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题目内容

Quantity A

The greatest factor of $$600$$ that is also the square of an integer

Quantity B

The greatest factor of $$288$$ that is also the square of an integer
The perimeter of a certain flat rectangular field in County $$X$$ is greater than the perimeter of a certain flat rectangular field in County $$Y$$

Quantity A

The area of the field in County $$X$$

Quantity B

The area of the field in County $$Y$$


$$RSTW$$ is a square, $$P$$ is the midpoint of side $$ST$$, and $$PW = 15$$

Quantity A

$$ST$$

Quantity B

$$6\sqrt5$$
$$N$$ is the units digit in the 3-digit positive integer $$45N$$ and is the tens digit in the 3-digit positive integer $$2N7$$. If the sum of the two 3-digit integers has $$7$$ as the hundreds digit, what is the least possible value of $$N$$?
$$N$$ is a two-digit odd integer.

Quantity A

The tens digit of $$50N$$

Quantity B

$$5$$
A list of data consists of the data points $$10, 10, 11, 12, 13, 13,$$ and $$13$$. If a data point is to be chosen at random from this list, what is the probability that the value of the data point chosen will be within 1 of the average (arithmetic mean) of the numbers in the list?
At a grocery store, each can of beans had the same regular price before it was discounted. The discounted price of each can was $$20$$ percent less than the regular price. If the sum of the discounted prices of 6 cans of beans was $$$3.84$$, what was the regular price of $$1$$ can of beans?
The units digit of the 2-digit positive integer $$N$$ is $$6$$.

Quantity A

The units digit of the product $$7N$$

Quantity B

$$2$$
When the positive integer $$k +2$$ is divided by $$7$$, the remainder is $$3$$. What is the remainder when $$k$$ is divided by $$7$$ ?
The operation $$\triangle$$ is defined for all numbers $$x$$ and $$y$$ by $$x \triangle y=(x+y)^2$$

Quantity A

$$r \triangle s$$

Quantity B

$$r \triangle (-s)$$
A piece of metal is in the shape of a solid, right circular cylinder with diameter $$10$$ millimeters and height $$h$$ centimeters. The cylinder will have some of its material removed so as to leave a smaller solid, right circular cylinder with diameter $$6$$ millimeters and height $$h$$ centimeters.

Quantity A

The volume of the smaller cylinder

Quantity B

The volume of the material removed
$$y$$ is an integer between $$6,000$$ and $$15,000$$

Quantity A

The thousands digit of $$y$$

Quantity B

$$4$$
A sewing basket contains several pieces of ribbon, each of which is either $$8$$ inches long or $$13$$ inches long. The total length of all of the pieces is $$100$$ inches.

Quantity A

The number of pieces of ribbon in the basket that are $$8$$ inches long

Quantity B

The number of pieces of ribbon in the basket that are $$13$$ inches long
A string of length $$n$$ inches was cut into equal pieces of length $$\frac{3}{2}$$ inches, and no string remained after the cutting was completed. If $$n$$ is a positive integer, what is the least possible value of $$n$$?
Which of the following is the graph of the inequality $$|x + 1| \leq 3$$ ?


Greg' s income last year was $$$45,000$$. The graph above shows the distribution of his income, by income source. Based on the information given, which of the following statements about his income last year are true?
Indicate all such statements.
In triangle $$ABC$$, point $$D$$ lies on side $$AB$$ so that $$AD$$ is twice as long as $$DB$$. Point $$E$$ lies on side $$BC$$ so that $$DE$$ is parallel to $$AC$$. If the length of $$DE$$ is $$5$$, what is the length of $$AC$$?
Let $$a$$, $$b$$, and $$c$$ be positive integers such that $$x^2 + cx + 16 = (x+a)(x+b)$$ for all values of $$x$$. What is the largest possible value of $$c$$ minus the smallest possible value of $$c$$?
$$x^2 = (x-1)^2$$

Quantity A

$$x$$

Quantity B

$$\frac{1}{4}$$


The circle is inscribed in the square.

Quantity A

The ratio of the area of the circular region to the area of the square region

Quantity B

$$\frac{3}{4}$$

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