Sets A, B, and C have some elements in common. If 16 elements are in both A and B, 17 elements are in both A and C, and 18 elements are in both B and C, how many elements do all three of the sets A, B, and C have in common?

(1) Of the 16 elements that are in both A and B, 9 elements are also in C.
(2) A has 25 elements, B has 30 elements, and C has 35 elements.

What is the value of the positive integer m ?

(1) When m is divided by 6, the remainder is 3.
(2) When 15 is divided by m, the remainder is 6.

Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each. If Juan bought more than 10 paperback books, how many hardcover books did he buy?

(1) The total cost of the hardcover books that Juan bought was at least $150.
(2) The total cost of all the books that Juan bought was less than $260.

Each of the 105 students in a certain club is either a freshman, a sophomore, or a junior. How many of the students in the club are sophomores?

(1) The ratio of the number of freshmen to the number of sophomores is 1 to 2.
(2) The ratio of the number of freshmen to the number of juniors is 1 to 4.

If n and p are integers, is p > 0 ?

(1) n + 1 > 0
(2) np > 0

One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8 ?

(1) y > 0.15
(2) C ~$\geq $~ 7.30

The operation @ represents either addition, subtraction, or multiplication of integers. What is the value of 1 @ 0 ?

(1) 0 @ 2 = 2
(2) 2 @ 0 = 2

If x, y, and z are integers, is x + y + 2z even?

(1) x + z is even.
(2) y + z is even.

The sale price of a certain jacket was 15 percent less than its original price, and the sale price of a certain shirt was 10 percent less than its original price. How much greater was the original price of the jacket than the original price of the shirt?

(1) The sale price of the jacket was $83 greater than the sale price of the shirt.
(2) The original price of the jacket was $140.

If w and z are positive, is ~$\frac{w}{z}$~ < 1 ?

(1) w < z
(2) z < 4