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54 is divisible by $$3^{N}$$, while 192 is divisible by $$3^{K}$$ (N and K are both integers)

Quantity A

N


Quantity B

K


The "reflection" of a positive integer is obtained by reversing its digits. For example, 321 is the reflection of 123 The positive difference between a five-digit integer and its reflection must be divisible by which of the following?
If a, b, c are three consecutive positive even integers, which of the following must be an integer?

Indicate all that`s possible.
If n is a positive integer greater than 1, then n($$n^{2}$$-1) must be a multiple of which of the following integers?

Indicate all such numbers.
$$s$$ and $$t$$ are both positive integers

Which of the following statements individually provide(s) sufficient additional information to determine $$\frac{t}{s}$$ is an integer?

Indicate all such statements.
The decorating committee for a dance plans to fringe the 3-inch-wide end of a streamer by making small cuts every 1/16 inch. How many cuts must be made to fringe the end?
How many positive integers less than 100 have a remainder of 2 when divided by 13?
x is a positive integer. When x is divided by 2, 4, 6 or 8, the remainder is 1.

Quantity A

x

Quantity B

24


If the remainder is 27 when an integer is divided by 36, then the integer must be a multiple of which of the following integer?
If the remainder is 1 when integer n (n>1) is divided by 3, then ($$n^{2}$$+n-2) must be divisible by which double-digit number?

Indicate all such numbers.
x is a positive integer greater than 1. k is the remainder when $$x^{3}$$-x is divided by 3.

Quantity A

k

Quantity B

1


p is a positive odd number, while 5 is a factor of p+$$p^{2}$$

Quantity A

The remainder when p is divided by 5

Quantity B

0


When the even integer $$n$$ is divided by $$7$$, the remainder is $$3$$.

Quantity A

The remainder when $$n$$ is divided by $$14$$

Quantity B

$$10$$


k and n are both positive even integers

Quantity A

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

Quantity B

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


X=12$$3^{4}$$-12$$3^{3}$$+12$$3^{2}$$-123

What is the remainder when X is divided by 122?
What is the remainder when (12$$3^{3}$$+12$$4^{2}$$-12$$3^{2}$$+124) is divided by 122?
n is a positive integer. n is not divisible by 4. n is not divisible by 5.

Quantity A

The remainder when n is divided by 4

Quantity B

The remainder when n is divided by 5


n is a positive integer

Quantity A

The remainder when n is divided by 7

Quantity B

The remainder when 2n is divided by 7


What's the unit digit of the positive difference between $$27^{13}$$ and 27?
n, k and r are all positive integers

If $$n^{k}$$=10r+3, then k could be?

Indicate all that are possible.

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