What is the sum of the first four terms of sequence S ?

(1) After the first two terms of S, the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 10.

Is the integer n a prime number?

(1) 24 ≤ n ≤28

(2) n is not divisible by 2 or 3.

What is the value of x ?

(1) x + 1 = 2 - 3x

(2)~$1 \over 2x$~ =2

For a recent play performance, the ticket prices were $25 per adult and $15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults?

(1) Revenue from ticket sales for this performance totaled $10,500.

(2) The average (arithmetic mean) price per ticket sold was $21.

If p, s, and t are positive, is |ps - pt| > p(s - t) ?

(1) p < s

(2) s < t

The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner?

(1) Each of the k employees who shared the cost of the dinner paid $19.

(2) If the total cost of the dinner had been shared equally by k + 1 of the n employees who attended the dinner, each of the k + 1 employees would have paid $18.

If x and y are integers, what is the value of x ?

(1) xy= 1

(2) x ≠ -1

During a certain bicycle ride, was Sherry's average speed faster than 24 kilometers per hour?

(1 kilometer = 1,000 meters)

(1) Sherry's average speed during the bicycle ride was faster than 7 meters per second.

(2) Sherry's average speed during the bicycle ride was slower than 8 meters per second.

Is the median of the five numbers a, b, c, d, and e equal to d ?

(1) a < c < e

(2) b < d < c

If x is a positive integer, what is the value of x ?

(1)x² = ~$\sqrt{x}$~

(2)~$n \over x$~ =n and n≠ 0.