Virtual Reality 3 Explanations

1.
D
Since the veteran boxer won most of his bouts by knockouts, you can assume that
he was pretty successful.
Unb r oken
is the only choice that describes his series of
wins in a way that suggests success; an
unb r oken
series of victories would be a
winning streak with no losses. (A) and (B) are both contradicted by the rest of the
sentence. Choice (C)
able-bodied
may seem to fit in a sentence about a boxer,
but what’s an
able-bodied
series of wins? This choice sounds odd when you plug
it in. Only (D) makes sense.
2.
E
Sitting still for hours and remaining alert to the slightest sound or motion amounts to
having (E)
limitless
patience and keen powers of
obse r vation .
Powers of (A)
persuasion,
(C)
reasoning,
or (D)
trust
have nothing to do with the description

of bird watching given. In (B), powers of
concentration
are certainly required but
it doesn’t make sense to speak of patience as
skilled.
3.
B
One of the main things with Sentence Completions is to look for context clues—
words and ideas in the sentence that strongly suggest the answer you’re looking for.
Here, the first major clue in the sentence is the word “everyday.” You know
you’re looking for a word with a similar meaning for the first blank. In the second
blank,
you need something to describe what the everyday objects were transformed into, a
word to contrast with “everyday.” That takes you to (B).
Mundane
is almost a
synonym for “everyday.” The second word in (B),
r esplendent ,
or extraordinary,
is
a good contrast, and fits when plugged into the sentence: Weston’s camera
transformed
mundane
things into objects of
r esplendent
beauty. (C) and (E)
can be eliminated because their first words don’t work. Everyday things like
vegetables are not always
small
or

artificial
. In (A),
inexpensive
might seem to
fit with the idea of “e v e r yd a y items such as vegetables.” But (A)’s second word,
tawdry,
or cheap and gaudy, makes no sense. In (D), you might imagine that
vegetables can be
decorative,
but (D)’s second word
functional
doesn’t provide
the contrast we’re looking for.
4.
B
Here, you know that the issues “go far beyond” the immediate controversy referred
to in the sentence. So you can predict they have “implications” or “consequences”
beyond the matter presently under discussion. The best match for this prediction is
(B)
ramifications. Ramifications
are resulting developments or consequences.
(C)
proponents
are advocates or supporters. (D)
inferences
are conclusions.
5.
D
The phrase “even accepting” in the second part of the sentence implies that
Chamberlain’s approach to German aggression was not a particularly tough or

militant one, especially since he tolerated Germany’s annexation of Austria.
Therefore, it’s likely that Chamberlain adopted a non-aggressive, accepting
approach to Hitler. The choice that comes closest to this prediction is (D)
conciliato r y ,
meaning “tending to pacify or accommodate.” Choice (B)
precarious
means “uncertain or dangerous,” and choice (C)
haughty
means
“arrogant, snobby, huffy.”
section one
Section
1
(V
erbal)
SAT
Virtual Reality III
1
section one
6. C Although we don’t know what kind of performance Redgrave gave, we can infer that
it was either good or bad. If it was good, we can predict people who were lucky
enough to see the performance say it was the height of his career. Basically, we
want two positive words if Redgrave did a good job, or two negative words if he
bombed. The only choice showing this relationship is (C): those
fortunate
enough to witness Redgrave’s performance say it was the
pinnacle,
or height, of
his
career. (A)

scourge
means “something that annoys or destroys.” (B)
astute
means shrewd or perceptive. (D)
hapless
means “unlucky.” (E)
nadir
means “the
lowest point.”
7. C This woman relieves her after-work exhaustion by walking along the beach. Thus
the implied adjective in the first blank, describing the sea air, will reinforce this idea.
In the second blank, we need a synonym for “relieve.’’ Thus (C): the
bracing,
or
invigorating, sea air always manages to
alleviate
her fatigue. The other choices
make no sense. The sea air might be (A)
humid,
(B)
salty,
(D)
damp,
or (E)
chilly
, but those qualities wouldn’t
hasten, exacerbate
(worsen),
r
epr

