A wooden rod is cut into two pieces. What is the length of the longer piece?

(1) One of the pieces is 20 inches longer than the other piece.
(2) The length of the shorter piece is ~$\frac{1}{3}$~ the length of the longer piece.

Is x > 0.05 ?

(1) x > ~$\frac{3}{40}$~
(2) x is greater than 3 percent of 50.

If a, b, k, and m are positive integers, is a^k a factor of b^m ?

(1) a is a factor of b.
(2) k ~$\leq $~ m

If $1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of interest, I , earned by the deposit in the first n years is given by the formula I =1000〔(1 + ~$\frac{r}{100}$~ )ⁿ - 1〕 , where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank greater than 8 percent?

(1) The deposit earns a total of $210 in interest in the first two years.
(2) ( 1 + ~$\frac{r}{100}$~ )² > 1.15

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR ?

(1) The measure of angle QPR is 30°
(2) The sum of the measures of angles PQR and PRQ is 150°

At a certain pet shop, ~$\frac{1}{3}$~ of the pets are dogs and ~$\frac{1}{5}$~ of the pets are birds. How many of the pets are dogs?

(1) There are 30 birds at the pet shop.

(2) There are 20 more dogs than birds at the pet shop.

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.