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The product of five consecutive integers is not 0.

Which of the following statements individually provide(s) sufficient additional information to determine all these integers are negative?

Indicate all such statements.
n=1234567891011.........499500

The digits of the integer n above are the digits of the integers from 1 to 500 written in consecutive order. How many digits does n have?
List L consists of an odd number of consecutive integers. The median of the integers in L is 3. Which of the following statements must be true?

Indicate all such statements.
$$q$$, $$r$$ and $$s$$ are consecutive positive integers and $$q \lt r \lt s$$.

Quantity A

$$\frac{qs}{r}$$

Quantity B

$$r-\frac{1}{r}$$


Quantity A

The number of odd integers between $$\sqrt{12}$$ and $$12^{2}$$

Quantity B

70


If $$x=2y+1$$, and $$y=2w$$, where $$w$$, $$x$$, and $$y$$ are integers, which of the following must be an odd integer?
If r, s, t, and u are positive integers such that (r+s)(t+u) is an odd integer and (r+s+t)(s+t+u) is an odd integer, which of the following statements must be true?
If x+y=8x+22, then which of the following statements must be true?

Indicate all such statements.
Among all the positive integers in 1-100(inclusive).

Quantity A

The number of the odd integers that are perfect square

Quantity B

The number of the even integers that are perfect square


Which of the following statements are true for all integers a and b?

Indicate all such statements.
If $$x$$, $$y$$ and $$z$$ are consecutive positive integers and if $$x+y+z$$ is even, how many of the four integers $$xy$$, $$yz$$, $$zx$$, and $$xyz$$ are even?
x < 0

Quantity A

$$(x^{-1})^{-3}$$

Quantity B

$$x^{-4}$$


Quantity A

$$(-7)^{52}$$

Quantity B

$$(-7)^{81}$$


If -x < y < 0, which of the following statements is true about the three quantities $$(x+y)^{2}$$, $$y^{2}$$ - $$x^{2}$$, and $$x^{2}$$ - $$y^{2}$$ ?

Quantity A

$$(24-25)^{50}$$

Quantity B

$$(77-76)^{-1}$$


x and y are consecutive positive integers (x < y)

Quantity A

$$(-3)^{(x)^{2}}$$

Quantity B

$$(-3)^{(y)^{2}}$$


n is an integer

Quantity A

$$\frac{(-1)^{11n+7}}{(-1)^{5n-2}}$$

Quantity B

-1


Quantity A

The number of odd integers between $$\sqrt{12}$$ and $$12^{2}$$

Quantity B

70


The median of n consecutive odd integers is 0

Quantity A

The sum of these n integers

Quantity B

The sum of the least and the greatest number


If the least of 19 consecutive even integers is -14, then what is the median of these integers?

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