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

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1072 1 12 Practice Tests for the SAT Practice Test Twelve Answers and Explanations Getting to the Answer: (A) 2 + _l_ = 21- 2 2 (B) 2 - _l_ = l _l_ 2 2 (C) _l_ - 2 = -1 _l_ 2 2 (D) 2x+= 1 (E) 2 -+- _l_ = 4 2 Choice (C) is the smallest. 5. B Difficulty: Medium Strategic Advice: The side opposite a larger angle is the larger side. Find the missing angle, then use the relationships between the angles to find the relationships between the sides. Getting to the Answer: LS = 180 - ( l 10 + 55) = 15 PS is the longest side because it is opposite the 110° angle. RS is shorter than PS but longer than PR. Therefore, 6 + y > 6 + z > 6. You can simplify this inequality to y> z > 0. (A) This may or may not be true; eliminate (B) This may or may not be true; eliminate (C) Not possible; eliminate (D) Correct (E) Not possible; eliminate 6. A Difficulty: Medium Strategic Advice: Don't let the A scare you. Just plug the values into the equation. Getting to the Answer: x=4 andy=2 (x - yy + (x + y)Y (4 - 2)4 + (4 + 2)2 (2)4 + (6)2 16 + 36= 52 7. c Difficulty: Medium Strategic Advice: When a transversal crosses parallel lines, all acute angles are equal and all obtuse angles are equal. So the angle opposite the transversal from c is equal to d, and the angle opposite the transversal from b is equal to a, as shown: -+ el ---r e2 ....,- 00 e3 Getting to the Answer: Since c and d make up a straight line, c + d = 180. Since a and b make up a straight line, a + b = 180. So a + b + c + d = 180 + 180 = 360. 8. B Difficulty: Medium - Strategic Advice: This is a great problem to help you practice your English-to-math translation skills. Translate each part of the word problem into an equation and then solve. Getting to the Answer: x+4-2=2x X=2 9. c Difficulty: Medium Strategic Advice: Sketching a figure may help you organize the information quickly. Getting to the Answer: The question asks for the measure of the largest angle, so set that equal to x. The measure of the middle-sized angle is 40 degrees less than the degree measure of the largest angle, or x - 40. The measure of the smallest angle is 20 degrees. The sum of the measures of the three interior angles of any triangle is 180 degrees. x + (x - 40) + 20 = 180 x + x - 40 + 20 = 180 2x - 20= 180 2x = 200 X= 100
12 Practice Tests for the SAT Practice Test Twelve Answers and Explanations I l073 10. A Difficulty: Medium Strategic Advice: Even though there are variables only in the question, Picking Numbers would still be a great strategy to try here. Getting to the Answer: Pick 7 for your positive odd integer: (d - 1 )(d - 2) = (7 - 1 )(7 - 2) = (6)(5) = 30 Too large. Try a smaller number, such as 5: (d- l)(d-2)=(5-1)(5-2)=(4)(3) = 12 11. A Difficulty: Medium Strategic Advice: To find the area, add the dimensions of the square and the triangle. First relabel the diagram as follows: a Getting to the Answer: a a b-a The area of a square is the length of a side squared, so the area of this square is a2. The area of this right triangle is: _!_ (leg x leg ) = J_(a)(b - a) = ab - a2 2 1 2 2 2 2 So the combined area is: a2 + Q'2._ 2 _ i3._ 2 = 2a2 2 _ a2 2 + ab 2 = a2 ab 2 + 2 a2 +ab 2 _- a(a + b) 2 12. E Difficulty: Medium Strategic Advice: Getting comfortable with the average formula means points on Test Day. Getting to the Answer: average = (sum of numbers) (quantity of numbers) You know that the sum of these four numbers is between 53 and 57. Therefore, the average of this group is between 21 = 13_!_ and 2_ = 14 _!__ Only one answer choice fits in 4 4 4 4 this range: (E), 14. 13. A Difficulty: Medium Strategic Advice: Don't let questions about volume intimidate you. You already know how to calculate area: length x width. To find volume, simply add another dimension: length x width x depth. Getting to the Answer: There are boxes of two sizes in this problem. The larger box is 24 inches long, 1 O inches wide, and 15 inches high. Its volume is 24 in. x 10 in. x 15 in. = 3,600 cubic inches. You know that there are 60 identical smaller boxes that fit perfectly into the larger box's volume. What is the volume of each of these? Divide the large box's volume by the number of smaller boxes to find your answer. (3600 cu. in.) = 60 c ·n 60 U. I . Check the dimensions in each answer choice to see which results in a volume of 60 cu. in. (A) 2 x 5 x 6 = 60; that's your answer (B) 3 x 4 x 6 = 72 (C) 3 x 5 x 6 = 90 (D) 4 x 5 x 6 = 120 (E) 5 x 6 x 12 = 360 14. A Difficulty: Medium Strategic Advice: The first graph deals with 1975. You can see that, of the 600 graduates, 1 2 percent chose to enter the workforce and 22 percent chose to go to vocational school. Adding the percents gives you 12% + 22% = 34%. Getting to the Answer: 34% of 600 = 1 3 06 x 600 = 204 So 204 graduates chose either to enter the workforce or go to vocational school.
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