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

12 Practice Tests for the SAT
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Practice Test Eight Answers and Explanations
Getting to the Answer:
This question is really just a rearrangement of the average
formula. Since we are dealing with prices in this question,
the average formula is this:
sum of the pr _
ices = average of the prices
number of prices
If we multiply both sides of the formula by the number
of prices, we get that the sum of the prices = average of
the prices x number of prices, the quantity quoted in the
question. Thus, (D) is the correct choice.
16. E
Difficulty: Medium
Strategic Advice: Equilateral means equal in length. So
an equilateral triangle is a triangle whose three sides are
all equal in length. So if the expressions 3x + 1 and x +
7 represent sides of an equilateral triangle, they must be
equal.
Getting to the Answer:
Use this to set up an algebraic equation, 3x + 1 =x + 7,
which can be solved for x. The result is x = 3, and all you
have to do is plug that into either expression. That will tell
you that the length of a side of this equilateral triangle is
10, so the perimeter, which is the sum of the length of the
sides, is equal to 10 + 1 0 + 10, or 30, (E).
17. c
Difficulty: Medium
Strategic Advice: Since we have a word problem with
numbers in the answer choices, Backsolving might be a
good strategy to try here.
Getting to the Answer:
Since we are dealing with crayons, we know that the
number of crayons of each color will have to be an integer.
Using choice (C), 20 x i = 8, which is a whole number,
and 20 x ± = 5, also a whole number, so 20 is a possible
value for the number of crayons, and (C) is the correct
choice.
18. A
Difficulty: High
Strategic Advice: Picking Numbers is always a good choice
for a question with multiple variables in the question stem
and answer choices.
Getting to the Answer:
Let's have x = 8 and y = 7. We know that the initial
amount + 6 liters - 7 liters must equal 8 liters. In other
words, the initial amount decreased by 1 liter becomes
8 liters, so the initial amount of water must have been
9 liters. Now we just have to substitute x and y into the
answer choices to see which one gives us 9 liters.
8 + 7 - 6 = 9, so (A) is the correct choice.
19. D
Difficulty: High
Strategic Advice: Anytime you are given a diagram that does
not show all the information given in the question, it is a good
idea to draw that information into the diagram.
Getting to the Answer:
/I
/I
y
I I
I I
I I
,J_ I
12 1
I
In the diagram above, we have drawn in the height of the
pyramid and labeled the known lengths. We can find YZ
by recognizing that it is the hypotenuse of the right triangle
XYZ as labeled in the diagram above. If we can find the
lengths of the other two sides, we can use the Pythagorean
theorem to find YZ. We already know that XY = 12, and
XZ is equal to half of the diagonal of the square base.
To find the length of this diagonal, we know that it is the
hypotenuse of another right triangle whose legs are sides
of the base. Therefore, since the length of both legs is 1 6,
we know this is a 45-45-90 triangle, making the length
of the diagonal 1 6\/2. Therefore, XZ = 8\/2. Using the
Pythagorean theorem,
(YZ)2 = 122 + (8\/2)2
(\'2')2 = 144 + 128
yz=\/272
yz= 4'\/'17
z