If a > 0, b > 0, and c > 0, is a(b - c) = 0 ?

(1) ~$b-c=c-b$~

(2) ~$\frac{b}{c}=\frac{c}{b}$~

Is positive integer n divisible by 3 ?

(1) ~$\frac{n^{2}}{36}$~ is an integer.
(2) ~$\frac{144}{n^{2}}$~ is an integer.

If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece?

(1) The length of the longest piece is twice the length of the shortest piece.
(2) The sum of the lengths of the two shorter pieces is 15 meters.

If n is an integer, is ~$\frac{n}{7}$~ an integer?

(1) ~$\frac{3n}{7}$~ is an integer.
(2) ~$\frac{5n}{7}$~ is an integer.

Is the positive integer n odd?

(1) n = 2k + 1, where k is a positive integer.
(2) 2n + 1 is an odd integer.

A certain movie depicted product A in 21 scenes, product B in 7 scenes, product C in 4 scenes, and product D in 3 scenes. The four product manufacturers paid amounts proportional to the number of scenes in which their product was depicted in the movie. If each manufacturer paid x dollars per scene, how much did the manufacturer of product D pay for this advertising?

(1) The manufacturers of products A and B together paid a total of $560,000 for this advertising.
(2) The manufacturer of product B paid $60,000 more for this advertising than the manufacturer of product C paid.

Does set S contain any even numbers?

(1) There are no prime numbers in S.
(2) There are no multiples of 4 in S.

If x and y are integers, is the value of x(y + 1) even?

(1) x and y are prime numbers.
(2) y > 7

If x and y are greater than 0, is x = 1 ?

(1) ~$\frac{x}{y}$~ = 1
(2) xy = 1

One member of a committee of 5 men and 8 women resigned and was not replaced. What fraction of the remaining members were men?

(1) ~$\frac{7}{12}$~ of the remaining members were women.
(2) The member who resigned was a woman.