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.

For each landscaping job that takes more than 4 hours, a certain contractor charges a total of r dollars for the first 4 hours plus 0.2r dollars for each additional hour or fraction of an hour, where r > 100. Did a particular landscaping job take more than 10 hours?

(1) The contractor charged a total of $288 for the job.

(2) The contractor charged a total of 2.4r dollars for the job.

The sequence s₁, s₂, s₃, ..., s_n, ... is such that ~$s_n=\frac{1}{n}-\frac{1}{n+1}$~for all integers n ≥ 1. If K is a positive integer, is the sum of the first k terms of the sequence greater than ~$\frac{9}{10}$~ ?

(1) k > 10

(2) k < 19

If x and y are nonzero integers, is~$ x ^y< y^x$~ ?

(1)~$ x = y^2$~

(2) y > 2

In the sequence S of numbers, each term after the first two terms is the sum of the two immediately preceding terms. What is the 5th term of S ?

(1) The 6th term of S minus the 4th term equals 5.

(2) The 6th term of S plus the 7th term equals 21.

Is the positive integer n a multiple of 24 ?

(1) n is a multiple of 4.

(2) n is a multiple of 6.