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Quantity A

The number of odd integers between $$\sqrt{12}$$ and $$12^{2}$$

Quantity B

70


Which of the following could be a factor of $$\frac{9!}{(6!*3!)}$$?

Indicate all such numbers.
If $$2^{n}$$ is the highest power of 2 that is a divisor of the product ($$10^{2}$$) ($$12^{5}$$) ($$18^{6}$$), then n=
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) + 360


Quantity A

The number of positive divisors of 16,000

Quantity B

The number of positive divisors of 18,000


What is the sum of all the integers between 100 and 400 that have exactly three positive factors?
How many positive integers less than 40 have six positive factors?
The positive integer x is 7 greater than a multiple of 13, and 2512 < $$x^{2}$$ < 3596

Quantity A

x

Quantity B

55


n is a positive integer and 26n is a multiple of 12.

Quantity A

n

Quantity B

11


Set A includes all the integers from 1 to 100, inclusive with the exception of all the multiples of 3.

Quantity A

The number of multiples of 7 in the set

Quantity B

10


When the integer n is divided by 33, the remainder is 24. Which of the following must be a divisor of n?
The remainder is 2 when 17 is divided by positive integer k.

Quantity A

k

Quantity B

4


n is an integer such that 111 ≤ n ≤ 114.

Quantity A

The remainder when n is divided by 31

Quantity B

16


X=1!+2!+3!+4!+5!+6!+7!+8!+9!+10!

What is the remainder when X is divided by 20?
Let $$\frac{1}{3}$$+$$\frac{1}{5}$$+$$\frac{1}{7}$$+$$\frac{1}{9}$$+$$\frac{1}{11}$$=$$\frac{m}{(3)(5)(7)(9)(11)}$$, where m is a positive integer. What is the remainder when m is divided by 5?
N and P are both positive integers.

The remainder when N is divided by 53 is 21.

The remainder when P is divided by 53 is 25.

What is the remainder when N*P is divided by 53?
0 < k < n, $$k^{2}$$ + n is even

Quantity A

The remainder when n-k is divided by 2

Quantity B

1


s is a positive integer

r is a positive odd integer

Quantity A

The remainder when (s+r)(r+1) is divided by 2

Quantity B

1


k is a positive integer

Quantity A

The remainder when k is divided by 7

Quantity B

The remainder when 2k is divided by 7


Let n be an integer greater than 30. When n is divided by 12, the remainder is 11. What is the remainder when (6n+1) is divided by 9?

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