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In a plane, points P and Q are 20 inches apart. If point R is randomly chosen from all the points in the plane that are 20 inches from P, what is the probability that R is closer to P than it is to Q ?
m and n are integers.

Quantity A

$$\sqrt{( 10^{2m} )}\sqrt{( 10^{2n} )}$$

Quantity B

$$10^{mn}$$


$$\frac{60!-59!}{58!}=$$
n is an integer.

Quantity A

$$(-1)^{n}(-1)^{n+2}$$

Quantity B

1


Which of the following is most nearly equal to$$\frac{2.5*10^{6}}{2.5*10^{6}-3.5*10^{-6}}$$
Amy and Jed are armong the 35 people, who are standing in a line, one behind the other, waiting to buy movie tickets. The number of people in front of Amy plus the number of people behind Jed is 24. If there are 15 people behind Amy, including Jed, how many people are in front of Jed?
For which of the following values of x is the units digit of the product $$(2)(3^{x})$$ equal to 4?
How many 6-digit integers greater than 400,000 can be formed such that each of the digits 2, 3, 4, 5, 6, and 7 is used once in each 6-digit integer?
What's the number of n that are either multiples of 5 or multiples of 7 from 1 to 1000, inclusive?
Which of the following must be a factor of the product of 5 consecutive positive integers?

Indicate all such numbers.
m is a positive integer

Quantity A

The remainder when the sum of $$1999^{m}$$ and $$2001^{m}$$ divided by 7

Quantity B

4


The ratio of A to B is 1:4 before a chemical reaction,   $$\frac{1}{4}$$of A was transformed into B, while at the same time,  $$\frac{1}{4}$$ of B was transformed into A, then what is the ration of A to B after the reaction.

Give your answer as a fraction.
x > y > $$\sqrt{2}$$

Quantity A

x*y

Quantity B

x + y


A regular hexagon is inscribed in a circle,the diameter of the circle is d. What is the perimeter of the hexagon?
List L consists of 11 different positive numbers. The sum of the 6 smallest numbers in L is 35, and the sum of the 6 greatest numbers in L is 125. If the sum of all the numbers in L is 142, what is the median of the numbers in L?


The figure consists of 14 identical equilateral triangular regions. If the area of the figure is $$56\sqrt{3}$$, what is the perimeter of the figure?

In the figure, the square ENFM is inscribed in the rectangle ABCD, E and F are the midpoints of side AB and DC. If the area of ENFM is 64, G and H are the midpoints of AD and BC, and GM=NH=5, then what is the area of ABCD?

The figure above shows five congruent circles each with radius 2 such that each of the five circles is tangent to two other congruent circles and to a smaller inner circle. The perimeter of the figure is composed of 5 line segments of length X and 5 circular arcs of length Y. What is the perimeter of the figure?

If 20 red cubes and 7 white cubes, all of equal size, are fitted together to form one large cube, as shown above, what is the greatest fractional of the surface area of the large cube that could be red?

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