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

If the set S consists of five consecutive positive integers, what is the sum of these five integers?

(1) The integer 11 is in S, but 10 is not in S.

(2) The sum of the even integers in S is 26.

What is the value of the positive integer n ?

(1) n⁴ < 25

(2) n ≠ n ²

In a certain order, the pretax price of each regular pencil was $0.03, the pretax price of each deluxe pencil was $0.05, and there were 50% more deluxe pencils than regular pencils. All taxes on the order are a fixed percent of the pretax prices. The sum of the total pretax price of the order and the tax on the order was $44.10. What was the amount, in dollars, of the tax on the order?

(1) The tax on the order was 5% of the total pretax price of the order.

(2)The order contained exactly 400 regular pencils.

What was the amount of money donated to a certain charity?

(1) Of the amount donated, 40 percent came from corporate donations.

(2) Of the amount donated, $1.5 million came from noncorporate donations.

If x and y are positive integers, what is the remainder when 10^x + y is divided by 3 ?

(1) x = 5

(2) y = 2