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

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984 12 Practice Tests for the SAT Practice Test Eleven Answers and Explanations 4. E Difficulty: Low Strategic Advice: If part of a problem seems complicated, try to rewrite it in a simpler way. In this case, 9.87654 x l 0 4 can be written much more simply. Getting to the Answer: 9.87654 x l 0 4 = 98,765.4 5. c Difficulty: Medium Strategic Advice: To find the average of a set of numbers, divide the sum of the numbers by the number of numbers. This is a very important formula. Getting to the Answer: 0(5) + l (4) + 2(5) + 3(4) + 4(2) 20 0 + 4 + 10 + l 2 + 8 34 = = = 1 20 20 ·7 6. B Difficulty: Medium Strategic Advice: This problem involves two concepts that appear very frequently on the SAT. First, the sum of the interior angles of any triangle is 180 degrees. Second, all the variables in the problem can be written in terms of one variable, in this case a. Getting to the Answer: a+b +c= 180 a + 2a + 3a = 180 7. c 60 = 180 a=30 Difficulty: Medium Strategic Advice: This problem revolves around translating from English to math. You'll need to choose a variable to represent the number of apples in the sack before the addition (for instance, x), then set up an equation using the information in the first sentence, and finally solve that equation for x. Getting to the Answer: x+4=3x 8. E 4=2x 2=x Difficulty: Medium Strategic Advice: In many geometry problems, you'll need to draw your own figure or (as in this case) add something to a given figure to help you solve a problem. You'll also need to remember that the sum of the interior angles of a triangle and the sum of the angles along a straight line are both 180 degrees. Getting to the Answer: First, sketch a line perpendicular to I and m: 100° 60° 80° The three angles along the new line add up to l 80 degrees: l 0 + d + 30 = l 80 9. c d+40= 180 d= 140 · Difficulty: Medium Strategic Advice: Always read the question carefully. This question doesn't ask for the value of x or the sum of x + 6 and x - 2. Instead, it asks for the difference between the two expressions. Although the algebraic method is shown below, Picking Numbers is also a good way to solve this problem. Getting to the Answer: (x + 6) - (x - 2) = 6 - (-2) = 8
12 Practice Tests for the SAT Practice Test Eleven Answers and Explanations I 985 10. D Difficulty: Medium Strategic Advice: This problem asks about the properties of negative numbers. If you forget any of the number properties, Picking Numbers can help you rule out incorrect answers. Getting to the Answer: I. a - b < c is not necessarily true. For instance, if a, b, and c were -3, -2, and -1, then this inequality would be -3 - (-2) = -1 < -1. Since a number cannot be less than itself, statement I is not true. Eliminate (A), (C), and (E). 11. A II. a< c, so --a> -c. When you multiply or divide by a negative number, switch the inequality. Eliminate (B). The answer must be (D), but for the sake of practice, go on to consider the third statement. Ill. a < c, so a + b the percentages given in the first sentence of this problem is a percent of Jo's monthly income, which you might call J when setting up your equation. Since Jo gives half her remaining income to charity and saves the rest, the amount of income that remains after she has spent everything listed in the first sentence is twice the amount she saves. Getting to the Answer: 0.25 ) + 0.3 ) + 0. 1 ) + 0.2 ) + 150 =) 12. c Difficulty: Medium 0.85 ) + 1 50 =) 150 = 0.15) 1,000 =) Strategic Advice: This problem tests your ability to read carefully more than your ability to do math. Be sure to pay attention to which variables are subtracted from which, and don't be fooled by answers that look similar to the correct answer. You may find it helpful to write out your answer before looking at the answer choices so that plausible but incorrect answers will not distract you. Getting to the Answer: Vr+s - q2 = (t + r)2 13. E Difficulty: Medium Strategic Advice: Don't do more work than you have to! Remember that the slope of a line represents the change in the value of the y-coordinate over the change in the value of the x-coordinate. If the slope of the line is 1, that means that for every unit of change in y, there is a corresponding unit of change in x. Getting to the Answer: From the point (1, 2), you can move one unit up and one unit to the right (that is, along a slope of 1) to reach the point (2, 3). No other choice satisfies this condition. 14. B Difficulty: Medium Strategic Advice: Don't worry when you see an odd symbol like the one in this problem: the operation defined by the symbol will always be given in the problem. All you need to do is plug the given numbers into the given equation and solve it carefully. Be sure to work all parts of the problem in the correct order. Getting to the Answer: (3 ... 2) = 32 - 2 = 9 - 2 = 7 4 ... (3 ... 2) = 4 ... 7 = 42 - 7 = 16 - 7 = 9 15. c Difficulty: Medium Strategic Advice: A prime number is a number whose only distinct factors are itself and 1. (The number 1 itself is not prime.) If you get stuck on a problem like this, Pick Numbers. Getting to the Answer: The number qr will have q and r as factors, so it cannot be prime. All other answer choices can be prime if q and r are prime numbers. 16. A Difficulty: Medium Strategic Advice: This question hinges on the triangle inequality theorem: the length of each side of a triangle must be greater than the difference between the other two sides and less than the sum of the other two sides. Therefore, the third side of this triangle must be greater than the difference between, and less than the sum of, 9 and 1 5.
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