Is the product of a certain pair of integers even?

(1) The sum of the integers is odd.

(2) One of the integers is even and the other is odd.

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.

In a certain board game, a stack of 48 cards, 8 of which represent shares of stock, are shuffled and then placed face down. If the first 2 cards selected do not represent shares of stock, what is the probability that the third card selected will represent a share of stock?

When 2/3 of the garments in a shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the uninspected garments must pass inspection in order that 90 percent of the garments in the shipment pass?

At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?

If m lies between the integers p and s on the number line shown, which of the following is a possible value for m ?

Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest. If that interest was approximately 6.5 percent of the bond's selling price, approximately what was the bond's selling price?