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Quantity A

The greatest prime number that is less than $$91$$

Quantity B

The least prime number that is greater than $$84$$
Pat has $$7$$ identical pieces of paper. One or more of the pieces are cut into $$7$$parts each, then one or more of the smaller pieces are cut into $$7$$ parts each again. Which of the following could be the total number of pieces of paper after these cuts have been made?
How many two-digit positive integers are equal to the product of two different prime numbers greater than $$0$$?
A total of $$77$$ coins are to be divided equally among n people, where $$n \gt 1$$.

Quantity A

$$n^2$$

Quantity B

$$81$$
$$x$$, $$y$$, and $$z$$ are integers such that $$1 \lt x \lt y \lt z$$ and $$xyz=105$$.

Quantity A

$$x+z$$

Quantity B

$$2y$$
A total of $$143$$ players arrived on the first day of football practice. The coaches divided them into n groups, each with the same number of players, where $$n \gt 1$$.

Quantity A

$$n^2$$

Quantity B

$$125$$
$$N$$ is the least 3-digit positive integer for which the product of its digits is equal to $$24$$.

Quantity A

$$N$$

Quantity B

$$234$$
$$1575=3^m \times 5^n \times 7^p$$, where $$m$$, $$n$$, and $$p$$ are positive integers.

Quantity A

$$m+n+p$$

Quantity B

$$5$$

Quantity A

The number of distinct prime factors of $$1,001^{1,001}$$

Quantity B

The number of distinct prime factors of $$210^{210}$$
What is the number of distinct prime factors of $$n$$?
$$n=13!+15!$$
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.

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