#### Quantity A

The number of primes that are divisible by 9

#### Quantity B

The number of primes that are divisible by 19

If a, b, x, and y are positive integers, and $13^a \times 13^b=(13^x)^y=13^{13}$, what is the average (arithmetic mean) of a, b, x, and y?

_____
A rectangle is drawn in a standard xy-coordinate plane. If the sides of the rectangle are not parallel to the axes, what is the product of the slope of the four sides?
In a certain state, each license plate consists of either three digits (between 0 and 9, inclusive) followed by two letters or three letters followed by two digits. For example, 055-XY, 123-PP, and AAA-70 are all acceptable plates. How many different license plates can the state issue?

_____
n is an even integer

#### Quantity A

The number of prime factors of n

#### Quantity B

The number of prime factors of $\frac{n}{2}$

A positive integer is a palindrome if it reads exactly the same from right to left as it does from left to right. For example, 5 and 66 and 373 are all palindromes. How many palindromes are there between 1 and 1,000, inclusive?

_____
Line l passes through points in both quadrants II and III. Which of the following statements are true?

Indicate all such statements.
a and b are primes. a+b=12

b

8

#### Quantity A

The number of 3-digit integers all of whose digits are even

#### Quantity B

The number of 3-digit integers all of whose digits are odd

Consider the following list of numbers that represent the number of text messages that Geraldine received on 10 consecutive days: 10, 9, 1, 3, 7, 7, 8, 3, 4, 3. Which of the following statements concerning this set of data are true? Indicate all such lengths.
Last year Leo bought two paintings. This year he sold them for $2,000 each. On one, he made a 25% profit, and on the other he had a 25% loss. What was his net loss or profit? If c and d are odd positive integers, which of the following could be odd? Indicate all such expressions. xy>0 $xy^{2}$<0 #### Quantity A x #### Quantity B y In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry? _____students The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a$10 bill and received the correct change, which was less than \$3.00. Which of the following statements must be true?

Indicate all such statements.
If $\frac{1}{((2^{11})(5^{17}))}$ is expressed as a terminating decimal, how many nonzero digits will the decimal have?
Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle ABC above?

Indicate all such statements.
What is the least positive integer that is not a factor of 25! and is not a prime number?

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