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1

MATH LINES AND ANGLES
In the figure above, what is the sum of
a þ b þ c?
(A) 126
(B) 135
(C) 177
(D) 184
(E) 196

Remember there are 1808 in a line. 123 þ a ¼ 180
Subtract 123: a ¼ 57
116 þ b ¼ 180
Subtract 116: b ¼ 64
124 þ c ¼ 180
Subtract 124: c ¼ 56
a þ b þ c ¼
Substitute: 57 þ 64 þ 56 ¼ 177
(Chapter 11 Lesson 1: Lines and Angles)

2

MATH - RATIO AND PROPORTION
B3 If 1
w ¼ 3
16, then what is the value of w?
(A) 4
3
(B) 5
3
(C) 10
3
(D) 16
3
(E) 19
3

. D 1
w ¼ 3
16
Cross-multiply: 16 ¼ 3w
Divide by 3: 5:33 ¼ w ¼ 16
3
(Chapter 8 Lesson 4: Ratios and Proportions)

3

MATH - RATIO AND PROPORTION

The ACME plastic company requires p pounds of plastic to produce c storage containers. How many containers can be produced from x pounds of plastic?

xc/p

px/c

xcp

xp/c

pc/x

Set up a ratio to solve this problem.
c containers
p pounds ¼ ? containers
x pounds
Cross-multiply: cx ¼ p
Divide by p: cx
p ¼ ?
(Chapter 8 Lesson 4: Ratios and Proportions)

4

MATH - PERCENTS ANS SOLVING EQUATIONS

The senior class at Weston High School has
40 fewer boys than girls. If the class has
n boys, then what percent of the senior
class are boys?
(A) n
2n þ 40 %
(B) n
2n 40 %
(C) 100n
2n þ 40 %
(D) 100n
2n 40 %
(E) 100n
n þ 40 %

16. C Because there are 40 more girls than boys,
the number of girls is n þ 40. If the class has n boys,
then the total number of seniors is
n þ 40 þ n ¼ 2n þ 40. Now find out what percent of
2n þ 40 is n.
n is what percent of 2n þ 40? n ¼ x
100 (2n þ 40)
Divide by (2n þ 40): n
2n þ 40 ¼ x
100
Multiply by 100: 100n
2n þ 40 % ¼ x
(Chapter 8 Lesson 5: Percents)
(Chapter 9 Lesson 1: Solving Equations)

5

MATH - WORKING WITH EXPONENTS
If 2k 8w ¼ 220, what is the value of k þ 3w?
(A) 8
(B) 12
(C) 16
(D) 20
(E) 24

18. D You can only compare exponents if they have
the same base. Change 8w into a base 2 exponential.
Since 8 ¼ 23
, you can substitute 23 in for 8.
2k  (23)
w ¼ 220
Simplify: 2k  23w ¼ 220
Combine: 2kþ3w ¼ 220
Eliminate bases: k þ 3w ¼ 20
(Chapter 9 Lesson 3: Working with Exponents)

6

READING - Passage
None of my friends understand the care
with which I preserve a scrap of paper that has
no value whatever: it merely keeps alive the
memory of a certain day in my life, and to it
5 I owe a reputation for sentimentality which is
considered unworthy of my social position:
I am the assistant manager of a textile firm. But
I protest the accusation of sentimentality and
am continually trying to invest this scrap of
10 paper with some documentary value. It is a tiny,
rectangular piece of ordinary paper, the size,
but not the shape, of a stamp—it is narrower
and longer than a stamp—and although it
originated in the post office it has not the
15 slightest collector’s value. It has a bright red
border and is divided by another red line into
two rectangles of different sizes; in the smaller
of these rectangles there is a big black R, in the
larger one, in black print, “Du¨ sseldorf” and a
20 number—the number 634. That is all, and the
bit of paper is yellow and thin with age, and
now that I have described it minutely I have
decided to throw it away: an ordinary
registration sticker, such as every post office
25 slaps on every day by the dozen.
And yet this scrap of paper remi

The first paragraph establishes that the narrator regards his "scrap of paper" line 2 with

deep disgust
sad nostalgia
ambivalence
light-hearted amusement
fear

10. C The ambivalence of the narrator toward the
scrap of paper is clearly demonstrated by the conflict
between his attachment to it and his desire to get rid
of it. He mentions the care with which I preserve (lines
1–2) the paper because of its value in [keeping] alive
the memory of a certain day (lines 3–4) on the one
hand and his decision to throw it away (line 23) on
the other hand.

