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For all a ≠ 0 and b ≠ 0,






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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

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