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题目内容
What is the greatest prime divisor of the product of $$123$$ and $$255$$?

Quantity A

The least positive prime factor of $$7!+7$$

Quantity B

The greatest prime factor of $$7!$$
The number of volunteers at a local fund-raising event was between $$40$$ and $$50$$. Which of the following statements individually provide(s) sufficient additional information to determine the number of volunteers?
Indicate all such statements.
Which of the following is NOT a factor of $$(1,001)(1,002)(1,003) (1,004)$$?
Given that $$x^{2n}-1=(x^n+1)(x^n-1)$$, which of the following is NOT a factor of $$5^8-1$$?
Which of the following integers has the greatest number of positive divisors?
When positive integer $$n$$ is divided by $$11$$, the remainder is $$5$$.

Quantity A

The remainder when $$7n$$ is divided by $$11$$

Quantity B

$$2$$
How many positive odd factors does $$1,575$$ have?
If $$r$$ is a multiple of $$4$$ and $$t$$ is a multiple of $$5$$, which of the following statements must be true?
Indicate all such statements.
The operation $$\odot$$ is defined for all integers $$n$$ and $$p$$ as follows.



Quantity A

$$(a \odot b)+(b \odot a)$$

Quantity B

$$0$$
$$-6, |-8|, 4, \sqrt17, 7$$
How many of the five numbers shown have the property that the square of the number is 4 more than a multiple of 5?

Quantity A

The range of four consecutive multiples of $$2^3$$

Quantity B

$$24$$
In a list of $$16$$ consecutive multiples of $$5$$, ordered from least to greatest, the difference the $$2$$nd and $$15$$th numbers is what fraction of the difference between the first and last numbers?
Sixteen fence posts are equally spaced in a straight line along a property line. The distance between the first post and the last is $$240$$ feet.

Quantity A

The distance between the $$5$$th post and the $$8$$th post

Quantity B

$$45$$ feet
There are $$16$$ integers between $$1$$ and $$200$$ that are multiples of $$12$$. If one of these integers is randomly chosen, what is the probability that the chosen integer will be a multiple of $$9$$?
How many multiples of $$5$$ are there from $$55$$ to $$505$$, inclusive?

Quantity A

The number of multiples of $$3$$ between $$1$$ and $$10,000$$

Quantity B

The number of multiples of $$7$$ between $$1$$ and $$23,000$$
How many positive two-digit integers are not divisible by $$4$$?
Fred receives $$40$$ channels, numbered with the integers from $$1$$ to $$40$$, on his television set. If he is to select a channel randomly, what is the probability that the channel number will be divisible by $$4$$ or $$5$$ or both?
$$S$$ is the set of all 2-digit integers that are multiples of $$3$$.

Quantity A

The number of even integers in $$S$$

Quantity B

$$15$$

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