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The tick marks shown on the number line are evenly spaced. Points D and E have coordinates of $$4^{10}$$ and $$4^{11}$$, respectively. The point that has a coordinate of $$4^{9}$$ is?
$$a=\frac{x}{x+y+z}$$ , $$b=\frac{y}{x+y+z}$$ , $$c=\frac{z}{x+y+z}$$


Quantity A

The average of a, b and c

Quantity B

$$\frac{1}{2}$$


If a set S has a total of 6 subsets that consist of 2 members each, then S consists of how many members?
If n is a positive integer greater than 1, then n($$n^{2}$$-1) must be a multiple of which of the following integers?

Indicate all such numbers.
What is the units digit of $$2^{2222}$$?
What is the remainder when $$(345,606)^{2}$$ is divided by 20?
What is the greatest prime divisor of $$3^{100}$$- $$3^{97}$$?
Student A, B, and C together need 6 hours to finish a task, while A and B together need 8 hours to finish the same task. How many hours will it take for Student C to finish the task alone?
To obtain an FHA mortgage for $50,000 or more, the home buyer must have a down payment equal to 4 percent of the first $25,000 of the mortgage amount and 5 percent of the portion in excess of $25,000. At settlement the buyers pays a mortgage-insurance premium equal to 3 percent of the mortgage amount. What is the maximum FHA mortgage, if any, a buyer can obtain if the buyer has only $6,000 available for the down payment and insurance premium?
x and y are real numbers and x+y > 1

Quantity A

$$x^{2}$$+$$y^{2}$$

Quantity B

1


In an isosceles triangle △ABC, ∠A=62°

Quantity A

∠B

Quantity B

∠C



The figure above shows a rectangle and five circles. Each circle is tangent to the other circles and to the sides of the rectangle that it touches. If the diameter of each circle is 4, what is the area of the rectangle?
n > 10,000

Quantity A

The thousands digit of $$\frac{n}{8}$$

Quantity B

7


When positive integer n is divided by 53, the remainder is 21, and when positive integer p is divided by 53, the remainder is 25. What is the remainder when the product np is divided by 53?

Quantity A

The remainder when 11,999,999 is divided by 12

Quantity B

11




A certain charity is conducting a fund-raiser. For the first $9,000 raised by the charity, Company B will contribute $1 for every $3 collected by the charity. For any amount over $9,000 raised by the charity, Company B will contribute $2 for every $5 collected by the charity. How much money must the charity raise in order to reach a total of $68,000, including the contribution from Company B?
x((75+y)+(15-y))=900

Quantity A

xy

Quantity B

10


The function f is defined by f(x) = $$2^{-x^{2}}$$ for all integers x. Which of the following could be the value of f(x)?

Indicate all such values.
Which of the following values is the largest?
3x-2k=7

9x-6k=21

Quantity A

x

Quantity B

k




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