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What is the greatest prime factor of 510?
A certain factory has 8 identical machines that process a certain chemical product at the same constant rate. If it takes 40 hours for 5 of the machines, working simultaneously at their constant rate, to process a totaI of one ton of the product, how many hours does it take the 8 machines, working simultaneously at their constant rate, to process a total of one ton of the product?

_____hours
x is a negative integer

Quantity A

$$(2^x)^2$$

Quantity B

$$(x^2)^x$$


A certain number of toys were packed into x boxes so that each box contained the same number of toys, with no toys left unpacked. If 3 fewer boxes had been used instead, then 12 toys would have been packed in each box, with 5 toys left unpacked. What is the value of x ?


The boxplot above summarizes a list of 240 numbers. Which of the following statements must be true?

Indicate all such expressions.
n > 2

List M={2, n, n, n}

List N={2, 2, 2, n}

Quantity A

The standard deviation of List M

Quantity B

The standard deviation of List N


The probability that a component fails during first use is 0.1. If the component doesn`t fail during first use, then the probability that the component won`t fail in the following six months is 0.8

Quantity A

The probability that the component won`t fail within six months

Quantity B

0.75


If a two-digit number that has x as the tens digit and y as the units digit is multiplied by 5, then the value of the product is
N is an integer between 200 and 300, with tens digit x and units digit 5.

Quantity A

$$\frac{N}{5}$$

Quantity B

40+2x


x and y are positive integers, and x=10y+2

Quantity A

The value of the tens digit of x

Quantity B

The value of the units digit of y


In each round of a certain game, either 1, 3, 7, or 10 points are awarded to the winner of the round. Which of the following CANNOT be the total number of points awarded to the winner of three rounds?
$$q$$, $$r$$ and $$s$$ are consecutive positive integers and $$q \lt r \lt s$$.

Quantity A

$$\frac{qs}{r}$$

Quantity B

$$r-\frac{1}{r}$$


m is an odd number and greater than 1

Quantity A

The greatest prime factor of 2m

Quantity B

The greatest prime factor of $$m^{2}$$




N is an integer between 10 and 100. When N is divided by 4, 6, and 7, the remainder is 2.

Quantity A

The remainder when N is divided by 11

Quantity B

9


When r percent is expressed as a fraction and the fraction is reduced to lowest terms, the result is $$\frac{n}{20}$$, where n is an integer. Which of the following could be the value of r?
If $$y=1-\frac{1}{x}$$, where $$x$$ is a nonzero integer, which of the following could be the value of $$y$$?

Indicate all such values.
If k and n are each positive integers between 12 and 30, then $$\frac{5+k}{7+n}$$will be equal to $$\frac{5}{7}$$for how many pairs of (k, n)?
$$k \gt m$$

Quantity A

|$$m$$| - |-$$k$$|

Quantity B

|$$k$$| - |-$$m$$|


|x| < 1-x

Quantity A

x

Quantity B

0


In a certain university, 60 percent of all sophomores are liberal arts majors, 24 percent are education majors, and the rest are majoring in other subjects or have not yet chosen a major. At the university, 55 percent of all sophomores are currently taking a psychology course. If x percent of all sophomores are liberal arts majors who are currently taking a psychology course, what is the least possible value of x?

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