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If the least of 19 consecutive even integers is -14, then what is the median of these integers?

Quantity A

The number of positive integers between 0 and 10, inclusive

Quantity B

The number of odd integers between 10 and 30, inclusive


If the median of 15 consecutive even integers is m, what is the greatest integer of the 15 numbers?
X is the sum of all the even positive integers less than or equal to 50.

Y is the sum of all the odd positive integers less than or equal to 49.

Quantity A

X-Y

Quantity B

25


If k, n and p are consecutive positive even integers and k < n < p, which of the following must be an integer?
List K consists of 20 consecutive odd integers, list L consists of 20 consecutive even integers, and list M consists of 20 consecutive multiples of 3. The least integer in L is 9 greater than the greatest integer in K, and the greatest integer in L is 10 greater than the least integer in M.

Quantity A

The range of the integers in K and L combined

Quantity B

The range of the integers in L and M combined


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


k is an integer such that 33 ≤ k ≤ 35

Quantity A

The number of positive factors of k, including 1 and k

Quantity B

4


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 only 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?
z is a positive integer. When 17 is divided by z, the remainder is 2.

Quantity A

z

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?

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