If R = 1 + 2xy + x²y², what is the value of xy ?

(1) R = 0
(2) x > 0

Three friends rented a car for a week and divided the cost equally. What was the total cost of renting the car?

(1) If the three friends had kept the car for a second week, they could have obtained the two-week rate, which was 1.5 times the cost of a one-week rental.
(2) If a fourth friend had joined the three friends and the cost had been divided equally among the four friends, the cost to each of the original three would have been reduced by $15.

A combined total of 55 lightbulbs are stored in two boxes; of these, a total of 7 are broken. If there are exactly 2 broken bulbs in the first box, what is the number of bulbs in the second box that are not broken?

(1) In the first box, the number of bulbs that are not broken is 15 times the number of broken bulbs.
(2) The total number of bulbs in the first box is 9 more than the total number of bulbs in the second box.

What is the value of x ?

(1) y - x = y - 6
(2) x + 2y = 10

A certain bag contains red, blue, and green marbles. What is the ratio of the number of green marbles to the number of red marbles in the bag?

(1) The number of blue marbles in the bag is 2 times the number of green marbles in the bag.
(2) The number of blue marbles in the bag is 3 times the number of red marbles in the bag.

If M is a finite set of negative integers, is the total number of integers in M an odd number?

(1) The product of all the integers in M is odd.
(2) The product of all the integers in M is negative.

If the sum of three different numbers is 54, what is the largest number?

(1) The largest number is twice the smallest number.
(2) The sum of the two smaller numbers is 30.

What is the value of 5x² + 4x - 1 ?

(1) x(x + 2) = 0

(2) x = 0

If x and y are integers greater than 1, is x a multiple of y ?

(1) 3y² + 7y = x.

(2) x² – x is a multiple of y.

What is the value of y ?

(1) y is an odd integer between 28 and 34.
(2) 31 < y < 36