ove
(scold), or
aggravate
the woman’s exhaustion.
8. A The word in the blank will describe terms which refer indirectly to some thing or
idea. The right answer is (A) —
euphemisms
are polite, inoffensive or less
explicit terms which are used to name an unpleasant, frightening or offensive reality.
"Passed away" is an example of a euphemism. You say “passed away” instead of
“died.” (B)
banalities
are things that are commonplace or worn-out. (D)
apostrophes
are marks used to indicate the omission of one or more letters in a
word, as in the word “can’t.” (E)
eulogies
are formal speeches of praise. At a
funeral, speakers might deliver
eulogies
about the person that died.
9. E A good vocabulary will help you figure out this one. The bookkeepers altered some
financial records and completely fabricated others, so you need a word like
“altered,” “falsified,” or “fake” for the blank. (E)
spurious
means “false, lacking
authenticity,” so it’s a good match.
10. D
LEMONADE
is a type of BEVERAGE just as a

magazine
is a type of
periodical
.
11. C The related prefixes CO-, COL-, and COM- mean “with” or “together.”
COLLABORATE
contains the prefix CO- and the root LABOR, so it means “to
WORK together.” The word habit has come a long way from its root, HABIT, over
the centuries, but the original root meaning is still visible in such words as inhabit,
habitat, and habitation. In those words, HABIT means “to live or reside.” So
cohabit
means “to live together,” and (C) is correct. In (D), SYN-, like CO-,
means “with” or “together”; CHRON- means “time.” So
synchronize
means “to
make happen at the same time.” When one watch is synchronized with another, it
displays the same time as the other watch. But
watch
in choice (D) isn’t a noun,
it’s a verb. Always “watch” the parts of speech in an analogy to make sure you
understand
what meaning of a word is intended.
SAT
Virtual Reality III
2
12. E In questions where the vocabulary is easy it is very important to state the
connection between the stem words absolutely precisely. In this case an
APRON
section one
is worn to protect one’s CLOTHES. Once this is clear, answer choice (E) jumps

out as correct: a
helmet
is worn to protect the head. The other answer choices,
even those with strong bridges, can be eliminated easily: (A) is strong—a
parasol
is used to protect against the sun—but that bridge is inappropriate. (B) is
moderately strong:
gloves
are sometimes worn to protect against the
cold;
since
this bridge is identical to that in (A), both answer choices would have to be
eliminated because only one answer can have the same bridge as the stem words.
(C) and (D) have totally different bridges—so (E) is the correct answer.
13. B Answer choice (B) is correct. A PULPIT is a platform on which a
PREACHER
stands in church when addressing the congregation. In (B), the
podium
is a
raised platform where the
conductor
stands. Choice (A) has a strong bridge
—
every
teacher
has a
student—but
it is not the one which we need here. Choices
(C), (D) and (E) can be eliminated because they have weak bridges: an
artist

, if he
or she is a painter, may use a
canvas
(C) but the connection is not a really strong
one; (D) and (E) are even weaker. In (D) a
gallery
is a balcony in a theater.
14. A Here’s a tougher stem pair, but, as always, there is a strong bridge: The word
ADULATION
is a very strong kind of PRAISE. In the same way, with (A),
loathing
is a very strong kind of
dislike.
(B) doesn’t work because
disdain
and
contempt
mean practically the same thing. The stem pair involves one word that’s
an extreme form of the other.
Scholarship
is not an extreme kind of eloquence
(C).
Sympathy
is not an extreme kind of
emotion
(D). And
pleasure
is not an
extreme form of
hedonism.

If you had trouble, you might have tried eliminating
choices—(C) and (D) both seem like weak bridges (words with unclear
relationships)—and then guessing.
15. B An
ANALGESIC
is used to relieve PAIN. Likewise, an
emollient
is used to
relieve
d r yness .
There were a lot of “doctor” words here—especially in
choices (D) and (E). You might have spotted them as SST’s (same subject
temptations), especially since this was supposed to be a tough question. On
tough questions, the ones at the end of the set, the “obvious” answer is usually
wrong. In (A), a
purgative
is a medicine that purges or cleans you out, like
mineral oil. But a
purgative
doesn’t produce
purity,
exactly. In (C) a
humidifier
provides moisture, not
ventilation
(air circulation).
Leisure Time Passage
This is a not-too-difficult social science passage, which only has a few big ideas. If
you felt confused at any point, it would’ve been worthwhile to check the questions.
They clarify things and are fairly straightforward. Your first reading should’ve given

