How many different prime numbers are factors of the positive integer n ?

(1) Four different prime numbers are factors of 2n.

(2) Four different prime numbers are factors of n².

Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students, ~$\frac{2}{3}$~ dislike lima beans; and of those who dislike lima beans, ~$\frac{3}{5}$~ also dislike brussels sprouts. How many of the students like brussels sprouts but dislike lima beans?

(1) 120 students eat in the cafeteria.

(2) 40 of the students like lima beans.

A garden store purchased a number of shovels and a number of rakes. If the cost of each shovel was 14 dollars and the cost of each rake was 9 dollars, what was the total cost of the shovels and rakes purchased by the store?

(1) The ratio of the number of shovels to the number of rakes purchased by the store was 2 to 3.
(2) The total number of shovels and rakes purchased by the store was 50.

On the number line above, is the product of w, x, y, and z negative?

(1) z is positive.
(2) The product of w and x is positive.