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

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 $$x^{12}-x^{10}+x^8-x^6 > 0?$$
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?
$$S={1.2, 0.9, 1.3, 1.5}$$

$$T={1.2x, 0.9x, 1.3x, 1.5x}$$

$$x$$ is a positive number.

Quantity A

he standard deviation of the numbers in set S

Quantity B

The standard deviation of the numbers in set T
If one letter is to be randomly selected from the 7 letters in the word JOHNSON and one letter is to be randomly selected from the 5 letters in the word JONES, what is the probability that the two selections will be the same letter?
Machine A and machine B, working simultaneously and independently at their respective constant rates, processed $$\frac{3}{4}$$ of the shipment of a certain product in 4.5 hours. Then machine A, working alone at its constant rate, processed the rest of the shipment in 6 hours. How many hours would it have taken machine B, working alone at its constant rate, to process the entire shipment of the product?
How many distinct solutions does the equation $$|1-|x-215||=1$$ have?
Each copy of Magazine X is sold either at the cover price of $3.25 per copy or at the subscription price of $1.75 per copy. The average (arithmetic mean) price of the copies of Magazine X that were sold last month was $2.25 per copy.

Quantity A

The number of copies of Magazine X that were sold last month at the subscription price

Quantity B

Twice the number of copies of Magazine X that were sold last month at the cover price


In quadrilateral ABCD shown, what is the value of x?

Give your answer to the nearest 0.1.
What is the greatest prime divisor of $$3^{100}$$- $$3^{97}$$?
Which of the following is the graph of $$|x-5| \leq 2$$?

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