you these ideas: Paragraph 1 says that people have less free time now than they
used to, because people are choosing to work overtime to be able to afford
expensive leisure-time activities. Paragraph 2 says that although people have less
free time during the week, on weekends they feel compelled to participate in
strenuous, skill-testing activities. Paragraph 3 explains that this is because
technology has removed “craft” from most professions, so people try to prove their
competency by mastering demanding leisure activities.
SAT
Virtual Reality III
3
section one
16. C Go back and read a few lines around the quoted line to see the context in which
“skiing and sailing” are mentioned. The author’s point is that if you want to go
skiing or sailing in your free time, unless you are rich, you’ll have to spend some of
that “free time” working to be able to afford those expensive pastimes. That makes
(C) correct. The point is not that expensive sports are “inaccessible” for the
average person (A), but that they require a sacrifice of time. The author is not
commenting on the cost of sports like skiing and sailing (D), or whether they are
“unnecessarily expensive” (B). (E) is out because the author is not giving out
advice about what type of recreation to choose.
17. B Don’t over-interpret the passage with a question like this one—the answer is fairly
straightforward. For example, choices (C), (D), and (E) give way too much
information for what is found in the text. The author simply says that either because
advertising is very effective, or because people just want to own stuff, they choose
to work more hours. So the “effectiveness of advertising” is one possible reason
why people spend so much on recreation (B). Choice (A) sounds much too
extreme--the author never “condemns” the average consumer for anything.
18. B After reading a line or two around the word “indulgences,” it should be clear that the
author uses that word to refer to items like “elaborate running shoes” and
“monogrammed warm-up suits.” These clearly are not (E) favors. There’s nothing

in the context to support the idea that they are (A) rewards; they certainly are not
expenses (D), and while (C) whims comes close, (B) luxuries is the better answer.
19. D The author’s point in lines 38-43 is that until recently, many leisure activities could
only be pursued once a year. The example of taking swimwear out of mothballs
illustrates this point ironically — people swam so infrequently, they had to put their
swimwear in long-term storage (D). Choice (A) is wrong because the author
expresses no particular opinion about annual vacations today. “Household chores”
(B) is a distortion of the idea of “digging equipment out and dusting it off.” (C) is out
because despair is too strong a word — watch our for these kinds of wrong choices
— and because taking out swimwear hardly fits the description of a “traditional
custom.” Finally, there was no “lack of enthusiasm for swimming” in the past —
it was just enjoyed in a different way than it is now.
20. A The “casual attitude” is described at the end of paragraph 2. It is the emphasis on
“having a good time” during recreation, rather than focusing on “technique.” You’ll
save time by scanning the answer choices before going back to the passage. (C)
and (D) jump out as wrong, because they’re never discussed. (E) is also off-base;
people never had “a resistance towards buying sports equipment.” You can scan
paragraph 1 to be sure, but there was never a restriction on working overtime, so
(B) is out. That leaves (A), which may not seem like a very precise answer, but by
process of elimination, it has to be correct. Remember not to argue with what
you’re given—choose the best answer, and move on.
SAT
Virtual Reality III
4
21. B Scan the end of paragraph 3 to identify “the author’s conclusion.” That’s where the
author argues that people “work at recreation” because technology has taken the
craft out of their jobs. Now check the choices. (B) should jump out as correct—
describing the skills that people employ in their leisure time would support the idea
that people are doing “meaningful work” on the weekends. Information about jobs
that still require a level of expertise (A) would weaken the author’s point. Information

section one
about (C) and (D) woudn’t affect the author’s conclusion — these choices refer to
earlier points. Choice (E) may have been tempting — but information about
technologies in the workplace would not support the author’s conclusion as directly
as information about the skills now involved in leisure activities — choice (B).
Frederick Douglass Passage
SAT
Virtual Reality III
5
The introduction tells you that this is an excerpt from an autobiography. Your first
read-through should’ve given you a general idea of the main points: Douglass
learned to read and write through his own resourcefulness; he was influenced
greatly by two specific pieces of writing; and the more he read, the more tormented
he became by his conviction that having freedom was rightfully his.
22.
C
Remember that with “primary focus” questions you need to find a choice that covers
the main points of the passage, without being too broad or too narrow. In this case,
(A) is much too narrow. Douglass mentions that he made friends with some White
boys only to let the reader know how he learned to read. How learning to read
influenced his ideas about slavery (C) is the primary focus of the passage, because
that’s the idea everything in the passage relates to. (D) is an example of an overly
broad choice. It blows up the two books that influenced Douglass into “literature,”
and the discussion of slavery into “civil rights movements.” It doesn’t mention
Douglass, reading, or slavery at all. If you have trouble with a primary focus
question, you can either: do the other questions first, which might clarify the main
idea for you; or eliminate any too-broad or too-narrow choices and guess.
23.
E
Don’t be put off by the vocabulary in this (or any) question stem. Use the

