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题目内容
$$ab^4 \lt 0$$

Quantity A

$$a^3b^2$$

Quantity B

$$0$$
$$r^2t \lt 0$$ and $$r \lt 0$$
Which of the following must be a positive number?
Indicate all such numbers.
$$a$$ and $$b$$ are negative, and $$(a+b)(a-b) \lt 0$$.

Quantity A

$$a$$

Quantity B

$$b$$
If $$x=y$$, which of the following must be positive?
If $$-3 \leq x \leq 4$$, and $$-9 \leq y \leq 3$$, what is the greatest possible value of $$xy$$?
The manager of dining services at a small company plans to purchase at least $$225$$ hotdogs and at least $$225$$ buns for the company picnic. The hot dogs can be purchased only in packages of $$10$$, and the buns can be purchased only in packages of $$8$$. If the cost of each package of hot dogs is $$$2.99$$ and the cost of each package of buns is $$$1.48$$, which of the following is closest to the least total cost of the hot dogs and buns that the manager plans to purchase?
A list of $$12$$ consecutive integers contain more negative numbers than positive numbers.

Quantity A

The sum of the numbers on the list

Quantity B

$$-4$$
If an integer is chosen at random from the integers between $$101$$ and $$550$$, inclusive, what is the probability that the chosen integer will be between $$542$$ and $$550$$, inclusive?
$$d = 0.123456789101112...$$ is the decimal obtained by writing all the positive integers in succession after the decimal point.

Quantity A

The $$100$$th digit to the right of the decimal point

Quantity B

$$5$$
Along a certain highway, the first milepost a motorist encountered was numbered $$350$$, the second encountered was numbered $$349$$, and so on in decreasing consecutive order. The twenty-fifth milepost encountered was numbered
$$x$$, $$y$$, and $$z$$ are consecutive integers such that $$x \lt y \lt z$$

Quantity A

The average (arithmetic mean) of $$x$$, $$x$$, $$y$$, and $$z$$

Quantity B

$$y$$
$$x$$, $$y$$, and $$z$$ are consecutive positive integers
$$x \lt y \lt z$$

Quantity A

$$\frac{xy}{z}$$

Quantity B

$$z-\frac{1}{z}$$
The present ages of 3 people are consecutive whole numbers of years. Ten years from now their average (arithmetic mean) age will be 3 times their average age now. What is the present age of the oldest person?
If the median of $$19$$ different integers is $$236$$, what is the least possible range of the integers?
If $$x$$ and $$y$$ are integers such that $$x+y=2m$$ and $$x+2y=2n+1$$ for some integers $$m$$ and $$n$$, which of the following are possible values for $$x$$ and $$y$$, respectively?
If $$k$$ and $$n$$ are integers and if $$k-n$$ is an odd integer, which of the following must be an odd integer?
When the integer $$n$$ is divided by $$21$$, the remainder is $$12$$. Which of the following must be a divisor of $$n$$?
Set $$S$$ consists of all integers greater than $$7$$ and less than $$60$$ such that when each of the integers is divided by $$7$$, the remainder is $$3$$. How many integers are in $$S$$?
$$x$$ is an integer

Quantity A

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

Quantity B

$$(-1)^{(x+1)}$$
$$k$$, $$x$$, and $$y$$ are positive integers, and $$x=2k+6$$.

Quantity A

$$(-1)^{xy}$$

Quantity B

$$0$$

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