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

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12 Practice Tests for the SAT 824 Practice Test Nine Answers and Explanations 2. E Difficulty: Low Strategic Advice: With combination problems, the trick is to multiply the components together. This should make sense-just think that for each of the 7 entrees, there are 4 appetizer choices, so you need to multiply 7 times 4. Getting to the Answer: 7(4) = 28 3. A Difficulty: Low Strategic Advice: This is just a substitution problem; the only catch is that it has two steps. Since you have a numerical value for z, plug that in first, and then you'll have a numerical value for y to plug into the first equation. Getting to the Answer: y =z+2 y =4+2 y =6 Then, substitute 6 for y: x+ 2y = 14 x + 2(6) = 14 x+ 12=14 X=2 4. A Difficulty: Medium Strategic Advice: If a fraction equals zero, then its numerator equals zero. (If the denominator of a fraction equals zero, then that fraction is undefined.) Getting to the Answer: =0 x 5. c x+y=O x=-y Difficulty: Low Strategic Advice: Don't let yourself get confused by word problems with lots of variables. Getting to the Answer: Laurel is taller than Nick: N < L Laurel is shorter than Vince: L < V So, N
12 Practice Tests for the SAT Practice Test Nine Answers and Explanations 825 I that has c in it. The second equation is c - b = 5, so that becomes 8 - b = 5. That means that b is 3. Plugging b = 3 into the first equation gives you 3a = 6, which means that a= 2. Now you know that a is 2, b is 3, and c is 8, so a + b + c = 2 + 3 + 8 = 13. Grid that in. 10. 87.5 Difficulty: Medium Strategic Advice: In this percent word problem, if 50 out of 400 seniors are majoring in economics, then 400 - 50 or 350 seniors are not majoring in economics. Since percent x whole = part, then percent = p art woe h l . Because 350 is the part and 400 is the whole, the percent you're looking for is just gg. Getting to the Answer: Dividing bo:h numbers by 4 gives you ·jg, which is 87.50/o, so iust gnd m 87.5. 11. 1.25 Difficulty: Medium Strategic Advice: This is another problem in which you solve two equations with two variables. Another way of saying that 5 pens cost as much as 2 notebooks is the equation SP = 2N. That's just translating from words to math, by using N to represent the cost of a notebook and P to represent the cost of a pen. Getting to the Answer: If one notebook plus one pen cost $1.75, then N + P = $1.75. If you take the first equation and solve for P, you get P = 2 . You can plug that into the second equation to get N + 2 = $1.75, or 7 = $1.75. Solving for N gives you N = tx (1.75) = $1.25, so put 1 .25 in the grid. 12. 44 Difficulty: Medium Strategic Advice: The 4 scores you're given here average to 86, and you can use this average to find the unknown score. That means that the sum of the 4 scores divided by 4 is 86, so the sum of the scores is 4 x 86, or 344. That's just another way of stating the average formula: sum of the terms if average = number of terms • then sum of the terms = average x number of terms. If you have four scores that add up to fl particular number, and you want one score to be as low as possible, you have to make the other three scores as high as possible. Getting to the Answer: The highest possible value for any 1 score is 100, so the lowest score occurs when the other 3 scores are each 1 00, and 100 + 1 00 + 100 + the lowest score = 344. A little bit of arithmetic will tell you that the lowest score must be 44, which is what you should put into the grid. 13. 122, 182, or 242 Difficulty: Medium Strategic Advice: Here you're told that v leaves a remainder of 2 when it's divided by 3, 4, or 5. This means that v - 2 is a multiple of 3, 4, and 5. Since 3, 4, and 5 have no common factors greater than 1, v - 2 must be a multiple of 3 x 4 x 5 = 60. Getting to the Answer: So vis 2 more than a multiple of 60. Keep in mind that v is a three-digit number less than 250. So v can't be 2 + 60 or 62. But v could be 2 + 2(60) = 122, v could be 2 + 3(60) = 182, and v could be 2 + 4(60) = 242. Notice that 2 + 5(60) = 302 is greater than 250. So v can't be 302, or 2 more than any larger multiple of 60. So v could only be 122, 182, or 242. 14. 81 Difficulty: Medium Strategic Advice: Since you're given that angle ADF is 36°, the first thing to do is to label that angle 36° in the diagram. Do you see any other angles that you know the measure of? Getting to the Answer: Since ABCD is a square, the corner angles are all 90°, and since AC is a diagonal, it cuts those corner angles in half. Therefore, angles OAF, FA B, BCF, and DCF are all 45° angles. If you write all that on the diagram, you should notice that you now know the measure of two out of the three angles of triangle ADF. Since angle ADF is 36° and angle OAF is 45°, angle AFD must be 1 80° - 36°- 45° = 99°. Since AFD and the angle measuring x 0 lie on a straight line, x must be 180 - 99 = 81. Grid in 81.
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