information you’re given—the line reference—to figure it out. What does Douglass
say about his mistress in paragraph 1? Simply that she started to teach him to
read and write, but then (influenced by her husband) stopped, and wouldn’t let
anyone else teach him either. That’s what correct choice (E) says. If you were
confused by the word “absolutely” in this choice (since she had started to teach
him), you should eliminate the rest of the choices, which should then lead you back
to (E). (A) is wrong because we found in paragraph 1 that Douglass’s mistress
finally took her husband’s advice—not that she “persisted in ignoring it.” (B) is
wrong because there is no mention of Douglass’s opposition to slavery in paragraph
1—if you chose (B) you’re inferring too much. The same goes for choices (C) and
(D).
24.
E
Read a few lines after the line you’re referred to. Douglass says he made friends
with some White boys, and that “with their help, [he] finally succeeded in learning to
read.” Learning to read was the goal of his plan, and choice (E) is correct.
Douglass never mentions that he even thought of trying to persuade his mistress to
continue teaching him, so (A) is out. If you chose (B), (C) or (D), you’re inferring
too much. Again, keep the main idea in mind, and remember some questions are
straightforward.
25.
D
In a question where you’re dealing with an analogy, you don’t want to be too literal.
In the lines you’re referred to, Douglass describes how he gave bread to hungry
boys in exchange for lessons—“the bread of knowledge.” Since he says this kind of
section one
“bread” is “more valuable” than actual food, it must’ve been very important to him,
as (D) has it. If you chose (B), you’re focusing too much on details and losing sight
of the main points. (E) distorts a small fact (the availability of bread) into an
improbable inference. (C) takes the word “valuable” to mean financially valuable,

but Douglass means knowledge is valuable in other ways.
26. C This is another question where you need to make an inference, but be sure that
your answer is based on the lines that you’re referred to. First, Douglass says it
would not injure him to give the names of the boys who taught him to read, so you
can eliminate (D) and (E). Instead, he points out that it might embarrass the boys
because it was considered an “offense” to teach slaves to read. It is a short leap
from this information to correct choice (C). There’s no evidence for the inference
(A) makes, and nothing in the passage mentions Douglass being “advised” about
whom to associate with (B).
27. B “Bear” has a number of different definitions, so you must go back to the context to
figure out the answer. You should do this with all vocabulary-in-context questions.
(B) makes the most sense. (D) might’ve tempted you, since Douglass is “suffering”
at the thought of being a slave for life. But it’s the situation that implies suffering,
not the word “bear.”
28. C When Douglass discusses Sheridan’s speech he says that “I read [it] over and
over,” and that what he got from it was “a bold denunciation of slavery and a
powerful vindication of human rights.” You should realize from this tone—before you
go to
the answer choices—that you need a positive-sounding answer. From the first
words in the answer choices, you can quickly eliminate (B) “disappointment” and (E)
“skepticism.” At this point you’ve eliminated enough choices to guess, if you happen
to be running out of time. If not, read the rest of the choices. (A), “interest,” is
probably the least likely; Douglass was really psyched about Sheridan’s ideas, not
merely “interested” in them. (C) has a strong enough first word, “enthusiasm,” and
the rest of the choice proves it’s correct: what was Douglass so enthusiastic about?
Sheridan’s views of slavery, of course. That relates to the main idea of the
passage, which you should keep in mind when you answer any question.
29. D This question’s a little harder than most, so if you had trouble with it, you should’ve
come back to it, or eliminated choices and guessed. Remember, all questions are
worth the same, so don’t lose time on any single one. In this case, a good

approach is to figure out the point of the paragraph, and then find an answer that
makes sense. What’s Douglass’s main point there? He says that the more he
read, the more he realized that slavery was a large-scale form of robbery, which
increased his outrage. So Douglass describes slaveowners as “robbers” to
emphasize that as his knowledge increased, so did his anger (D). (A) is tricky. The
description of slaveowners as “robbers” may indicate that Douglass’s
misconceptions about the legitimacy of slavery had been dispelled, but it’s not
Douglass’s goal here to do that for others. (B) and (C) don’t make much sense in
this context. (E) is wrong because it’s not Douglass’s goal to prove his master’s
predictions.
SAT
Virtual Reality III
6
30. D Read the lines you’re referred to, and a line or two more, to understand the context
where the phrase “eternal wakefulness” is used. Douglass says that he “saw” and
“heard” freedom everywhere—that the idea of freedom tormented him, since he was
section one
supposed to be a slave for life. “Eternal wakefulness” refers to the way his soul had
been affected by the idea of freedom. Now check the choices to see which one fits
with these ideas. (D) matches, and is the right answer. (A) is out because
Douglass knows all too well the causes of his unhappiness. (B) is wrong because
it’s too positive—it doesn’t capture the “torment” Douglass discusses. (C) might be
the next step he takes, but he doesn’t mention his “plans” for freedom in this
excerpt. Finally, Douglass says nothing about “researching his African origins”
anywhere in the passage.
SAT
Virtual Reality III
7
section two
Section

