12.Practice.Tests.for.the.SAT_2015-2016_1128p

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110 12 Practice Tests for the SAT Practice Test One Answers and Explanations 8. c Difficulty: Medium Strategic Advice: Keep in mind that probability is defined by: total favorable outcomes = probability total possible outcomes Getting to the Answer: If every 1 Oth person puts his shoes through a machine, then person 10, person 20, person 30, and so on will put his shoes through the machine. If every 20th person has his bag searched, then person 20, person 40, person 60, and so on will have his bags searched. Since all the people who have their bags searched also have their shoes checked, you just need to find the number of people who will have their bags searched and divide that by the total number of people. People 20, 40, 60, 80, and 100 will have their bags searched, so the probability that a passenger will have his or her bags searched is 160 = 2 1 0 · 9. D Difficulty: Medium Strategic Advice: Pick numbers. To make your work as easy as possible, make rectangle A a 10-by-10 square. Getting to the Answer: The area of A is 1 00. So the width of rectangle B is 7 and the length of B is 13. The area of rectangle B is 13 x 7 = 91, which is 9 percent less than that of rectangle A. 10. B Difficulty: Medium Strategic Advice: Sometimes the figure as drawn doesn't contain enough information. Feel free to add to it. Remember that the interior angles of a triangle add up to 1 80° and that straight angles add up to 1 80°. Getting to the Answer: Extend one of the interior line segments to meet line n. This creates a triangle in which one angle is 1 80° - 120° = 60°, one angle is 55° because it is an alternate interior angle along the transverse, and one angle is 1 80° - z0• 60 + 55 + 180 -z = 180 11. D Difficulty: Medium 115=z Strategic Advice: On graph problems, all of the information you need to solve the problem is presented to you! Take a minute to identify the labels on the x- and y-axes and find the information you need. Remember that average . (arithmetic . mean ) = sum of terms . number of terms Getting to the Answer: Take the average of the points per game as determined from the graph: 10 + 14 + 8 + 18 + 20 + 16 = 14.33 6 12. E Difficulty: Medium Strategic Advice: Don't feel intimidated by negative or fractional exponents. Convert negative exponents into fractions. Express any fractional exponents as the product of two exponents so that it is easier to reduce the equation. Backsolving, or plugging the answers into the question stem, also works well for this type of question. Getting to the Answer: .::£ 1 X 3 = - 36 1 2 = 36 X3 .2 X3 = 36 55 _l X3 = 6 _l (X3)3 = 53 x=216
12 Practice Tests for the SAT j Practice Test One Answers and Explanations 111 13. D Difficulty: Medium Strategic Advice: Don't be intimidated by radicals in the denominator. Cross-multiply to remove the radical from the denominator and then square both sides. This converts the problem into a familiar form, a quadratic equation. Backsolving, or plugging the answers into the question stem, would also work well. Getting to the Answer: 14x =7 V2x + 2 14x= 7Y2x + 2 2x = V2x + 2 4x2 = 2x + 2 4x2 - 2x-2 = O Simplify the equation further by dividing both sides by 2, then factor the equation to solve for x. 2x2 -x- 1=0 (2x + l)(x - 1) =0 14. D Difficulty: Medium 2x + 1 = 0 or x - 1 = 0 x = -- 1 - or x = 1 2 Strategic Advice: Remember that there are always two possibilities when solving absolute value equations. If you get stuck, try Backsolving, or plugging the answers into the question stem. Getting to the Answer: 2r -2=8 2r = 10 r=5 3r + 2 = 17 or -(3r + 2) = 17 3r = 1 5 or 3r = -19 -19 r=5 or r=-- 3 The only value that solves both equations is r = 5. 15. E Difficulty: Medium Strategic Advice: This problem is designed to let you try out this procedure. Don't worry about having major insightsjust plug in the given number and see what happens. This will help you gain the insight you need for the next two questions. Getting to the Answer: Choose 6. 127. 6.127 x 100=612.7 The smallest integer greater than or equal to 612.7 is 613 Gust round up). 613 + 12 = 625 Print 625. 16. D Difficulty: Medium Strategic Advice: You can attack this by either trying to work backward with each of the answers or thinking about what kinds of results you can get from the procedure. Getting to the Answer: Choose a number between 0 and 9.9. The result is between 0 and 990. Round up to nearest integer-now the number is an integer between O and 990. Add 12-now the number is an integer between 12 and 1,002. Print the number from step 4. (A) Doesn't work because it's too small (B) Doesn't work because it's too small (C) Not an integer (D) Correct (E) Too large 17. c Difficulty: Medium Strategic Advice: Try plugging a number into the reordered steps to see if you still get the same answer. Getting to the Answer: We can try 6.1 27 again (the number doesn't change in 5, so we'll only show 1-4).
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