If xyz > 0, is x > 0 ?

(1) xy > 0
(2) xz > 0

If m, r, x, and y are positive, is the ratio of m to r equal to the ratio of x to y ?

(1) The ratio of m to y is equal to the ratio of x to r.
(2) The ratio of m + x to r + y is equal to the ratio of x to y.

In the xy-plane, does the line with equation y = 3x + 2 contain the point (r, s) ?

(1) (3r + 2 - s)(4r + 9 - s) = 0
(2) (4r - 6 - s)(3r + 2 - s) = 0

Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?

(1) The average (arithmetic mean) salary of the managers on the task force is $5,000 less than the average salary of all employees on the task force.
(2) The average (arithmetic mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force.

If the symbol △ represents either addition or multiplication, which operation does it represent?

(1) a △ b = b △ a for all numbers a and b.
(2) a △ ( b – c ) = ( a △ b ) – ( a △ c )for all numbers a, b, and c.

On her way home from work, Janet drives through several tollbooths. Is there a pair of these tollbooths that are less than 10 miles apart?

(1) The first tollbooth and the last tollbooth are 25 miles apart.
(2) Janet drives through 4 tollbooths on her way home from work.

If x is a positive integer, what is the least common multiple of x, 6, and 9 ?

(1) The least common multiple of x and 6 is 30.
(2) The least common multiple of x and 9 is 45.

To fill an order on schedule, a manufacturer had to produce 1,000 tools per day for n days. What is the value of n ?

(1) Because of production problems, the manufacturer produced only 600 tools per day during the first 5 days.
(2) Because of production problems, the manufacturer had to produce 1,500 tools per day on each of the last 4 days in order to meet the schedule.

A certain theater has a total of 884 seats, of which 500 are orchestra seats and the rest are balcony seats. When tickets for all the seats in the theater are sold, the total revenue from ticket sales is $34,600. What was the theater's total revenue from ticket sales for last night's performance?

(1) The price of an orchestra seat ticket is twice the price of a balcony seat ticket.
(2) For last night's performance, tickets for all the balcony seats were sold, but only 80 percent of the tickets for the orchestra seats were sold.

If x is an integer, is (x² + 1)(x + 5) an even number?

(1) x is an odd number.
(2) Each prime factor of x² is greater than 7.