Is ~$\sqrt{\left ( x-5 \right )^{2}}=5-x$~ ?

(1) ~$-x\left | x \right |> 0$~
(2) ~$5-x> 0$~

If v and w are different integers, does v = 0 ?

(1) vw= v²
(2) w = 2

If |x + 2| = 4, what is the value of x ?

(1) ~$x^{2}\neq 4$~
(2) ~$x^{2}=36$~

The lifetimes of all the batteries produced by a certain company in a year have a distribution that is symmetric about the mean m. If the distribution has a standard deviation of d, what percent of the distribution is greater than m + d ?

(1) 68 percent of the distribution lies in the interval from m - d to m + d, inclusive.
(2) 16 percent of the distribution is less than m - d.

X and Y are sets of positive integers. Is the greatest integer in X greater than the greatest integer in Y ?

(1) X is a set of 5 consecutive odd integers, each less than 20.
(2) Y is a set of 3 consecutive even integers, each less than 15.

In the rectangular coordinate system, are the points (r, s) and (u, v) equidistant from the origin?

(1) r + s = 1
(2) u = 1 - r and v = 1 - s.

What is the value of a⁴ - b⁴ ?

(1) a² - b² = 16
(2) a + b = 8

What is the ratio of p to r ?

(1) The ratio of p to 3r is 5 to 9.
(2) The sum of p and r is 16.

If ~$x+y\neq 0$~, what is the value of ~$\frac{ax+ay}{x+y}$~ ?

(1) x = 4 and y = 5.
(2) a = 6

Is the integer n a multiple of 15 ?

(1) n is a multiple of 20.
(2) n + 6 is a multiple of 3.