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If n,k, and r are positive integers such that $$n^{k}$$=10r+3, which of the following could be the value of n?
The repeating decimal $$1.\overline{ab}$$, where a and b are different digits, is equivalent to the fraction $$\frac{n}{d}$$, where n and d are positive integers whose greatest common factor is 1. What is the greatest possible value of n+d ?
Jamie claimed that if n is a positive integer, then $$4n^{2}- 3$$ must be a prime number. Which of the following values of n could be used as a counterexample to show that Jamie's claim is not true?

Indicate all such values.
The integer k is the product of four different prime numbers. If k divided by 22 is a multiple of 13, which of the following could be equal to k divided by 11?
x> 0

Quantity A

$$\frac{1}{9}$$ of x

Quantity B

11 percent of x


What is the least possible product of 4 different integers, each of which has a value from -5 to 5, inclusive?
The product of nine consecutive integers is 0.

Quantity A

The sum of the nine integers

Quantity B

30


How many of the eleven integers greater than $$10^{7}$$ and less than $$10^{7}$$+12 are divisible by 11?
n is a positive even integer

Quantity A

The greatest possible value of x such that $$2^{x}$$ is a factor of n(n+2)(n+4)(n+6)

Quantity B

The greatest possible value of y such that $$2^{y}$$ is a factor of n(n+2)(n+4)(n+6) + 320


Claire regularly backs up both of the computers that she owns. On the first day of June, she backs up both computers. Thereafter, she backs up one of the computers every sixth day during June (that is, on June 7 and so on), and she backs up the other computer every eighth day during June. On how many of the 30 days in June $$\underline{does}$$ she not back up either of the two computers.

_____days
r is the remainder obtained when dividing $$7^{995}+7^{50}-4$$ by 7

Quantity A

r

Quantity B

4


15,000 is divisible by $$25a^{k}b^{2}$$, where a and b are prime numbers, a ≠ b, and k is a positive integer.

Quantity A

The greatest possible value of k

Quantity B

3


Of the artists in the graphics department of a multimedia company, 60 percent are working or digital projects, and the remaining artists are working on hard-copy projects. Of the artists working on digital projects. 20 percent attended a fine arts school. Of the artists working on hard-copy projects, 10 percent attended a fine arts school. Of the artists in the graphics department who attended a fine arts school, what percent are working on digital projects?


Each of the eight faces of an octahedron is labeled with a different number form 1 to 8. The octahedron was rolled 36 times, and the results are shown in the graph above, where the "Number Rolled" is the number on the top face of the octahedron after it was rolled. If the octahedron is to be rolled 4 additional times, what is the greatest possible value of the average (arithmetic mean) of the 40 number rolled?
$$7^{n}$$ is a positive integer whose units digit is 9. Which of the following can be the value of n?

Indicate all such numbers.
How many different positive 7-digit integers begin with 555 and end with 22?
x is an integer greater than 1.

$$N=(15)^{x}(4)^{x-1}$$?

Quantity A

The tens digit of N

Quantity B

0


If $$\sqrt{108}$$ =a*$$\sqrt{b}$$, where a and b are positive integers.

Quantity A

The number of the possible values of a+b

Quantity B

3


$$x=(8q)^{n}$$, where q and n are integers greater than 5 and q is odd.

Quantity A

The ratio of the number of odd positive factors of x to the number of even positive factor of x

Quantity B

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




The boxplot shown summarizes the numbers in a certain list, where all the numbers are positive integers. Based on the boxplot, which of the following statements are true?

Indicate all such statements.

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