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Quantity A

The number of different prime factors of 12

Quantity B

The number of different prime factors of 9


Quantity A

The number of prime factors of 27

Quantity B

The number of prime factors of 18


$$m$$ is an odd integer greater than $$1$$.

Quantity A

The greatest prime factor of $$2m$$

Quantity B

The greatest prime factor of $$m^{2}$$




k and n are consecutive positive odd integers.

Quantity A

The least common multiple of k and n

Quantity B

kn


If $$a$$, $$b$$, and $$c$$ are positive integers such that $$\frac{a}{c}=0.075$$, and $$\frac{b}{c}=0.09$$, What is the least possible value of $$c$$?
$$y=105n$$ ($$n$$ is a positive integer)

$$y$$ is both the square of an integer, and a multiple of $$30$$

What is the least possible value of $$n$$?
N is an integer between 10 and 100. When N is divided by 4, 6, and 7, the remainder is 2.

Quantity A

The remainder when N is divided by 11

Quantity B

9


How many positive two-digit integers have a remainder of 3 when divided by both 10 and 6?
If $$a$$, $$b$$ and $$c$$ are integers such that $$0 \lt a \lt b \lt c \lt 2a$$, what is the greatest common factor of $$84^{a}$$, $$126^{b}$$, and $$98^{c}$$?
When $$r$$ percent is expressed as a fraction and the fraction is reduced to lowest terms, the result is $$\frac{n}{20}$$, where $$n$$ is an integer. Which of the following could be the value of $$r$$?
In a pile of books, $$\frac{1}{3}$$ are biography books, $$\frac{1}{4}$$ are chemistry books, while another $$\frac{1}{5}$$are math books. What ratio of all books are books other than the three subjects of books listed above?

Give your answer as a fraction.
If ($$\frac{3}{5}$$)x-($$\frac{1}{3}$$)x=$$\frac{2}{15}$$, then $$\frac{1}{x}$$=?
$$n$$ is a positive integer

Quantity A

$$\frac{n+2}{n+1}$$ - $$\frac{n+1}{n}$$

Quantity B

0


The function f is defined by f(n)= $$\frac{2n-1}{2n+1}$$for all positive integers n. What is the least positive integer m for which the product (f(1))(f(2))......(f(m)) is less than or equal to $$\frac{1}{15}$$?
If $$\frac{x^{2}-16}{x^{2}+6x+8}$$=y, and x > -2, which of the following is an expression for x in terms of y?
List L consists of the numbers $$\frac{m+1}{m}$$ for all integers m from 1 to 100, inclusive.

Quantity A

The sum of all the numbers in list L

Quantity B

101


If $$y=1-\frac{1}{x}$$, where $$x$$ is a nonzero integer, which of the following could be the value of $$y$$?

Indicate all such values.
x ≠ -1 and x ≠ 0

Quantity A

$$\frac{1}{1+\frac{1}{x}}$$

Quantity B

$$\frac{x}{x+1}$$


The reciprocal of n equals 8 times the square of n.

Quantity A

$$\frac{1}{n}$$

Quantity B

2


p > 1

Which of the following could be the value of $$\frac{p}{p+1}$$?

Indicate all such values.

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