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

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132 12 Practice Tests for the SAT Practice Test One Answers and Explanations 7. B Difficulty: Medium Strategic Advice: Be sure to read the question carefully and draw the extra points on the diagram. This will help you prevent careless errors on Test Day. Getting to the Answer: First, find FG. R = FG + GH + HI= 32, so FG = 32 - 6 - 14 = 12. One endpoint of the new line is the midpoint of FG. The distance from this endpoint to G is 6. The distance from G to H is 6. The total length of the new line segment is 6 + 6= 12. 8. A Difficulty: Medium Strategic Advice: Don't be intimidated by algebraic expressions with fractions in them. You can always crossmultiply to get rid of the fractions. It is important to know how to make the problem as simple to calculate as possible. Getting to the Answer: If you have fractions on both sides of the equation, you can cross-multiply to get them out of fractional form. 2x+4 _4 ---x=-3 - 3 3(2x + 4) = 4(x - 3) 6x+ 12=4x- 12 2x = -24 X =-12 9. D Difficulty: Medium Strategic Advice: Even though this question uses the word percent, you are never asked to find the actual percent itself. Set this problem up as a ratio to get the answer more quickly. Getting to the Answer: 16-6 _x- 12 _6_ _ _ 1_2_ 10 _x-12 6-12 120 = 6(x - 12) 120= 6x - 72 192 = 6x 32 =x 10. D Difficulty: Medium Strategic Advice: A question involving variables in both the stem and answer choices is a perfect candidate for Picking Numbers. Getting to the Answer: Let a= 2 and b = 3. So % = t· (A) 2> 1_ 3 (B) (C) (D) (E) 11. c -1 > 1- 2 3 1 2 3 = 3 2 1_ < 1- 6 3 ± > 1- 3 3 Difficulty: Medium Strategic Advice: Use the formula for averages to find the missing pieces of an averages question. Getting to the Answer: The average is the sum of the terms divided by the number of terms. So, 10 students got 1 00, leaving 20 to get y scores each (we can assume each will have the same score), so we set up: 100(1 0) + 20y =92 30 1,000 + 20y = 2,760 12. D Difficulty: Medium 20y = 1,760 y=88 Strategic Advice: You've got variables in the question and only numbers in the answer choices, so Backsolving would be a great strategy for this question. Start with (C), then work your way through the problem backward.
12 Practice Tests for the SAT Practice Test One Answers and Explanations I 133 Getting to the Answer: Start with (C) and assume that there are 60 employees in Company X. Then i of the total staff would be 30, so when the 30 more employees arrived at 1 PM, that would mean that there were 0 employees at work at noon. That doesn't make sense. We need more total employees in the company, so now choose between (D) and (E). Work with (D) and assume that there are 120 employees at Company X. That would make i of the total staff 60. When the 30 more employees arrived at 1 PM, that would mean that there were 30 employees to start off with at noon (60- 30 = 30). Then 30 t equals of Company X's total employees, so (D) works. 13. A Difficulty: Medium Strategic Advice: A bisecting line cuts another line in half. For this problem, take the information you know and fill in the diagram. We know that BO and AC bisect each other, so we know the base of MCO is 16, and since the height of MCO is half of BO, the height is 6. A = .lbh 2 A = + (16)(6) A=48 Getting to the Answer: 14. B Difficulty: Medium Strategic Advice: When solving a question with multiple variables, plug in for the values you know and then solve as you would a single-variable equation. Getting to the Answer: 50 ...;- 50 = 2- 4 (2)t 50 = _!Q 4 t J.Q = 50 x _1._ 4 10 = 20 t=20 15. E Difficulty: Medium Strategic Advice: For geometry problems that do not provide a figure, take the time to sketch a figure. This will help you visualize the problem. Getting to the Answer: Test the answer choices by sketching m in different positions. 0 1 2 4 Since all of the answer choices other than (E) are possible, (E) is the correct answer. It also helps to remember that a line can intersect a circle at most twice. Therefore, a line can intersect two circles at most four times. 16. B Difficulty: High Strategic Advice: Use your knowledge of special triangles and the Pythagorean theorem to find the length of the sides of right triangles. Getting to the Answer: In the new position, the ladder is 15 feet away from the wall, and the ladder is 25 feet long. Therefore, the sides of the triangle that the ladder forms are 15, x, 25. This fits the pattern of the 3-4-5 special triangle (3, 4, and 5 are all multiplied by 5 to get the sides of our triangle). The missing side xis therefore 20, so the ladder in the new position touches the wall 20 feet above the ground. In the original position, the ladder was 4 feet higher, or 24. The triangle formed by the original position has sides measuring (y, 24, 25). Use the Pythagorean theorem to find the missing base: y 2 + 24 2 = 25 2 y 2 + 576 = 625 y 2 =49 y = 7, which is (B)
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