In the xy-plane, point (r,s) lies on a circle with center at the origin. What is the value of r² + s² ?

(1) The circle has radius 2.

(2) The point(~$\sqrt{2}$~,-~$\sqrt{2}$~) lies on the circle.

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.

(2) The sum of the numbers on the remaining 35 cards is 176.

If x, y, and z are three integers, are they consecutive integers?

(1) z - x = 2

(2) x < y < z

If rs ≠0, is~$1 \over r$~ +~$1 \over s$~=4 ?

(1) r + s = 4rs

(2) r = s

If y = x² - 6x + 9, what is the value of x ?

(1) y = 0

(2) x + y = 3

In the triangle above, does a² + b² = c² ?

(1) x + y = 90

(2) x = y

If a, b, c, and d are numbers on the number line shown and if the tick marks are equally spaced, what is the value of a + c ?

(1) a + b = -8

(2) a + d = 0

Was the range of the amounts of money that Company Y budgeted for its projects last year equal to the range of the amounts of money that it budgeted for its projects this year?

(1) Both last year and this year, Company Y budgeted money for 12 projects and the least amount of money that it budgeted for a project was $400.

(2) Both last year and this year, the average (arithmetic mean) amount of money that Company Y budgeted per project was $2,000.

A total of 20 amounts are entered on a spreadsheet that has 5 rows and 4 columns; each of the 20 positions in the spreadsheet contains one amount. The average (arithmetic mean) of the amounts in row i is R_i (1 ≤ i <≤5). The average of the amounts in column j is C_j (1 ≤ j ≤ 4). What is the average of all 20 amounts on the spreadsheet?

(1) R₁ + R₂ + R₃ + R₄ + R₅ = 550

(2) C₁ + C₂ + C₃ + C₄ = 440

Which of the positive numbers x or y is greater?

(1) y = 2x

(2) 2x + 5y = 12