If it took Carlos ~$\frac{1}{2}$~ hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (Note: 1 mile = 5,280 feet)

(1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.
(2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.

In the sequence of positive numbers x₁, x₂, x₃, . . . , what is the value of x₁ ?

(1) x_l = ~$\frac{x_{l-1}}{2}$~ for all integers l > 1
(2) x₅ = ~$\frac{x_{4}}{x_{4}+1}$~

Is ~$\frac{x+1}{x-3}$~ < 0?

(1) -1 < x < 1
(2) x² - 4 < 0

Pat bought 5 pounds of apples. How many pounds of pears could Pat have bought for the same amount of money?

(1) One pound of pears costs $0.50 more than one pound of apples.
(2) One pound of pears costs ~$1\frac{1}{2}$~ times as much as one pound of apples.

What was Jean's insurance premium in 1995 ?

(1) The ratio of Jean's insurance premium in 1995 to her insurance premium in 1994 was ~$\frac{6}{5}$~ .
(2) Jean's insurance premium in 1995 was 20 percent more than her insurance premium in 1994.

What is the number of members of Club X who are at least 35 years of age?

(1) Exactly ~$\frac{3}{4}$~ of the members of Club X are under 35 years of age.
(2) The 64 women in Club X constitute 40 percent of the club's membership.

In the rectangular coordinate system shown above, does the line k (not shown) intersect quadrant II ?

(1) The slope of k is ~$-\frac{1}{6}$~.
(2) The y-intercept of k is -6.

If m > 0 and n > 0, is ~$\frac{m+x}{n+x}> \frac{m}{n}$~ ?

(1) m < n
(2) x > 0

Is ~$\sqrt{\left ( x-3 \right )^{2}}$~ = 3 - x ？

(1) ~$x\neq 3$~
(2) ~$-x\left | x \right |$~>0

Is ~$\frac{1}{a-b}$~ < b - a ?

(1) a < b.
(2) 1 < ~$\left | a-b \right |$~.