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

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12 Practice Tests for the SAT 576 Practice Test Six Answers and Explanations 2. B Difficulty: Medium Strategic Advice: The union of two sets consists of all the elements that are in either or both sets. The intersection of two sets consists of the elements that the sets have in common. Don't forget that you're looking for the difference between the number of elements in the union and the intersection, not just the number of elements in the union or the intersection. Getting to the Answer: The union of these sets contains the letters A, E, I, 0, U, B, C, and D. This is 8 elements. The intersection contains the letters A and E. This is 2 elements. 8-2=6 3. E Difficulty: Medium Strategic Advice: For Logic problems, be sure to know the difference between what may be true and what must be true. Getting to the Answer: According to the list, fruits 1 and 4 must be apples. Fruit 7 may be an apple. 4. E Difficulty: Medium Strategic Advice: Use the slope formula to find the missing coordinate. Getting to the Answer: Y 2 - Y1 m= -- X 2 - Xl _2, = z-(-1) 12 -7 -5 - - 5 z+ 1 -- 12 -12 S=z+l 4=z 5. c Difficulty: Medium Strategic Advice: Althougn this looks like a complicated problem, all you really have to do is plug the given information into the given equation and solve for x. Getting to the Answer: The problem states that there were 160 turtles in the pond 9 years after it was discovered, so n = 160 and t = 9. 9 160 = (x)23 = (x)23 = 8x 20 =x So there were 20 turtles in the pond the year it was discovered. 6. c Difficulty: Medium Strategic Advice: The graph of c(x) crosses the x-axis when c(x) equals 0. You can either set c(x) equal to zero and see how many values of x are solutions or just sketch the graph and observe the number of times it crosses the x-axis. Getting to the Answer: x2 - 6 = 0 7. c x2 = 6 x = ±\/6, so the graph crosses the x-axis twice. Difficulty: Medium Strategic Advice: See what information you can glean from the graph. What should the slope of the line be like? Where would the y-intercept be? Getting to the Answer: Because the position of the dots on the graph increases along the y-axis slightly faster than it increases along the x-axis, the slope of the graph must be slightly greater than 1. Although it is difficult to locate the y-intercept precisely, it must certainly be negative. Each of these pieces of information allows you to rule out some of the possible answers, leaving only one, y = 1 .3x - 3. 8. A Difficulty: High Strategic Advice: What geometry fact can you use to get a, b, and c in the same equation? The fact that the interior
12 Practice Tests for the SAT Practice Test Six Answers and Explanations 577 I angles of a triangle add up to 180 degrees. Figure out what each angle of the triangle is in terms of a, b, or c. Then set up an equation and solve for a - b. Getting to the Answer: The three interior angles of the triangle are 180 - a (since a is supplementary to the interior angle), b (since b is vertical to the interior angle), and c = 50. Therefore: 180 - a + b + 50 = 180 7 9. 5 Difficulty: Low -a +b =-50 a-b = 50 Strategic Advice: Whenever you are given two fractions that are equal to each other, think of cross-multiplying. Getting to the Answer: lOq = 14 14 7 q = 10 = 5 10. 1,300 Difficulty: Medium Strategic Advice: Think about what you can deduce from the given information to fill in the blanks. You can choose any row or column with two of the three numbers present to start. Getting to the Answer: Total - Large = Small 5,000 - 3,200 = 1,800 Total Small - Blue Small = Red Small 1,800 - 1,000 = 800 Red Small + Red Large = Total Red 11. 4 Difficulty: Medium 800 + 500 = 1,300 Strategic Advice: This type of problem is a good candidate for Picking Numbers. Getting to the Answer: Pick two prime numbers greater than 2, such as 3 and 5. Multiply them to get p, or 15. Factoring 15 only gives us 4 factors ( 1, 3, 5, 1 5), so our answer is 4. 12. 44 or 172 Difficulty: Medium Strategic Advice: Don't be afraid to draw a diagram if you are not given one. It usually helps make a complicated problem much simpler. Getting to the Answer: If I and ware integers, 5 and 17 fit so that 5 x 17 = 85 So the perimeter is: 5 + 5 + 1 7 + 1 7 = 44 85 and 1 also fit so that 85 x 1=85 So the perimeter is: 85 + 85 + 1 + 1 = 172 13. 1936 Difficulty: Medium Strategic Advice: You are given an equation that describes the population of the town in terms of the years that have passed since 1900. Plug the given population into the equation for n, then solve for t. Remember that the question asks for the year the population will reach 7,680, not just t. If you have trouble working with this equation, you can also make a chart of the year and the population, doubling every 6 years until you reach 7,680. This is rather time-consuming, however. Getting to the Answer: t 7,680 = (120)26 t 64 =26 t 26 =26 6= i 36 = t (years since 1 900) 1900 +36= 1936
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