2
(Math)
1.
A
We’ve got a lot of food and we’re making some skimpy sandwiches with only one
slice of ham and one slice of cheese in each one. If there are 75 slices of ham and
75 slices of cheese, then we should be able to make 75 sandwiches, right? One
slice of ham and one slice of cheese in each sandwich, and 75 slices of both ham
and cheese seems to indicate 75 sandwiches. Certainly you can’t make more than
75 sandwiches, so choices (D) and (E) can be eliminated. The question is: Is there
enough bread to make 75 sandwiches? There are 120 slices of bread, and each
sandwich gets 2 slices of bread, so there is enough bread for only 60 sandwiches.
So the caterer can only make 60 sandwiches. The correct answer is (A).
2.
B
This is a fairly straightforward algebra question. If you had trouble with it, you
probably need to do some review in your Math Reference Book.
To solve, simply plug the given values for x and y into the equation. You should
write down each step, otherwise it is easy to make a careless error. You’re given
the
expression x
2
+ 2xy + y
2
. Since x is 1 and y is –1, this expression becomes
x
2
+ 2xy + y
2
= (1)

2
+ 2(1)(–1) + (–1)
2
= 1 + (2)(–1) + 1
= 1 + (–2) + 1
= 1 – 2 + 1
= 0
Be careful here with the operations involving negative numbers. Remember that
when you square –1, or any other negative number, you get a positive number, and
that adding a negative number is the same as subtracting a positive number.
There’s a shortcut here that you may have noticed. The expression x
2
+ 2xy + y
2
is equivalent to (x + y )
2
. Since x + y = 1 + (–1) = 1 – 1 = 0, (x + y)
2
is also equal to
0.
3. C This is a translation problem, so you have to take the words a few at a time and find
the equivalent equation. Let’s start with the words “12 less than.” What if you were
asked “What is 12 less than 20?”. That’s easy, right? 12 less than 20 is just 20
minus 12. So 12 less than the product of something is going to look like something
minus 12. The next part of the phrase is “the product of 3 and b.” You should
know that a product is the result of multiplying two numbers together. So the
product of 3 and b is just 3 times b, or 3b. Therefore 12 less than the product of 3
and b is just
12 less than 3b, or 3b – 12. The next word is “is,” which means equals, so we have
“3b – 12 = .” What does it equal? 9, of course, so the entire equation is 3b – 12 =

9, choice (C). You might have been tempted by choice (A), which is similar, but
notice that in (A) the 12 is being subtracted from b, not from the product of anything.
SAT
Virtual Reality III
8
4. C If you look at the drawing, and think about how gears work, you’ll see that the teeth
of each gear pushes the gear next to it to make it go around. Let’s call the gears A,
B, C, etc. from left to right. If gear A is turned clockwise, then its teeth will push the
teeth on the left side of gear B down. This will make gear B turn counterclockwise.
Since gear B is turning counterclockwise, the teeth will be moving up when they are

,

section two

on the right side, touching gear C. That will push the teeth on the left side of gear C
up, and make gear C turn clockwise. Do you see the pattern now? This will make
D turn counterclockwise, E turn clockwise, and finally F turn counterclockwise.
Since A, C, and E will turn clockwise and B, D, and F will turn counterclockwise, 3
gears will turn counterclockwise, choice (C).
5 & 6. Whenever you have a graph question, it’s a good idea to spend at least a few
seconds examining the graph before you begin. Here you have what looks like part
of a pie chart and a bar graph, both describing the employees at Company X. From
the note under the title you know that there are 800 employees, and from the notes
under the graph you know that 75% of them work full-time and 25% of them work
part-time. Notice that the full-time employees are represented by the bar graph,
which gives the number of full-time employees in each department, whereas the
part-time employees are represented by the pie chart, which gives the numbers of
part-time employees as a percentage of the total number of employees.
5. D You already know from your examination of the graphs that 75% of the employees

