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

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.