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

1 2 Practice Tests for the SAT
Practice Test Eight Answers and Explanations
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12. A
Difficulty: High
Strategic Advice: Here you've got a rectangle with sides y
and y + 4 and area 32. Let's forget about the circles for a
minute. This means that y(y + 4) = 32. You can make this
into the quadratic equation y2 + 4y- 32 = 0 and solve for
y, but it's much easier just to try to guess the value of y.
What two numbers have 32 as their product where one is 4
greater than the other?
Getting to the Answer:
The numbers 8 and 4 should come to mind. Then
y = 4, the width of the rectangle is 4, and the length is 8.
Now to the circles. You have to notice something important
here-the diameter of each circle is the same length as
the width of the rectangle. If you draw a vertical diameter
in either circle, you'll see that. So what's the length of the
diameter? That's right, 4. So the radius is half of that, or 2,
and the area is 1t x 22, or 41t, (A).
This is also a good eyeballing problem. If the rectangle has
an area of 32, then half the rectangle has an area of 16. The
area of either circle looks like it's less than half the area of
the rectangle, or less than 1 6. Which answer choices are less
than 16? If you remember that 1t is a little more than 3, then
you'll know that only (A) and (B) are less than 16, so you
can narrow it down to two answer choices and guess.
13. D
Difficulty: Medium
Strategic Advice: Here you have to know something about
coordinate geometry. The easiest way to do this question is
to estimate values for the x- and y-coordinates of each point.
Getting to the Answer:
Look at point A. It looks like the x-coordinate of A is about 1-l
It also looks like the y-coordinate of point A is about t·
lsx - y < O in this case? No, because 1+-t = 1, so
choice (A) is out. Since point B is sitting right on the x-axis,
its y-coordinate is 0. Its x-coordinate looks like it's about t·
and+ - 0 = t· so (B) is out also. Point C looks like the
point (1, - lt), so x-y is 1 - (- lt), which is positive.
Eliminate (C). Choice (D) is (-1+, t), so x-y is -1+-t·
which is negative, so (D) is correct.
You might have wanted to approach this a little more
theoretically. Under what conditions would the expression
x - y be negative? If xis a positive number, or 0, then x - y
would be negative if y were greater than x. Are there any
points that meet those requirements? No, because although
points A, B, and Call have positive x-coordinates, they also
all have y-coordinates that are smaller than their respective
x-coordinates. What about when xis negative?
If x is negative and y is positive, then x - y must be negative,
so all you have to do is find a point where xis negative
(to the left of the y-axis) and y is positive (above the x-axis),
and you've found the answer, (D).
14. B
Difficulty: High
Strategic Advice: If a diagram in a question contains
unfamiliar shapes, try altering the diagram to make it contain
more familiar ones.
Getting to the Answer:
L M N
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By adding point Q and drawing in line OQ, you can
make the diagram look much friendlier. If we ignore MP,
the diagram now consists of rectangle LQOP and triangle
NOQ; summing the areas of these two figures will give us
the area of LNOP. We know that LP = 12 and OP = 1 3,
so the area of LQOP = 12 x 13, or 156. Since LP= 12,
OQ must also equal 12. If NO = 1 3, NOQ must be a 5-12-13
triangle, and QN 5. = The area of a triangle = ¥h, so the
area of NOQ = tCS)( 12) = 30, and the area of LNOP =
156 + 30 = 186.
15. D
Difficulty: Medium
Strategic Advice: Often, later questions will take a simple
concept and disguise it as a more difficult question.