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Quantity A:$$(2m+1)^{2}$$

Quantity B:$$(2(m+1))^{2}$$
2 < x < 5,$$\frac{1}{10}$$ < y < $$\frac{1}{5}$$

Quantity A: x+y

Quantity B: $$\frac{1}{x}$$+$$\frac{1}{y}$$
0 < a< b < 1 < c < d, c and d are both integers

Quantity A

$$a^{c-d}$$

Quantity B

$$b^{d-c}$$


0 < x < y

Quantity A

x+$$\frac{1}{x}$$

Quantity B

y+$$\frac{1}{y}$$


x and y are positive real numbers

Quantity A

$$\sqrt{(x^{2})(y^{5})}$$

Quantity B

$$\sqrt{(x^{3})(y^{5})}$$


$$ x\geq 0$$

Quantity A:$$2^{x}+2^{x}+2^{x}+2^{x}$$

Quantity B:$$4^{x}+4^{x}$$
x=$$2^{50}$$

y=$$2^{50}$$-1

z=$$2^{50}$$-2

Quantity A

$$x^{2}$$$$z^{2}$$

Quantity B

$$y^{4}$$


x > 0

Quantity A

$$2^{4}$$+$$\sqrt{x}$$

Quantity B

$$4^{2}$$+$$\sqrt{x^{2}}$$


Quantity A

$$3^{12}$$

Quantity B

$$5^{8}$$


The half-life period of 10 grams of a certain radioactive element is an hour. If the mass of the element drops to 0.1~1 grams after N hours, then N COULD be which of the following?

Indicate all such values.
If n is a positive integer and $$0.5^{n}$$ < 0.0002, what is the least possible value of n?
If a is an integer greater than 1, what is the possible value of $$(1+\frac{1}{a})^{-1}$$?

Quantity A

$$2^{-2002}$$ + $$2^{-2003}$$

Quantity B

$$2^{-2004}$$


If $$n$$ is an integer, and $$5^{n}$$+$$5^{-n}$$=$$\frac{626}{25}$$,how many values of $$n$$ satisfy the equation?
n > 0

Quantity A

$$n^{10}$$

Quantity B

$$n^{12}$$


n is a positive integer

Quantity A

The average (arithmetic mean) of $$2^{n}$$,$$2^{n+1}$$,$$2^{n+2}$$,$$2^{n+3}$$,$$2^{n+4}$$

Quantity B

The median of $$2^{n}$$,$$2^{n+1}$$,$$2^{n+2}$$,$$2^{n+3}$$,$$2^{n+4}$$


List P consists of the 5 numbers $$3^{n}$$, $$3^{n+1}$$, $$3^{n+2}$$, $$3^{n+3}$$, $$3^{n+4}$$ are five numbers, where n is a positive integer.

Quantity A

The average (arithmetic mean) of the numbers in P

Quantity B

The median of the numbers in P




n is a positive integer.

Quantity A

$$(\frac{1}{3})^{n}$$

Quantity B

$$(\frac{1}{10})^{n}$$


1 < a < b < c < 2

What of the following is the closest to the estimated value of a+b*$$10^{6}$$+c*$$10^{12}$$?
What is the number of integers between 1 and 226,inclusive,that are both multiples of 4 and perfect square numbers?

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