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$$p$$ and $$r$$ are different prime numbers greater than 3

Quantity A

The number of positive factors of $$pr^{2}$$

Quantity B

The number of positive factors of $$(p+3)(r+3)$$


S is the set of all integers x such that 100 < x < 200.

Quantity A

The number of integers in S that are multiples of 5, but NOT multiples of 4

Quantity B

15


Set Q consists the integers from 1 to 1,000 that are divisible by 3. How many integers in Q are not divisible by 5?
If an integer is randomly selected from integers between 100 and 1000 inclusive, what's the probability that the number is divisible by 7?

Give your answer as a fraction.
What's the number of n that are either multiples of 5 or multiples of 7 from 1 to 1000, inclusive?

Quantity A

The sum of the least and the greatest three-digit integer that can be divisible by 3

Quantity B

1100


Which of the following could be the value of x to make sure that $$x^{3}-x$$ is divisible by 10?

Indicate all such values.
If x=$$10^{6}$$-1,which of the following is not the factor of x?
If $$p$$ is an odd integer,and if $$5$$ is a factor of $$p+p^{2}$$,which of the following might be the remainder when $$p$$ is divided by $$5$$?

Indicate all such numbers.
If the tens digit and units digit of a three-digit integer N is x and y, respectively, then (N-100x-y) must be a multiple of which of the following integers?

Indicate all such values.
The integer n is the product of five consecutive positive integers. Which of the following integers must be a factor of n?

Indicate all such numbers.
The remainder is 10 when the sum of a positive integer n and 11 is divided by 12.

Quantity A

n

Quantity B

11


A positive integer n divided by 3 has a remainder of 2, and 50 < n < 60, Which of the following could be the value of n?

Indicate all such values.
n is an integer between 100 and 200 such that when n is divided by 9, the remainder is 4. What is the number of possible values of n?
The remainder is 10 when (x + 11) is divided by 12 (where x is a positive integer)

Quantity A

x

Quantity B

11


x is a positive integer

Quantity A

The remainder when(x+1)(x+2)(x+3)is divided by 5

Quantity B

1


If now the hour hand is at 4, then after 1196 hours, what number will the hour hand be at?
When the integer k is divided by 6, the remainder is 4. What is the remainder when 8k is divided by 6?
The units digit of a positive integer n is 8

Quantity A

The units digit of 3n

Quantity B

The units digit of $$n^{3}$$


The units digit of $$23^{n}$$ is 7, and if 9 ≤ n ≤ 14, what could be the value of n?

Indicate all such values.

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