work full-time, 25% work part-time, and that there are 800 employees in all. That
means that there are 75% × 800 = 600 full-time employees and 25% × 800 = 200
part-time employees. Since 600 is 400 more than 200, the number of full-timers is
400 more than the number of part-timers, and the correct answer is (D).
You could also have done this by finding the difference of the percents first. Since
75% are full-time and 25% are part-time, the difference between them is just
75 – 25% = 50%, since they are percents of the same whole. 50% of 800 is 400,
again choice (D).
6. A Now you have to figure out what percent of the employees work in the
manufacturing department. What makes this hard is that there are 2 kinds of
employees — part-time and full-time — and 2 kinds of graphs that represent them.
You’ll have to figure out the number of part-timers in manufacturing and the number
of full-timers in manufacturing separately, then add those 2 amounts together, and
then figure out what percent of the total that number represents. First, the number
of full-time employees in manufacturing. That’s easy — you can just read that off
the bar graph, which tells you that there are 240 full-time employees in
manufacturing. Now for the part-timers. The pie wedge that says “manufacturing”
also says “10%.” But 10% of what? Be careful here — it’s not 10% of the total
number of part-timers; it’s 10% of the total number of workers, or 10% of 800, which
is 80. So there are 80 part-timers and 240 full-timers in manufacturing, for a total of
320 workers in manufacturing. Since there are 800 workers total, the percent is just
SAT
Virtual Reality III
9
320
, or
800
40

100

, or 40%, answer choice (A).
7. B Maurice starts out with $80. He spends $32.45 on clothes, so after he buys the
clothes he has $80 – $32.45 = $47.55 left. Then he gives $27.55 to his sister so he
has $47.55 – $27.55 = $20 left. We’re trying to find what fraction of the original $80
he still has, or what fraction of $80 the $20 he has left is. That fraction is just
20
80
or
1
, choice (B).
4
section two
8. E In this question you don’t have to solve for x, so if you did a lot of work, solved for x,
and then plugged one or both of the values back into the expression 2x
2
– 8x, you
did a lot of unnecessary work. If you’re given an algebra problem where you’re not
solving for the value of one variable, you should always look carefully at the
expression you’re solving for. Can you see any similarities between the expression
you’re solving for and the information you’re given? In this problem, you should
have noticed that 2x
2
– 8x looks very similar to x
2
– 4x. In fact, 2x
2
– 8x = 2(x
2
–
4x).

So, if x
2
– 4x – 12 = 0, then x
2
– 4x = 12, and 2x
2
– 8x = 2(x
2
– 4x) = 2(12) or
24, answer choice (E).
9. E Don’t be scared by the term ”factor-rich.” It’s just a made-up expression that is
defined by concepts that you already know about. The question stem tells you that
all it means for a number to be factor-rich is that when you add up all the factors of
the number except for the number itself, that sum is greater than the number. All
you have to do is go through the answer choices and add up the factors of each one
except for the number itself. The factors of 6 are 1, 2, 3, and 6; adding all of them
except 6 gives us 1 + 2 + 3 = 6. The result is not greater than 6, so 6 is not factor-
rich. For choice (B) we add 1 + 2 + 4 = 7, which is not greater than 8. Choice (C) is
9, so we add 1 + 3 = 4. No good. The factors of 10 are 1, 2, 5, and 10, and 1 + 2 +
5 = 8, so 10 is not factor-rich either. Since we’re left with only one answer choice,
(E), it must be correct, but just to check add up 1 + 2 + 3 + 4 + 6 = 16, which is
indeed greater than 12 so choice (E) is correct.
10. D In this question you have 2 parallel lines, £
1
and £
2
, and 2 lines which cross both of
them, £
3
and £

4
. Let’s forget about £
3
for a minute, and look what happens where
£
4
crosses
£
1
and
£
2
. Since
£
4
is perpendicular to
£
2
, all the angles that are
formed where those 2 lines cross are right angles. And, since £
1
is parallel to
£
2
,
the angles that are formed where £
4
and £
1
meet are also right angles. That means

