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 ~$n^2$~.

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 and the cost of each rake was $9, 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.

A certain one-day seminar consisted of a morning session and an afternoon session. If each of the 128 people attending the seminar attended at least one of the two sessions, how many of the people attended the morning session only?

(1) ~$\frac{3}{4}$~ of the people attended both sessions.

(2) ~$\frac{7}{8}$~ of the people attended the afternoon session.

Is z equal to the median of the three positive integers x, y, and z ?

(1) x < y + z

(2) y = z

What is the hundredths digit of the decimal z ?

(1) The tenths digit of 100z is 2.

(2) The units digit of 1,000z is 2.

Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if Country A sent the second greatest number of representatives, did Country A send at least 10 representatives?

(1) One of the six countries sent 41 representatives to the congress.

(2) Country A sent fewer than 12 representatives to the congress.

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5,1).

(2) The y-intercept of line n is greater than the y-intercept of line p.

Is r to the right of -6 on the number line?

(1) r is between -4 and -1 on the number line.

(2) r is between -3 and 1 on the number line.