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

12 Practice Tests for the SAT
Practice Test Eight Answers and Explanations I
747
3. E
Difficulty: Medium
Strategic Advice: Here you're working with a system of
equations, one of which has two variables and one that has
one variable. A good way to solve this is substitution.
Getting to the Answer:
If 2a = 1 0, then dividing both sides by 2 gives you a= 5.
If a = 5, then a2 - 16 = b2 can be written 52 - 16 = b2, or
25 - 16 =b2, or 9 =b2. If b2 is 9, then b must be 3 or -3,
and (E), 3, could be a value for b.
4. A
Difficulty: Medium
Strategic Advice: The sequence that you're given has 8
numbers, 4 of which are odd and 4 of which are even. You
want to know how the sum of those numbers would change
if the individual numbers changed by various amounts.
You don't need to start adding up the numbers in the
sequence-you're only concerned with how the sum would
change, not what its value is.
Getting to the Answer:
There are 4 odd numbers in the sequence. The question
tells you that each odd-valued term will be increased by
3. Then the sum will increase by 4 x 3, or 12. If each
even-valued term is decreased by 2, that's the same as
decreasing 4 of the terms by 2 each, or the entire sequence
by 4 x 2, or 8. So the sum of the sequence will increase
by 12 and decrease by 8. That's like adding 12 and then
subtracting 8, which is the same as adding 4, (A).
5. E
Difficulty: Medium
Strategic Advice: If you're not sure what the various
transformations of y = x2 presented in the answer choices
look like, you can try plugging in a few points from the graph
to see which equation works. ( 1, 1) is a good point to test.
Getting to the Answer:
y= 1,x= 1
1 = 2 - (12)
1=2-1
1 = 1
Only (E) passes through this point.
6. E
Difficulty: Medium
Strategic Advice: You've got a bunch of lines and angles
here, with a triangle in the middle. One of the interior
angles of the triangle is 60°. The other two interior angles of
the triangle are unknown, but the one on the right and the
angle marked 11 5° make up a straight line, or 180°.
That means the interior angle on the right measures
1 80° - 115°, or 65°. The three interior angles of a triangle
add up to 1 80°, so the third interior angle of the triangle,
the one on the left, must measure 180 - 60 - 65, or 55°.
Getting to the Answer:
That 55° interior angle of the triangle is on the same side
of the straight line as the angle labeled r 0 , so r must be
180 - 55, or 1 25°. The 55° angle and the angle labeled 5°
are vertical angles, so they are equal and 5 = 55. Therefore,
r - 5 = 125 - 55, or 70, (E).
7. A
Difficulty: Medium
Strategic Advice: The date of the second Friday in
December depends on what day the first of the month falls
on. If the first of the month is a Friday, then the 8th of the
month is also a Friday, since 1 + 7 is 8. If the first of the
month is a Tuesday, then the first Friday is the 4th, and the
second Friday is the 1 1th.
Getting to the Answer:
If you try putting the first of the month on each of the days
of the week, you'll find that the latest possible date for the
first Friday occurs when the first of the month falls on a
Saturday. In that case, the first Friday falls on the 7th, and
the second Friday falls on the 1 4th, (A).
8. c
Difficulty: High
Strategic Advice: You want to find the ratio of the length of
a side of the square to the length of a side of the triangle.
You're told that the square and the triangle have equal
perimeters. The perimeter of any polygon is the sum of
the lengths of its sides. In an equilateral triangle, all three
sides have the same length. Call the length of each side of
the equilateral triangle t. Then the perimeter of equilateral
triangle Eis 3t. In a square, all four sides have the same
length. Call the length of each side of the square 5. Then the
perimeter of square S is 45.