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

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290 1 2 Practice Tests for the SAT Practice Test Three Answers and Explanations Getting to the Answer: Pick numbers: a=-1 b=2 (A) a + b = -1 + 2 = 1 (B) -ab = -(-1 )(2) = 2 (C) ab = (- 1 )(2) = -2 b 2 (D) - = - = -2 a -1 (E) b - a = 2 - (- 1) = 3 Choice (B) is correct. 8. D Difficulty: Medium Positive but not even Positive and even Even but not positive Even but not positive Positive but not even Strategic Advice: Set up two proportions of gallons of paint over square feet and cross-multiply. Getting to the Answer: 2 gallons _ q ga llons 875 ft2 - 4,375 ft2 2(4,375) = 875g 9. A 8,750 = 875g lO=g Difficulty: Medium Strategic Advice: First, determine the total volume of the bigger box (volume = length x width x height). Then divide that by 60 to determine the volume of each smaller box. Go through the answer choices to see which dimensions can work. Getting to the Answer: Volume bigger box = (24)(10)(15) = 3,600 Volume of each smaller box = 3,5 oo = 60 60 Check the answer choices: Volume = length x width x height (A) (2)(5)(6) = 60 (A) works. Stop here. The other answers are wrong: (B) (3)(4)(6) = 72 (C) (3)(5)(6) = 90 (D) ( 4)(5)(6) = 120 (E) (5)(6)(12) = 360 10. E Difficulty: Medium Incorrect Incorrect Incorrect Incorrect Strategic Advice: The average is the sum of the terms divided by the number of terms. The question stem gives you a range for the sum of the terms, so all you need to do is divide the smallest and the greatest by the number of terms ( 4) to determine the range of the average. Getting to the Answer: 53 = nl 4 4 57 =14 l 4 4 The average is between 13 ..!_ and 14 l . Only (E) works. 4 4 11. c Difficulty: Medium Strategic Advice: Use the Pythagorean theorem to determine the hypotenuse, which the triangles share, and use the theorem again to determine side AD. Getting to the Answer: First triangle (you may have recognized this as a multiple of a 3:4:5 triplet) : a2 +b2 = c2 (8)2 + (6)2 = c2 64 + 36 =c2 100 =c2 lO=C Second triangle: a2 + b2 =c2 (5)2 + b2 = (10)2 25 + b2 = 100 b2 =75 b=v7s = v25>
12 Practice Tests for the SAT Practice Test Three Answers and Explanations I 291 12. E Difficulty: High Strategic Advice: Use points C and D to determine the slope of the line and the y-intercept, which will give you the equation for the line. Then go through the answer choices to see which other point fits into that equation. Getting to the Answer: Y 2 -y 1 Slope =- X2 - Xl 5-2 = i =l 2-(-1) 3 Find the y-intercept (when x = 0): Slope = 1 = -1...=L = 1-=-t = -2 + y -1 -0 -1 1 =-2 + y 3=y Line equation: y= 1 (x) + 3 y=x+3 Eyeball the answer choices to see which one might fit. (E) (1, 4) 4=1+3 4=4 Choice (E) is correct. 13. E Difficulty: Medium Strategic Advice: First, determine the pattern in the repeating decimal. Then determine which of the numbers from 0 to 9 the 5 1st digit will equal. Getting to the Answer: 0.04761 90476 1904761 90 ... The pattern repeats after every 6 digits. So, 0 begins with the 1st, 7th, 13th, 19th, 25th, 31st, 37th, 43rd, 49th. The question is for the 5 1st digit. So if the 49th digit is 0, then the 51 st digit is 7. 14. B Difficulty: Medium Strategic Advice: Probability is the ratio of the number of desired outcomes to the total number of possible outcomes. Determine each of the two numbers after Sharon takes out a coin that is not a quarter. Getting to the Answer: # of desired outcomes = # of quarters = 6 # of possible outcomes = # of coins =original # - 1 = (6 + 5 + 10) - 1 = 20 6 Probability 2 0 = 3 1 0 Choice (B) is correct. 15. c Difficulty: Medium Strategic Advice: Go through each answer choice to see if it is possible given the rules in the question stem. Getting to the Answer: (A) a + b This could never be an integer. Only an integer plus an integer will result in an integer. An integer plus a fraction will be a fraction. (B) a - b This could never be an integer. Only an integer minus an integer will result in an integer. An integer minus a fraction will be a fraction. (C) ab This could be an integer. For example, 1 a=2 b=- ' 2 ab =2(t) = 1 (D) 2a - b This could not be an integer for the same reason as (B). 2a is an integer because a is an integer, but b is still a noninteger. (E) E_ Again, take a = 2 and b = _!_. a 2 1 b - 1 1 - = = -- = -. Th' 1s . 1s not an . integer. a 2 2x2 4 Choice (C) is correct.
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