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

12 Practice Tests for the SAT
Practice Test Eight Answers and Explanations
749
I
13. c
Difficulty: High
Strategic Advice: The figure shows two small triangles
joined together to form a larger triangle. Since the only side
you know the measure of is AB, it's probably a good idea
to start by just looking at the triangle ABO and the angles
of this triangle. Angle BOC is a right angle, and since angles
BOC and BOA lie on a straight line, BOA must also be a
right angle. You're given that angle DAB is 60°. Therefore,
angle ABO must be 30°, and you have a 30-60-90 right
triangle. Remember that the lengths of the sides of a 30-60-
90 right triangle are always in the ratio 1 : V3:2. AB is the
hypotenuse, or longest side of triangle ABO, so it must
correspond to the 2 in the 1 : V3:2 ratio.
Getting to the Answer:
Since 8 = 4 x 2, the other two sides must be 4 x 1, or 4,
and 4 x V3, which can just be written as 4V3. Which side
is which? The smallest side must be opposite the smallest
angle, so the side with length 4 must be AD, which is
opposite the 30° angle, and the remaining side, BO, must
measure 4 V3.
Now work with the other small triangle. You were given that
angle BOC is 90° and that angle BCD is 45°, so angle DBC
must also be 45°, which makes triangle BCD a 45-45-90
right triangle. You just figured out that BO measures 4 V3.
Remember the Pythagorean ratio for 45-45-90 triangles,
1 : 1 : v2. Even if you didn't remember that one, you could
probably figure out that sides BO and OC must be equal
in length since they are both opposite 45° angles. So if BO
measures 4V3, then DC also measures 4V3. The area of
a right triangle is just i (leg 1
)(1eg), or i x 4V3x4V3,
1
or 2 x 16 x 3, or 24, (C).
You also could have eyeballed it. Since it's given thatAB is
8, you could use the edge of your answer grid as a ruler to
compare the lengths of AB and OC. You'd find that DC is
a little bit shorter than AB, probably somewhere around 7.
Compare AB with BO and notice that BO is also a little bit
shorter than AB, and again guess 7 for the length of BO.
Since DC is around 7 and BO is around 7, the area of BCD
is around i x 7 x 7, or i x 49, or 24 i· which is closest to
24, (C).
14. A
Difficulty: Medium
Strategic Advice: Because the figure in the problem is
a square, you know that each angle of the quadrilateral
measures 90 degrees. Therefore, when a corner is divided
into 2 equal angles, the measure of each of those new
angles is 90 -+- 2, or 45 degrees, so s = 45.
Getting to the Answer:
When a corner is divided into 3 equal angles, those new
angles measure 90 -+- 3, or 30 degrees, so r = 30. The
question asks for the value of s - r, so subtract 30 from 45,
leaving 15.
15. E
Difficulty: High
Strategic Advice: Don't add up all these numbers on your
calculator. There is so much calculation involved here that
there must be an easier way to do the problem. Look at
the sets of numbers. There are 12 elements in each set.
For each element in the odd set, there is a corresponding
element in the even set that is 3 greater. That is 5 and 8, 7
and 10, and so on up to 27 and 30. So every element in the
even set is 3 greater than a corresponding element in the
odd set; the result of subtracting the odds from the evens
will be the number of elements in the sets times 3.
Getting to the Answer:
That is, 12 x 3 = 36.
16. c
Difficulty: High
Strategic Advice: This is a tricky multiple-figures problem.
You've got a rectangle in the middle of a triangle. The only
thing you know about the rectangle is that its perimeter
is 12. What do you know about the triangle? One angle is
a right angle and another angle is labeled 45°, so the third
angle, XYU, must also be 45°.
Getting to the Answer:
Since RSTU is a rectangle, all its interior angles are right
angles. Two of its interior angles, SRU and STU, lie on
straight lines. That means that angles SRX and STY are
also right angles. Now you have two small right triangles
next to the rectangle. Each of these right angles has an
angle that measures 45°, so the third angle in each of