7

MATH : NUMERICAL REASONING

X: {2, 4, 6, 8, 10}
Y: {1, 3, 5, 7, 9}
One number is to be chosen at random from
set X and added to a number chosen at
random from set Y. What is the probability
that the sum will be an odd number?

4. 1 If you look at set X, all of the members are
even. All of the members of set Y are odd. When an
even number is added to an odd number, the result
is always odd. Therefore the probability that the
sum would be odd is 1.
(Chapter 10 Lesson 3: Numerical Reasoning
Problems)

8

MATH - SEQUENCES
24, 2, 4, 24, 2, 4, 24, 2, 4...
The sequence above continues according to
the pattern shown. What is the sum of the
first 20 terms of this sequence?

7. 10
The first 9 terms are written out for you. Identify the
repeating pattern: 24, 2, 4...
The pattern repeats every 3 digits, and the sum of
each repetition of the pattern is 24 þ 2 þ 4 ¼ 2.
The pattern occurs 20 4 3 ¼ 6.67 times, or 6 with
remainder 2.
The 6 full repetitions have a sum of 6  2 ¼ 12.
The nineteenth term is 24 and the twentieth term is
2, so the overall sum is 12 þ (24) þ 2 ¼ 10.
(Chapter 10 Lesson 7: Sequences)

9

WRITING: COORDINATING IDEAS
The news that the house was no longer for sale came as a disappointment to him, in that he had been excited tohave the opportunity to buy the house for his wife as a wedding present.

(A) as a disappointment to him, in that he
had been excited to have the opportunity
(B) as a disappointment to him; he having
had the opportunity
(C) to him as a disappointment; having been
excited as to have had the opportunity
(D) disappointed him; he had been excited
(E) to him as a disappointment, in that he
was excited for the opportunity

D. The two clauses are not properly coordinated. THe semicolon is used to join two closely related independent clauses in a single sentence. (C) does not work becuase the second clause can not stand alone
Chapter 13 Lesson 15 Coordinating Ideas

10

WRITINGL DANGLING PARTICIPLES Upon reviewing the videotape footage of the
convenience store robbery, the verdict was
clear; the members of the jury quickly
agreed that the defendant was guilty.
(A) Upon reviewing
(B) Having been reviewing
(C) When they reviewed
(D) When reviewing
(E) Reviewing

C This is an error in word order. Choices (A),
(B), (D), and (E) are incorrect because of a dangling
participle. Answer choice (C) is the only one that
eliminates this error.
(Chapter 13 Lesson 7: Dangling and Misplaced
Participles

11

According to an outdated survey conducted
in 2002 by a San Francisco-based consulting
firm, Pittsburgh ranked among the cleanest
cities in the world.
(A) Pittsburgh ranked among the cleanest
cities in the world
(B) Pittsburgh ranks among the cleanest
cities in the world
(C) Pittsburgh has been ranked among the
cleanest cities in the world
(D) among the cleanest cities in the world is
ranked Pittsburgh
(E) ranked among the cleanest cities in the
world had been Pittsburgh

The sentence is correct

12

WRITING - Tricky Tenses
Portrayed as a power-hungry conquerer, Napolean Bonaparte, a great military commander of the eighteenth and nineteeth centuries, argues he was instead building a united federation of free people in Europe.
(A) argues he was instead building a united
federation of free people in Europe
(B) instead argued that he was building
Europe into a united federation of free
people
(C) argued he was instead building a united
federation of free people in Europe
(D) will argue that he was building a united
federation of free people’s in Europe
(E) argued he was building, for Europe, a
united federation of free people

B. Napolean Bonaparte lived in the eighteenth and nineteenth centuries. Thus his argument obviusly occured in the PAST. THis eliminates answer choices A and D. Answer choice B is the most concise and clear choice in the proper tense. Chapter 13, Chapter 9 Tricky tenses