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

12 Practice Tests for the SAT
826 Practice Test Nine Answers and Explanations
15.
5
24
Difficulty: Medium
Strategic Advice: You probably want to start this question
by drawing a number line.
Getting to the Answer:
Put i and t on your number line, with i to the left oft
since it is smaller:
1
6
What point is the same distance from i as it is from t?
x
Certainly it's the point that is halfway between i and *' so
that must be where point Xis. The distance from point X to
either i or t is half the distance from i tot· The distance
from i to t is just the difference of the two numbers, or
t-i· However, you can't subtract i from t because they
are fractions with different denominators.
You can find a common denominator, like 12. Because t =
1 3 2 and i = 1 , the difference between i and t (and
therefore the distance between them on the number line)
is 1
3
2
- 1
2
2
= *· The distance from X to i is half of '
or j- x * = 2
1
4
, so put everything in terms of 24ths.
1 2 4
d 1 3 6 h" h
6 = TI = 24 an 4 = TI = . If you put t 1s on t e
24
number line, it becomes clear what Xis since Xis halfway
between 2
and 2
6
4
:
4
24
x
5
24
4
6
24
The coordinate of X must therefore be ] 4
, so put that into
the grid.
Be very careful with fractions like this. Many students would
assume that the number equidistant from _!_ and _!_ is _!_.
4 6 5
T h. 1s . 1s not true! Ma k e sure you convert to common
denominators when working with fractions on a number line.
16. 54
Difficulty: Medium
Strategic Advice: The polygon ABCDE is clearly a five-sided
polygon, which is called a pentagon. OE and OD are radii of
the circle, and if you draw lines from 0 to A, B, and C, those
lines will also be radii of the circle. If you do that, you'll see
that since the sides of the pentagon are equal, those radii
divide the pentagon into 5 identical triangles. Therefore,
those radii divide the circle into 5 equal pieces. That means
that each of the central angles formed by those radii
measures i of the whole circle, or i x 360° = 72°.
Getting to the Answer:
So, angle DOE measures 72°. Since two of the sides of
triangle OED are radii of the circle and therefore equal in
length, the triangle is isosceles. That means that angles OED
and ODE are equal, so they both measure r0• So, r° + r° +
72° = 1 80°, which means that r = 54.
17. 19.5
Difficulty: High
Strategic Advice: The figure shows two triangles that
are formed by two lines that cross each other plus two
additional lines. Each triangle has an unlabeled angle, both
of which are formed where the two longer lines cross. That
means that the two unlabeled angles are vertical angles, so
they must be equal to each other. Label each of those two
angles y°. Then the triangle on the left has angles measuring
y°, x0, and (3x + 1 )0, and the triangle on the right has angles
measuring y°, (2x)°, and 40°. The sum of the angles of
any triangle is 180°, so y+ x + (3x + 1) = 180, and
y + 2x + 40 = 1 80. That gives you two equations and two
unknowns, so you should be able to solve for both x and y.
Getting to the Answer:
There are a number of different ways to do so, but the
easiest is to just forget the 180 and set the sums of the
angles equal to each other:
y + x + (3x + 1) = y + 2x + 40
y + 4x + 1 = y + 2x + 40
4x + 1=2x +40
2x + 1 =40
2x =39
X= 19.5
So just put 1 9.5 into the grid.