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Dr. Mosher call the roll ten days in a row. If Candy attended 8 times, Sam attended 7 times, and Amy attended 6 times. If they show in class simultaneously in only one day, and at least 1 student attend each day`s course, how many days in which exactly two of them attended?
There are 5!, or 120, ways of arranging 5 different solid-colored flags side by side. If the colors of the flags are red, blue, yellow, green, and orange, how many of those arrangements have either the red flag or the blue flag in the middle position?
What is the units digit of $$2^{2222}$$?

Quantity A

The number of positive factors of 87

Quantity B

The number of positive factors of 97


1 < x+y

Quantity A

$$x^{2}$$+$$y^{2}$$

Quantity B

1



Quantity A

x+y

Quantity B

$$\sqrt{(x^2+y^2)}$$



In a circle, the area of the shaded area is 16π

Quantity A

The radius of the circle

Quantity B

5.5


What is the probability that someone randomly selects a number from 100 to 159 inclusive such that the tens digit of the selected number is no more than 3 and the units digit of the selected number is no more than 4?
Give your answer as a fraction.
A telephone system has n telephone lines. For each of the n lines, the event that the line will fail during a certain reliability test has probability 0.3, and these n events are independent. If the probability that at least one of the n lines will not fail during the reliability test is greater than 0.99, what is the minimum value of n?
0 < a < b < 1

c and d are positive integers such that c < d

Quantity A

$$a^{c-d}$$

Quantity B

$$b^{d-c}$$


n > 10,000

Quantity A

The thousands digit of $$\frac{n}{8}$$

Quantity B

7


A certain truck takes 10 trips to transport 2,000 cartons from warehouse A to warehouse B. For each trip except the 10th trip, the truck is loaded to its full carrying capacity of x cartons. On the 10th trip, the truck is loaded with the remaining cartons.

Quantity A

x

Quantity B

210


Quantity A

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

Quantity B

70


Which of the following statements are true for all integers a and b?

Indicate all such statements.
If x, y and z are consecutive positive integers and if x+y+z is even, how many of the four integers xy, yz, zx, and xyz are even?
Which of the following could be a factor of $$\frac{9!}{(6!*3!)}$$?

Indicate all such numbers.
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?
x and y are prime numbers

x+y is odd

x < y

Quantity A

x

Quantity B

3


x ≠ -1 and x ≠ 0

Quantity A

$$\frac{1}{1+\frac{1}{x}}$$

Quantity B

$$\frac{x}{x+1}$$


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