## For all a ≠ 0 and b ≠ 0,

(A)

(B)

(C)

(D)

(E)

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.

Joy brings her dog to the same park and anchors her dog 30 feet away from Melissa's anchor along a walking trail. Joy's dog can roam only within a radius of 20 feet in all directions from its anchor. For how many feet along the walking trail can both dogs roam?

(Note: Assume the leashes can't stretch.)

（A）2 （B） 8 （C） 10 （D） 18 （E） 42

**Correct Answer: A**

Paulette, Quentin, and Rosie each donated money to a charity. Paulette gave as much money as Quentin and Rosie gave together. If Quentin had given three times more than he gave, he would have given $40 more than Paulette. And if Rosie had given $20 less, she would have given half as much as Paulette. How much did Paulette give?

(A) $80(B) $120(C) $160(D) $200(E) $240

**Correct Answer: D**

In the hiking trail shown below, X marks the trail's halfway point. If measures 24 kilometers and is the length of , what is the total length, in kilometers, of the trail?

(A) 144 (B) 104 (C) 96 (D) 72 (E) 48

**Correct Answer: A**

### More ACT Math Exam Questions

- 1
The percent

*P*of a population that has completed 4 years of college is given by the function*P*(*t*) = -0.001*t*^{2}+ 0.4*t*where*t*represents time, in years. What percent of the population have completed four years of college after 20 years, to the nearest tenth? - 2
If

- 3If the ratio of x:y is 4:5, and the ratio of y:z is 8:9, what is the ratio of x:z?
- 4A science tutor charges $60 an hour to help students with biology homework. She also charges a flat fee of $40 to cover her transportation costs. How many hours of tutoring are included in a session that costs $220?
- 5If 3(a - 6) = -21, then a = ?