Home->ACT Math

If xy = 144, x + y = 30, and x > y, what is the value of x – y ?

(A)4

(B)6

(C)18

(D)22

(E)24

Melissa attaches her dog's leash to a metal anchor in the grass so that the dog can roam only within a radius of 12 feet in any direction from the anchor. A map of the area accessible to the dog is shown below in the standard (x,y) coordinate plane, with the anchor at the origin and 1 coordinate unit representing 1 foot.

Which of the following is an equation of the circle shown on the map?

（A）(x - y)² = 12 （B） (x + y)² = 12 （C） (x + y)² = 12² （D） x² + y² = 12 （E） x² + y² = 12²

Correct Answer: E

A carpet company uses the following formula for estimating the number of square feet, a, of carpeting needed for a room x feet by y feet, containing a stairway w feet by z feet, with n stairs: a = xy + w[z(2n - 1) + 2n] What is the company's estimate for the number of square feet of carpeting needed for a room that is 15 feet by 18 feet, containing a stairway that is 6 feet by 6 feet with 8 stairs?

（A）826 （B） 894 （C） 906 （D） 1,086 （E） 1,636

Correct Answer: C

Sebastian bought a meal at a restaurant and left a 15% tip. With the tip, he paid exactly $35.19. How much did the meal cost without the tip?

(A) $28.98(B) $29.91(C) $30.15(D) $30.60(E) $30.85

Correct Answer: D