$$=0


Points P, R, and S are on the circle with cener O. The measure of angle ROS is 92°.

Quantity A

x

Quantity B

y
$$0 < a < b < c$$

The average of $$a$$, $$b$$, and $$c$$ is $$b$$.

Quantity A

The average (arithmetic mean) of $$a^2$$, $$b^2$$ and $$c^2$$

Quantity B

The median of $$a^2$$, $$b^2$$ and $$c^2$$

Quantity A

The area of a triangle with a perimeter of 40 and a side whose length is 12

Quantity B

72


0 < $$x$$ < 90

Quantity A

$$y$$

Quantity B

5
$$y=(x-1)(x-3)(x-5)(x-7)(x-9)(x-11)$$

For which of the following value of $$x$$ is the value of $$y$$ negative?

Indicate all such values of $$x$$.
Which of the following is a value of $$x$$ for which $$x^{12}-x^{10}+x^8-x^6 \gt 0?$$
In a mayoral election, Candidate X received $$33\frac{1}{3}$$ percent more votes than Candidate Y, and Candidate Y received 25 percent fewer votes than Candidate Z.

Quantity A

The number of votes that Candidate X received

Quantity B

8 percent more than the number of votes that Candidate Z received
A survey of 500 households found that 450 households had a microwave oven, 300 had a food processor, and 150 had a trash compactor. Each of the 500 households had at least one of the appliances, and more than 100 households had all three appliances. Which of the following could be the number of households that had a food processor and a trash compactor but no microwave oven?

Indicate all such numbers.

Quantity A

The median of the 115 scores

Quantity B

76
If twice the sum of the positive integers x, y, and z is divided by 7, the remainder is 1. What is the remainder if the sum of x, y, and z is divided by 7?
Calvin drives east along a straight road from point A to point B. His speed is never more than 60 miles per hour. Which of the following graphs could represent Calvin's distance from point A as a function of time?

Indicate all such graphs.
On a bookshelf, Pat arranges 7 different books: 2 history books, 3 philosophy books, and 2 science books. If Pat arranges the books so that the history books are next to each other, the science books are next to each other, and the philosophy books are next to each other, how many different arrangements are possible?

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