The integers m and p are such that 2 < m < p and m is not a factor of p. If r is the remainder when p is divided by m, is r > 1 ?

(1) The greatest common factor of m and p is 2.
(2) The least common multiple of m and p is 30.

A recent lunch meeting at a certain club was attended by members and guests. Each member paid $4 for the lunch, and each guest paid $8 for the lunch. How many of the people attending the meeting were members?

(1) A total of 20 people attended the meeting.
(2) A total of $92 was paid for the lunch.

If w, x, y, and z are integers such that ~$\frac{w}{x}$~ and ~$\frac{y}{z}$~ are integers, is ~$\frac{w}{x}+\frac{y}{z}$~ odd?

(1) wx + yz is odd.

(2) wz + xy is odd.

If r is the remainder when the positive integer n is divided by 7, what is the value of r ?

(1) When n is divided by 21, the remainder is an odd number.
(2) When n is divided by 28, the remainder is 3.

If x - y > 10, is x - y > x + y ?

(1) x = 8
(2) y = -20

Is xy > 0 ?

(1) x - y > -2
(2) x - 2y < -6

Is the positive integer j divisible by a greater number of different prime numbers than the positive integer k ?

(1) j is divisible by 30.
(2) k = 1,000

The numbers of books read by 7 students last year were 10, 5, p, q, r, 29, and 20. What was the range of the numbers of books read by the 7 students last year?

(1) 5 < p < q
(2) p < r < 15

In the xy-plane, the line k passes through the origin and through the point (a,b), where ~$ab\neq 0$~. Is b positive?

(1) The slope of line k is negative.
(2) a < b

Is x⁴ + y⁴ > z⁴ ?

(1) x² + y² > z²
(2) x + y > z