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How many 6-digit integers greater than 321,000 can be formed such that each of the digits 1, 2, 3, 4, 5, and 6 is used once in each 6-digit integer?


The figure above represents a game board with a chip at staring point M. On successive plays, the chip may be moved along the lines from one labled point to an adjacent labled point, but may not be moved to the same point twice. Along how many different paths can the chip be moved from M to N in this game?

Quantity A

The number of ordered triples ($$x_1$$, $$x_2$$, $$x_3$$), where $$x_1$$, $$x_2$$ and $$x_3$$ are non-negative integers such that $$x_1$$+$$x_2$$+$$x_3=9$$

Quantity B

$$55$$


The vehicles of Company W are numbered consecutively from 1 to 650. The vehicles with a number that ends with one of the digits 1, 2, 3, 4, or 5 are used by Division 1. Vehicles with a number between 130 and 389, inclusive, are trucks. What percent of the company vehicles are trucks used by Division 1?
Let $$n$$ be a nonnegative integer such that when $$6n$$ is divided by $$75$$, the remainder is $$30$$. Which of the following is a list of all possible remainders when $$7n$$ is divided by $$75$$?
The sum of three different positive integers is 11.

Which two of the following statements together provide sufficient information to determine the three integers?

Indicate two such statements.
If $$x \geq 0$$, $$y \geq 0$$, and $$x^{2}$$+$$y^{2}$$=$$1$$, which of the following statements must be true?

Indicate all such statements.
The lengths of the sides of triangle $$RST$$ are $$3$$, $$4$$, and $$y$$. Which of the following inequalities specifies those values of $$y$$ for which each angle measure of triangle $$RST$$ is less than $$90°$$?
During a certain month, $$20$$ percent of all the electricity used by a household was used by the water heater. The cost per kilowatt-hour of the electricity used by the water heater was half the cost per kilowatt-hour of the rest of the electricity used. For that month, the cost of the electricity used by the water heater was what fraction of the cost of the electricity used by the household?
Let x and y be positive integers such that when y is divided by x, the remainder is 4, and when y+10 is divided by x, the remainder is 2. Which of the following must be an integer?
The average (arithmetic mean) of the values of the homes in Town A is $100,000. The average of the values of the homes in Town B is $150,000. The number of homes in Town A is between 2 times and 3 times the number of homes in Town B. Which of the following values could be the average of the values of the homes in Town A and Town B combined?

Indicate all such values.
A hexagon with sides of equal length and interior angles of equal measure is inscribed in a circle. If the perimeter of the hexagon is 12, what is the perimeter of an equilateral triangle inscribed in the same circle?
From 1989 to 1992, there was a 10 percent increase in the percent of families that owned directly held stocks. Which of the following is closest to the percent of families who owned directly held stocks in 1989?
If 38.7 percent of the families who owned a home owed money on a home mortgage loan or home equity loan, or both, approximately what percent of United States families owned homes free of both home mortgage and home equity loans?
In 1992, if 7.9 percent of the families in the survey owned both savings bonds and mutual funds, what percent owned neither savings bonds nor mutual funds?
The top surface of a certain 1-inch-thick oak board is 8 inches wide and has an area of 960 square inches. What is the price of this board? (1 foot=12 inches)
For the 6-inch-wide boards listed, which of the following is closest to the ratio of the price per linear foot of the least expensive type of board to the price per linear foot of the most expensive type of board?
The price of one maple board that is 8 inches wide and n feet long is $1.50 less than the price of 2 maple boards that are each 4 inches wide and n feet long. What is the value of n?
The different committees consist of 8, 10 and 13 people, respectively. If N is the total number of different people in the 3 committees combined, what is the least possible value of N?
An urn contains 4 red balls, 8 green balls and 2 yellow balls. Five balls are randomly selected WITH replacement from the urn. What is the probability that 1 red ball, 2 green balls, and 2 yellow balls will be selected?

Give your answer as a fraction.

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