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For all negative even integers x, which of the following is a correct ordering of the terms x, xx, ((–x)!)x, and ((–x)!)(–x)!?

(A) ((-x)!)(-x)! ≥ ((-x)!)x ≥ x ≥ xx

(B) ((-x)!)(-x)! ≥ xx ≥ ((-x)!)x ≥ x

(C) xx ≥ x ≥ ((-x)!)(-x)! ≥ ((-x)!)x

(D) xx ≥ ((-x)!)x ≥ x ≥ ((-x)!)(-x)!

(E) x ≥ ((-x)!)x ≥ xx ≥ ((-x)!)(-x)!

The Correct Answer
Explanation

The centers of 3 identically sized circles lie on the diameter of a larger circle, as shown in the figure below. Each of the 4 circles is tangent to 2 other circles, as shown. If the circumference of each small circle is 8π inches, what is the circumference of the largest circle, in inches? image

(A)16π (B) 24π (C) 48π (D) 64π (E) 144π

Correct Answer: B

Dave is in Pikeston and needs to go to Danville, which is about 110 miles due south of Pikeston. From Danville, he'll head east to Rocketville, about 200 miles from Danville. As he sets out on his trip, a plane takes off from the Pikeston airport and flies directly to Rocketville. Approximately how far, in miles, does the plane fly?

(F) 310 (G) (H) (J) (K)

Correct Answer: K

If the lengths of the sides of the triangle below are shown in inches, how many inches long is side image? image

(A)2 image (B) 10 (C) 4image (D) 26 (E) 42

Correct Answer: A

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