In the quilting pattern shown above, a small square has its vertices on the sides of a larger square. What is the side length, in centimeters, of the larger square?

(1) The side length of the smaller square is 10 cm.

(2) Each vertex of the small square cuts 1 side of the larger square into 2 segments with lengths in the ratio of 1:2.

If x > 0, what is the value of x⁵?

(1) ~$\sqrt{x}$~= 32

(2)~$x^2 = 2^{20}$~

In a certain factory, hours worked by each employee in excess of 40 hours per week are overtime hours and are paid for at 1~$1 \over 2$~ times the employee's regular hourly pay rate.

If an employee worked a total of 42 hours last week, how much was the employee's gross pay for the hours worked last week?

(1) The employee's gross pay for overtime hours worked last week was $30.

(2) The employee's gross pay for all hours worked last week was $30 more than for the previous week.

If p and q are positive, is~$p \over q$~ less than 1 ?

(1) p is less than 4.

(2) q is less than 4.

Is 2x > 2y ?

(1) x > y

(2) 3x > 3y

For all z, [z] denotes the least integer greater than or equal to z. Is [x] = 0 ?

(1) - 1 < x < - 0.1

(2) [x+0.5] = 1

The circular base of an above-ground swimming pool lies in a level yard and just touches two straight sides of a fence at points A and B, as shown in the figure above. Point C is on the ground where the two sides of the fence meet. How far from the center of the pool's base is point A ?

(1) The base has area 250 square feet.

(2) The center of the base is 20 feet from point C.

If xy = -6, what is the value of xy(x + y) ?

(1) x - y = 5

(2)~$xy^2 = 18$~

[y] denotes the greatest integer less than or equal to y. Is d < 1 ?

(1) d = y - [y]

(2) [d] = 0

If m is a positive integer, then~$ m^3$~ has how many digits?

(1) m has 3 digits.

(2)~$ m^2$~ has 5 digits.