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A 20-foot ladder leaning against a vertical wall with the base of the ladder 10 feet from the wall is pulled 2 feet farther out from the wall, causing the top of the ladder to drop x feet.

Quantity A

x

Quantity B

2


In the figure, line segment RM, SM, and TM bisect the angles of △RST.

Quantity A

$$\frac{x+y}{2}$$

Quantity B

33
Last month a recycling facility received 175 used automobile batteries, all of which arrived at the facility in crates. Each of these crates contained 19, 20, or 21 used automobile batteries.

Quantity A

The number of crates containing used automatic batteries that arrived at the facility last month

Quantity B

9
The four-digit integer $$8,82X$$ is a multiple of 9, where $$X$$ is the units digit.

Quantity A

$$X$$

Quantity B

2
The operation @ is defined by a@b=3a-2b for all integers a and b. If x and y are two integers such that x@y=17, which of the following could be the value of y?

Indicate all such values.
Every positive integer can be represented uniquely in base 8 by

$$(a_n......a_2 a_1 a_0)_8$$= $$a_n(8^{n})+......a_2(8^{2})+a_1(8^{1})+a_0(8^{0})$$

for some nonnegative integer $$n$$, where the coefficient $$a_i$$ of $$8^{i}$$ is one of the digits from 0 to 7 for $$0 ≤ i ≤ n$$, but $$a_n ≠ 0$$. For example, $$197=(305)_8$$ because $$197= 3(8^{2})+0(8^{1})+5(8^{0})$$.

Quantity A

The product of the three integers $$(3123)_8, (21740)_8$$, and $$(14)_8$$

Quantity B

The product of the three integers $$(6246)_8, (2174)_8$$, and $$(60)_8$$
Every positive integer can be represented uniquely in base 9 by

$$(c_n......c_2 c_1 c_0)_9$$= $$c_n(9^{n})+......c_2(9^{2})+c_1(9^{1})+c_0(9^{0})$$

for some nonnegative integer $$n$$, where the coefficient $$c_i$$ of $$9^{i}$$ is one of the digits from 0 to 9 for $$0 ≤ i ≤ n$$, but $$c_n ≠ 0$$. For example, $$163=(201)_9$$ because $$163= 2(9^{2})+0(9^{1})+1(9^{0})$$.

Which of the following is equal to the product of the three integers $$(12)_9, (13)_9$$, and $$(14)_9$$ ?
Nancy invested $5,000 for $$x$$ years at an annual interest rate of 6 percent, compounded annually.

David invested $6,000 for $$y$$ years at an annual interest rate of 6 percent, compounded semiannually.

Quantity A

The total amount of interest that Nancy's investment earned

Quantity B

The total amount of interest that David's investment earned
Suppose there are 20 monkeys and they all have some number of chestnuts. If in average they have 88 chestnuts per monkey and only one of them has less than 60. If every monkey has an integer number of chestnuts and they all have different number of nuts. Then how many chestnuts does the monkey who has tenth most chestnuts have at least if given none of them has more than 100 chestnuts?
In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?
For how many of the types of transportation in the graphs was the number of ton-miles transported in 1991 more than 4 times the number transported in 1941?
If the total number of ton-miles that were transported increased at a constant rate from 1941 to 1991 approximately what was the total number of ton-miles that were transported in 1986?
From 1941 to 1991, approximately what was the percent increase in the number of ton-miles transported by railway?
Which of the following best represents the graph of y = |x| + x in the xy-plane?
A certain rectangle has perimeter 60.

Quantity A

The length of a diagonal of the rectangle

Quantity B

20
If a > 1, which of the following could be the value of $$(1+\frac{1}{a})^{-1}$$?

Indicate all such values.
$$0 < a < b < c$$

Quantity A

The standard deviation of the seven numbers $$-c, -b, -a, 0, a, b, c$$

Quantity B

The standard deviation of the seven numbers $$-c^{2}, -b^{2}, -a^{2}, 0, a^{2}, b^{2}, c^{2}$$


Quantity A

The standard deviation of data set Ⅰ

Quantity B

The standard deviation of data set Ⅱ

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