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Which of the following is a prime factorization of 2,100?

(A)2 · 3 · 5 · 7

(B) 2² · 3 · 5² · 7

(C) 2² · 3 · 5 · 35

(D) 2² · 5² · 21

(E) 2² · 550

If a⁵ for a ≠ 0, which of the following statements must be true?

(F) x ≠ 0 and y ≠ 0 (G) x + y = 5 (H) x - y = 5 (J) xy = 5 (K) = 5

Correct Answer: H

There are 45 musicians in an orchestra, and all play two instruments. Of these musicians, 36 play the piano, and 22 play the violin. What is the maximum possible orchestra members who play both the piano and the violin?

(F) 9 (G) 13 (H) 22 (J) 23 (K) 36

Correct Answer: H

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 ≥ x^x (B) ((-x)!)^(-x)! ≥ x^x ≥ ((-x)!)^x ≥ x (C) x^x ≥ x ≥ ((-x)!)^(-x)! ≥ ((-x)!)^x (D) x^x ≥ ((-x)!)^x ≥ x ≥ ((-x)!)^(-x)! (E) x ≥ ((-x)!)^x ≥ x^x ≥ ((-x)!)^(-x)!

Correct Answer: B