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题目内容
A set consists of all three-digit positive integers with the following properties. Each integer is of the form JKL, where J, K, and L are digits; all the digits are nonzero; and the two-digit integers JK and KL are each divisible by 9. HOW many integers are in the set?
The number 24 has the property that it is divisible by its units digit, 4. How many of the integers between 10 and 70 are divisible by their respective units digits?
If $$x$$ and $$y$$ are positive integers and $$\frac{(8)(7)(6)(5)(4)(3)}{(2^{x})(3^{y})}$$is an integer, what is the greatest possible value of $$xy$$?
The integer N is greater than 1,000.

Quantity A

The remainder when N is divided by 3

Quantity B

The remainder when N is divided by 17
$$k$$ is an integer.

Quantity A

The remainder when $$k^{2}-k$$ is divided by $$2$$

Quantity B

$$0$$

Quantity A

The remainder when $$10^{8}$$+$$10^{9}$$+$$10^{10}$$+$$10^{11}$$ is divided by 11

Quantity B

0
n is a positive integer, and $$n^{2}$$ is divisible by 7.

Quantity A

The remainder when n is divided by 7

Quantity B

1
Both m and n are positive integers.

Quantity A

The remainder when (m+n) is divided by 2

Quantity B

The remainder when ($$m^{n}$$ is divided by 2
x < y, the remainder of x when divided by 9 is equal to the remainder of y when divided by 9.

Quantity A

The remainder when x is divided by 3

Quantity B

The remainder when y is divided by 3
The remainder is 30 when 6n is divided by 75, which of the following could be the remainder when 7n is divided by 75?

Indicate all such numbers.
n=4$$(x+20)^{2}$$-1, where x is a positive integer. Which of the following statements must be true?

Indicate all such statements.
What is the units digit of $$23^{21}$$-23?
What is the units digit of the positive difference between $$32^{19}$$ and 32?
What is the units digit of 5$$x^{3}$$, where x is a positive even integer?
What is the units digit of $$2^{2012}$$+$$3^{2012}$$+$$5^{2012}$$+$$7^{2012}$$?
What is the units digit of the positive difference between $$3^{7}*5^{4}*7^{11}$$ and $$4^{2}*5^{3}$$*11?
$$x$$, $$n$$ and $$k$$ are integers, $$0 \lt x \lt10^{7}$$, $$x=n^{k}$$, and the units digit of $$x$$ is $$5$$. $$x$$ is both a perfect square and a perfect cube. What is the value of $$x$$?
If $$T=4n^{2}+3$$ and $$n$$ is an integer, which of the following could be the units digit of $$T$$?

Indicate all such digits.
What is the remainder when $$3^{100}$$ is divided by 8?

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