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Carolyn took out a one-year loan for $15,000 at 8 percent simple annual interest. She repaid the total amount, including the interest, by making 12 equal monthly payments on the last day of each month beginning in January. At the beginning of which of the following months did Carolyn have less than $10,000 of the total amount left to the repaid?

Indicate ALL such months.
For 7 soccer ball teams, each of them has to play with all the other teams. However, to decide which team wins, every two teams have to play 3 rounds and the team that win for the most times will ultimately win. How many rounds of game do all teams have to play in total?
There are n positive integers. The sum of the numbers is greater than 48, while the arithmetic average of the numbers is 1.2. What is the least value of n?
If $$1 \lt r \lt s \lt t$$, which of the following is closest in value to the product $$rst$$?
x≠0

Quantity A

$$ax^{4}$$

Quantity B

$$(ax)^{4}$$


n is a positive integer.

Quantity A

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

Quantity B

$$3(\frac{1}{4^{n}})$$


If $$x \geq 0$$, $$y \geq 0$$, and $$x^{2}$$+$$y^{2}$$=$$1$$, which of the following statements must be true?

Indicate all such statements.
The ratio of the lengths of sides of a certain triangle is 3 : 5 : 7.

Quantity A

Degree of the greatest angle of this triangle

Quantity B

85°


The lengths of the sides of triangle $$RST$$ are $$3$$, $$4$$, and $$y$$. Which of the following inequalities specifies those values of $$y$$ for which each angle measure of triangle $$RST$$ is less than $$90°$$?
d≠0

Quantity A

The area of a square region with sides of length d

Quantity B

The area of a circular region with diameter d


Quantity A

The range of 10 consecutive integers

Quantity B

10


x and y are integers. 4 ≤ x < 7< y ≤ 12, what`s the range of $$(x-y)^{2}$$?
In the sophomore class of a certain university, 85 percent of the students were taking English composition, 70 percent were taking biology, and 60 percent were taking both English composition and biology. What percent of the students in the class were taking neither English composition nor biology?
The number of elements in set A is 60 percent greater than the number of elements in set B, and the number of elements in the set A ∩ B is 15. If set B contains at least one element that is not in set A, what is the least possible number of elements in the set A U B?
30% of members in club R are also in club H and 20% of club H are also in club R.

Quantity A

The number of members in club H

Quantity B

The number of members in club R


$$a_1, a_2, a_3,........a_n,.........$$

In the sequence shown, $$a_1$$=6

and for each integer n greater than 1, $$a_n$$ is defined by

If $$n$$ is even, then $$a_n=2+a_{n-1}$$ (n≥2)

If $$n$$ is odd, then $$a_n=-8+a_{n-1}$$ (n≥2)

What is the value of $$a_7$$?
If $$a_1$$=2, $$a_2$$=3, $$a_n$$=$$a_{n-1}$$*$$a_{n-2}$$(n≥3),then $$a_8$$ is?
What is the value of $$\frac{51!-50!}{50!-49!}$$?

Give your answer as a fraction.
How many positive divisors of 210 can be expressed as a product of two prime factors?
How many positive factors of 210 can be expressed as the product of two prime numbers?

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