If n and t are positive integers, what is the greatest prime factor of the product nt ?

(1) The greatest common factor of n and t is 5.
(2) The least common multiple of n and t is 105.

If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of aⁿ, what is the value of a ?

(1) aⁿ = 64
(2) n = 6

On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?

(1) xyz < 0
(2) xy < 0

If x, y, and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer.
(2) y + xz is an odd integer.

Of the 1,400 college teachers surveyed, 42 percent said that they considered engaging in research an essential goal. How many of the college teachers surveyed were women?

(1) In the survey, 36 percent of the men and 50 percent of the women said that they considered engaging in research an essential goal.
(2) In the survey, 288 men said that they considered engaging in research an essential goal.

At a two-day seminar, 90 percent of those registered attended the seminar on the first day. What percent of those registered did not attend the seminar on either day?

(1) A total of 1,000 people registered for the two-day seminar.
(2) Of those registered, 80 percent attended the seminar on the second day.

Linda put an amount of money into each of two new investments, A and B, that pay simple annual interest. If the annual interest rate of investment B is 1.5 times that of investment A, what amount did Linda put into investment A ?

(1) The interest for 1 year is $50 for investment A and $150 for investment B.
(2) The amount that Linda put into investment B is twice the amount that she put into investment A.

What fraction of this year's graduating students at a certain college are males?

(1) Of this year's graduating students, 33 percent of the males and 20 percent of the females transferred from another college.
(2) Of this year's graduating students, 25 percent transferred from another college.

If the average (arithmetic mean) of the five numbers x, 7, 2, 16, and 11 is equal to the median of the five numbers, what is the value of x ?

(1) 7 < x < 11
(2) x is the median of the five numbers.

If Company M ordered a total of 50 computers and printers and Company N ordered a total of 60 computers and printers, how many computers did Company M order?

(1) Company M and Company N ordered the same number of computers.
(2) Company N ordered 10 more printers than Company M.