that £
1
and £
4
must also be perpendicular to each other, which means that
statement I is true. That means we can eliminate answer choices (B) and (E).
£
3
also crosses the two parallel lines and together with £
4
creates a triangle in
between them. Since all the angles formed where £
2
and £
4
meet are right angles,
the triangle is a right triangle. One of the other angles of the triangle measures a˚,
but what about the third angle of the triangle? Well, that angle is formed by the
same lines that form the angle labeled b˚, so that angle inside the triangle must also
measure b˚. Since the 3 angles inside the triangle measure a˚, b˚ and 90˚, and the
sum of the angles in a triangle is always 180˚, a + b + 90 = 180, which means that
a + b = 90, so statement III is true. Now we can eliminate answer choices (A) and
(C), and since choice (D) is the only one left, it must be correct.
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Notice that we didn’t even have to deal with statement II once we figured out that
statements I and III were true. This often happens in Roman Numeral questions.
Just for the record, though, statement II is not necessarily true. We know that a + b
= 90, so if a = b then a and b are each 45. However, although that’s how a and b

look in the figure, there’s no information there that would indicate that. b could just
as easily be a 46˚, a 43˚, or a 50˚ angle, so statement II is false.
section two




11. D If there were 1200 books on sale and
1
3
were sold on the first day of the sale, then
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1
× 1200 = 400 were sold on the first day of the sale. That means there were 1200
3
– 400 = 800 books left after the first day. On the second day
1
2
of the remaining
800 books were sold. Since
1
× 800 = 400, 400 books were sold on the second
2
day, which left 800 – 400 = 400 books, answer choice (D).
12. B Let’s take this question one step at a time. A bicyclist riding at 12 miles an hour for
2 hours travels twice as far as a hiker. How far does the bicyclist travel? That’s
easy, 12 miles an hour for 2 hours is just 12 × 2 or 24 miles. If the bicyclist travels
twice as far as the hiker, and the bicyclist travels 24 miles, the hiker must travel 12

miles, since 24 is twice 12. The hiker walks at 4 miles an hour for a total of 12
miles. Since 4 × 3 = 12, the hiker must walk for 3 hours at 4 miles an hour to go a
total of 12 miles, so the correct answer choice is (B).
13. D This is an inequalities question, so you might want to read the inequalities section of
your Math Reference Book if you had trouble with it. Remember, solving inequalities
is the same as solving equations with one exception — if you multiply or divide by a
negative number you have to change the direction of the inequality sign. You can
solve this one pretty easily. Start by adding 2b to each side, and then divide by 2:
2a – 2b < 0
2a < 2b
a < b
This tells you that 2a – 2b is less than 0 when, and only when, a is less than b, so
the correct answer is choice (D).
14. A This question is nowhere near as complicated as it seems. You’re given that the
figure shows a square, an isosceles right triangle, and an equilateral triangle, and
you have to find the total measure of the angles in between them. The first thing to
do is to think about what you know about the angles in squares and triangles. You
probably remember that each angle of a square measures 90˚, each angle of an
equilateral triangle measures 60˚, and that the 2 angles other than the right angle in
an isosceles right triangle each measure 45˚. That means that the angle in between
the x˚ and the y˚ angle measures 90˚, the angle in between the y˚ and the z˚ angle
measures 45˚, and the angle in between the z˚ and the x˚ angle measures 60˚.
Another thing that you should remember is that all the angles around a point add up
to 360˚. There are 6 angles around point D, the one in the square, the two in the 2
triangles, and the three measuring x˚, y˚, and z˚. So, x + y + z + 90 + 45 + 60 =
360, and x + y + z = 165, choice (A).
3
section two
15. C Here you’re given that a and b are integers, but you don’t know whether they are
positive or negative, so there are a lot of possible values of a and b that fit the

equation 2a + 5b = 15. One way to solve this one is to backsolve – to try each
answer choice. Plug in the given value for b and see if the equation works. If you
start with choice (C), which is a good idea when backsolving, you’re in luck here. If
b were equal to 2, the equation 2a + 5b = 15 would be 2a + 10 = 15, or 2a = 5, or a
= 2.5. But you’re given that a is an integer, so a cannot possibly be 2.5, so b = 2
doesn’t work and choice (C) is correct.
You might have noticed that in the equation 2a + 5b = 15 you have an even number,
2a, plus another number, 5b, being equal to an odd number, 15. An even number
plus an even number equals an even number, and an even number plus an odd
number equals an odd number, so the expression 5b must be an odd number. If 5b
is an odd number, then b must be an odd number (since odd × odd = odd and
odd × even = even). Therefore the correct answer choice is the one even
number, again choice (C).
16. B Since you’re given that y is between –1 and 0, why not pick an appropriate number
for y and plug it into each answer choice? Try y = –
1
. Then choice (A) is
2
1
2
1 1 1 1 1
y
2
=
(
–
3

