题目列表

题目内容

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 $$13^a*13^b=(13^x)^y=13^{13}$$, 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

Quantity A

b

Quantity 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


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