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Quantity A

The least common multiple of $$10, 15$$, and $$16$$

Quantity B

The least common multiple of $$20, 15$$, and $$16$$
$$E$$ is the set of all positive common multiples of $$7$$ and $$11$$ that are less than $$1,900$$.

Quantity A

The number of integers in $$E$$ that are divisible by $$6$$

Quantity B

The number of integers in $$E$$ that are divisible by $$5$$
$$n$$ is a positive integer.
The remainder when $$5n + 2$$ is divided by $$3$$ is $$1$$.
The remainder when $$5n + 1$$ is divided by $$4$$ is $$1$$.

Quantity A

$$n$$

Quantity B

$$3$$
A string of decorative lights consists of red, green and blue bulbs. The red bulbs flash every $$4$$ seconds, the green bulbs flash every $$6$$ seconds, and the blue bulbs flash every $$9$$ seconds. If all the lights flash simultaneously when the string is first lit, how many seconds will it take until all the lights flash simultaneously the next time?

Quantity A

The greatest common factor of $$5$$ and $$16$$

Quantity B

The greatest common factor of $$25$$ and $$256$$
Let $$n$$ be a positive integer such that the greatest common factor of $$n$$ and $$24$$ is $$12$$. Which of the following could be the least common multiple of $$n$$ and $$24$$?
If the sum of $$x$$ and $$5$$ is divided by $$y$$, the result is $$8$$.

Quantity A

$$x$$

Quantity B

$$y$$
When $$10$$ is divided by the positive integer $$k$$, the remainder is $$k$$-2. Which of the following could be the integer $$k$$?
Indicate all such integers.
When the positive integer $$n$$ is divided by $$35$$, the remainder is $$27$$. What is the remainder when $$n$$ is divided by $$7$$?
When the positive integer $$n$$ is divided by $$35$$, the remainder is $$29$$. What is the remainder when $$n$$ is divided by $$7$$?
If the positive integer $$n$$ is divided by $$30$$, the remainder is $$5$$. Which of the following must be divisible by $$30$$?
When the integer $$n$$ is divided by $$5$$, the remainder is $$2$$. If $$n$$ is between $$13$$ and $$29$$, which of the following integers could be the remainder when $$n$$ is divided by $$4$$?
Indicate all such integers.
$$k$$, $$m$$, and $$r$$ are positive integers and $$k \lt m \lt r$$.
When $$m$$ is divided by $$k$$, the remainder is $$0$$.
When $$r$$ is divided by $$k$$, the remainder is $$0$$.

Quantity A

The remainder when $$r$$ is divided by $$m$$

Quantity B

$$k$$
$$n$$ is a positive integer, and the remainder when $$23$$ is divided by $$n$$ is $$2$$.

Quantity A

$$n$$

Quantity B

$$8$$
When the positive integer $$M$$ is divided by $$6$$, the remainder is $$1$$. When $$M$$ is divided by the positive integer $$D$$, the remainder is $$0$$. Which of the following could be the integer $$D$$?
Indicate all such integers.
If $$x$$ is an integer and $$y=3x+2$$, which of the following integers could be a divisor of $$y$$?
Indicate all such integers.
For Year X, in how many of the six regions did grasses produce pollen for a period of less than three months?
For approximately what fraction of Year X was pollen produced by both grasses and weeds in the Southwest?
For Year X, which of the following is closest to the total length, in months, of the time period during which no pollen was produced by trees or grasses in any of the six regions?

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