If the average (arithmetic mean) of x, y, and z is 7x and X ≠ 0, what is the ratio of x to the sum of y and z ?

Of all the students in a certain dormitory, ~$1 \over 2$~are first-year students and the rest are second-year students. If ~$4 \over 5$~ of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?

On the number line, the shaded interval is the graph of which of the following inequalities?

A positive integer is divisible by 9 if and only if the sum of its digits is divisible by 9.

If n is a positive integer, for which of the following values of k is 25 x 10ⁿ + k x 10²ⁿ divisible by 9 ?

3r ≤ 4s+5
|s|≤5 

Given the inequalities above, which of the following CANNOT be the value of r ?

　AB
＋BA
  AAC

In the correctly worked addition problem shown, where the sum of the two-digit positive integers AB and BA is the three- digit integer AAC, and A, B, and C are different digits, what is the units digit of the integer AAC ?

For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula

s=~$60k \over d^2$~ where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

(~$1 \over 5$~)² -(~$1 \over 5$~)(~$1 \over 4$~ ) =

One inlet pipe fills an empty tank in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it take to fill ~$2 \over 3$~ of the tank?

Which of the following lines in the xy-plane does not contain any point with integers as both coordinates?