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.

An integer greater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite?

(1) The tens digit of n is a factor of the units digit of n.
(2) The tens digit of n is 2.

During a one-day sale, a store sold each sweater of a certain type for $30 more than the store's cost to purchase each sweater. How many of these sweaters were sold during the sale?

(1) During the sale, the total revenue from the sale of these sweaters was $270.
(2) During the sale, the store sold each of these sweaters at a price that was 50 percent greater than the store's cost to purchase each sweater.

An attorney charged a fee for estate planning services for a certain estate. The attorney's fee was what percent of the assessed value of the estate?

(1) The assessed value of the estate was $1.2 million.
(2) The attorney charged $2,400 for the estate planning services.

At a certain company, the average (arithmetic mean) number of years of experience is 9.8 years for the male employees and 9.1 years for the female employees. What is the ratio of the number of the company's male employees to the number of the company's female employees?

(1) There are 52 male employees at the company.
(2) The average number of years of experience for the company's male and female employees combined is 9.3 years.