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SAT 1. If p = – 2 and q = 3, then p3q2 + p2q = ? P (A) – 84 x⁰ (B) – 60 (C) 36 (D) 60 (E) 84 (B) – 60 M 105⁰ N Q p3 q2 + p2 q = ? (– 2)3(3)2 + (– 2)2 (3) = ? (– 8) (9) + (4) (3) = ? (– 72) + (12) = – 60 SAT 2. In this figure, B is the midpoint of AC and D is the midpoint of CE. If AB = 5 and BD = 8, what is the length of DE ? (A) 8 (B) 6 (C) 5 (D) 4 (E) AB = 5 A • B • DE = ? C • D • E • BD = 8 3 (E) 3 BC = 5 by definition of midpoint, then 8 – 5 = 3 Thus DE = 3 by definition of midpoint SAT 3. Which of the following equations describes the relationship of each pair of numbers (N,P) in this table ? (A) P = N + 5 N P (B) P = 2 N + 3 2 7 (C) P = 2 N + 5 4 13 (D) P = 3 N + 1 6 19 (E) 8 25 P = 3 N +1 (D) P = 3 N + 1 P = 3 N + 1 works for all entries 7 = 3 (2) + 1 13= 3 (4) + 1 19 = 3 (6) + 1 25 = 3 (8) + 1 SAT 4. In this figure MQ is a straight line. If PM = PN, what is the value of x ? P (A) 30 x⁰ (B) 45 (C) 60 (D) 75 (E) 90 105⁰ M N (A) 30⁰ Q < MNP = 180⁰ – 105⁰ = 75⁰ Since < PMN = < MNP , < PMN = 75⁰ Thus, x = 180⁰ – 150⁰ = 30⁰ SAT 5. Marty has exactly five blue pens, six black pens, and four red pens in his knapsack. If he pulls out one pen at random from his knapsack, what is the probability that the pen is either red or black ? (A) 11 15 (B) 2 3 (C) 1 2 (D) 1 3 (E) 1 5 (B) What is the probability of Red or Black ? Blue 5 Black 6 Red 4 Total 15 2/3 10 out of 15 or 2/3 SAT 6. Two hot dogs and a soda cost $ 3.25 If three hot dogs and a soda cost $ 4.50, what is the cost of two sodas ? (A) $ 0.75 (B) $ 1.25 (C) $ 1.50 (D) $ 2.50 (E) $ 3.00 (C) $ 1.50 Since the difference of the 2 costs is 1 hot dog, then the cost for 1 hot dog is $1.25. Thus, 2 hot dogs cost $ 2.50 which leaves $ .75 for the soda. And, 2 sodas would be $ 1.50 SAT 7. In this figure , if L1 ⁄ ⁄ L2, which of the following must be = to a ? (A) b + c (B) b + e d⁰ c⁰ e⁰ f⁰ L1 (C) c + d (D) d + e (E) d+f b⁰ a⁰ L2 Because f = c + d by exterior < of a ∆ must = the 2 remote interior <‘s and a = f by corresponding <‘s congruent Thus a = c + d by transitive property (C) c + d SAT A certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute. If the call lasted x minutes and x is an integer greater than 3, which of the following expresses the cost of the call, in dollars ? 8. (A) 0.75 [3] + 0.15 x (B) 0.75 [3] + 0.15 [x + 3 ] (C) 0.75 [3] + 0.15 [3 – x ] (D) 0.75 + 0.15 [x – 3 ] (E) 0.75 + 0.15 x .75 for first 3 minutes + .15 each additional minute Since the call lasted x minutes and x is an integer > 3, then x – 3 represents minutes over 3, such as 4 – 3 = 1 minute over the baseline cost of .75 (D) 0.75 + 0.15 [x – 3 ] SAT 9. This figure shows a piece of wire in the shape of a semicircle. If the piece of wire is bent to form a circle without any of the wire overlapping, what is the area of the circle ? (A) 6 π (B) 9 π (C) 12 π (D) 18 π (E) 36 π 12 B) 9 π C=πd C = 12 π Since figure is a half circle = 6 π, so if d = 6, then r = 3 Thus, A = π r2 or π (3) 2 or 9 π SAT If a2 – a = 72, and b and n are integers such that bn = a, which of the following 10. cannot be a value for b ? (A) – 8 (B) – 2 (C) 2 (D) 3 (E) 9 (C) 2 a2 – a = 72 a2 – a – 72 = 0 (a – 9 ) (a + 8 ) = 0 a = – 8, 9 bn = a bn = – 8 or bn = 9 b = n√– 8 or b = n√ 9 – 8 works as – 8 = 1√– 8 – 2 works as – 2 = 3√– 8 2 doesn’t work as 2 ≠ 3√– 8 or 2 ≠ 3√9