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$$a=\frac{x}{x+y+z}$$ , $$b=\frac{y}{x+y+z}$$ , $$c=\frac{z}{x+y+z}$$


Quantity A

The average of a, b and c

Quantity B

$$\frac{1}{2}$$


A box contains 10 red balls and 6 blue balls. A volunteer takes two balls one by one without replacement. What is the probability that the two balls are both red?
Give your answer as a fraction.
If a, b, c are three consecutive positive even integers, which of the following must be an integer?

Indicate all that`s possible.
1 < x+y

Quantity A

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

Quantity B

1


The coordinates of three points in an x-y rectangular coordinate system are (0,3), (3,3b) and (b,3) respectively (b is a constant). If the area of the triangle is 18 when connecting the three coordinates, then b equals?

Indicate all such possible values.
Among 120 students, $$\frac{3}{5}$$ take Course A, while $$\frac{1}{2}$$ take Course B. The number of students who take Course A but not Course B could be?
Indicate all such possible numbers.
All of the 80 science students at a certain school are enrolled in at least one of three science courses: biology, chemistry, and physics. There are 60 students enrolled in physics, 50 students enrolled in chemistry, and 35 students enrolled in biology. None of the students are enrolled in all three courses. Which of the following could be the number of students enrolled in both chemistry and biology?
Indicate all such possible values.
Someone needs to import a number of sets of bottles. Each bottle charges $12.04, and it also charges $4.8 for shipping each set (not single bottle but a whole set). The standard deviation of numbers of bottles in each set is 1.5. What is the standard deviation of the prices for each set?
Give your answer as a decimal.
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.

Quantity A

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

Quantity B

70


Anne pays 20 percent more for a wholesale widget than Bart pays. Anne`s retail price per widget is 8 percent less than the wholesale price she paid. Bart`s retail price per widget is 12 percent greater than the wholesale price he paid.

Quantity A

Anne's retail price

Quantity B

Bart's retail price


One day in 1997 at a gas station in the United States near the border of Canada, gasoline was selling for $1.20 per gallon (United States dollars). On that day, 1 United States dollar could be exchanged for 1.25 Canadian dollars. If gasoline was being sold at an equivalent rate at a gas station across the border in Canada, which of the following calculations gives an approximate price, in Canadian dollars, for a liter of gasoline at the Canadian gas station that day? (1 gallon is approximately 3.785 liters.)
Three printers, $$X_1$$, $$X_2$$ and $$X_3$$, work only at their respective constant rates. Working together,$$X_1$$, $$X_2$$ and $$X_3$$ can complete a certain job in 9 hours; working together, $$X_2$$ and $$X_3$$ can complete the same job in 12 hours. Working alone, how many hours will it take $$X_1$$ to complete the job?
Which of the following is equal to an integer raised to the third power?
x, n and k are all integers, 0 < x < $$10^{7}$$, x=$$n^{k}$$

If the units digit of x is 5, and x could be transformed into both the square of an integer and the cube of an integer, then x must be?
An apartment building contains 60 apartments. Of the apartments in the building,$$\frac{3}{5}$$ have one bedroom and the rest have 2 or 3 bedrooms. If the 60 apartments have a total of 94 bedrooms, how many of the apartments have 3 bedrooms?


ABCDE is a regular pentagon.

Quantity A

x

Quantity B

36


List A include five numbers: x, x+1, x+1, x+1, x+2

List B can be achieved by adding 3 times the range of List A to each data in List A.

The average of all the numbers in List B is how much higher than that of List A?
Larry and Tony work for different companies. Larry`s salary is the $$90^{th}$$ percentile of the salaries in his company, and Tony`s salary is the $$70^{th}$$ percentile of the salaries in his company.

Which of the following statements individually provide(s) sufficient additional information to conclude that Larry`s salary is higher than Tony`s salary?

Indicate all such statements.
Among all the 24 different positive four-digit integers formed out of 6, 7, 8, 9, at which place will 8697 rank from the least to the greatest?

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