)
=

3

; (B) is 1 – y = 1 –
(
–
3

)
= 1
3
; (C) is 1 + y = 1 +
(
–
3

)
=
3

; (D)
is
2 4 2 2 2 2
1 1
1 1
2
2y = 2
(
–
3

)
= –1; and (E) is
3
=





=
3
=
3

.
2 y + 2 1 3


−

2


+
2
2
Choice (B) is the greatest.
17. C A good way to solve this question is by making yourself a little table. Each
employee is described by two different things. Each one is a woman or a man and
each one either drives to work or takes public transportation. So make this table:

W M
D
P
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In this table each box will contain the number of employees having the two
appropriate attributes. For example, the box in the lower right-hand corner is the
number of men who take public transportation. We can also put numbers in the
6
10
19
6
section two
margins. For example, we can put the number of women in the company below the
box in the lower left-hand corner. Now let’s begin to put numbers in the table from
the information in the question stem. The question stem tells us that there are 25
women and 25 men, and that 29 employees drive to work. Each of these three
pieces of information describes only one attribute of the employees, so these
numbers will go in the appropriate margins. We’re told that 6 men take public
transportation. This describes both attributes, so put a 6 in the lower right-hand box.
Now your table should look like this:
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13
W M
D 29
P
25 25
What we want to find is the number of women who drive to work which is the

number that must go in the upper left-hand box. So let’s fill in information in the
table, hoping that we can work our way to the upper left-hand box. We know that
there are a total of 25 men in the company and that 6 men drive to work. This
means that the remaining 25 – 6 or 19 men take public transportation. So put a 19
in the upper right-hand box. Now we’re going to be able to find the number of
women who drive to work. Since 29 employees drive to work and 19 men drive to
work, 29 – 19 or 10 women drive to work. If you also put a 10 in the upper left-hand
box, your table should look like this:
W M
D 29
P
So 10 women drive to work.
25 25
18. B Careful here! If you said to yourself: “This is simple, pages 10-25 are empty, that’s
25 – 10 = 15 pages at 4 photos a page, that’s 60 photos all together....,” then you fell
into a trap! NEVER pick an obvious answer on a hard problem. The catch here is
that page 10 is empty, too, and if you count from 10 to 25 while including both 10
and 25 you’ll see that there is a total of 16 empty pages, not 15. Since 16 × 4 = 64,
the correct answer is (B).
3
section two
3
In general, if a and b are integers and a < b, the number of integers from a through
b inclusive (meaning that we’re including a and b) is b – a + 1.
19. E This is much more of a logic question than a math question, so you have to think it
through carefully. Since you’re asked which answer choice must be true, one way
to do it is to go look at each answer choice and try to find a possible situation in
which that choice is not true. Let’s start with choice (A), which says that at least one
stereo was sold on each day of the month. That’s not necessarily true, maybe all 63
stereos were sold on one day and none the rest of the month. Cross out choice (A).

Is it necessarily true that exactly 2 stereos were sold on a particular day? No, again
it’s possible that all 63 stereos were sold on one day and none the other days. You
can eliminate choice (B). Do we know if a stereo was sold on a Monday,
Wednesday or a Friday? What if all 63 were sold on a particular Tuesday? So
choice (C) is not necessarily true. Our useful scenario with all 63 stereos being sold
on one particular day is good enough to eliminate choice (D) as well, which leaves
us with only choice (E), which must be correct. Just to be sure, take a look at it. It
says that at least 3 stereos were sold on one day. If all 63 were sold on one day,
then on that day at least 3 stereos were sold. If the sale of stereos was more evenly
distributed, would there necessarily be a day in which 3 or more stereos were sold?
Since a month has at most 31 days, if 2 or less stereos were sold each day of the
month, then at most only 62 stereos would have been sold in that month. In order
for 63 stereos to be sold, there has to be at least one day where 3 or more stereos
were sold, so choice (E) is correct.
20. E If the slope of a line is –
3
, that means every time the y-coordinate decreases by 3,
2
the x-coordinate increases by 2. So, if the y-coordinate goes from 6 to 0, as it does
if you travel along line £ from point A to point B, it decreases by 6, or 2 × 3.
Therefore the x-coordinate must increase by 2 × 2, or 4. Since the x-coordinate of A
is 0, the x-coordinate of B must be 4, so point B ’s coordinates are (4, 0). That
means that the length of OB is 4. Since the length of OA is 6, the area of the
triangle is
1
× 4 × 6 = 12, choice (E).
2
21. C You’re given that a and b are positive integers that add up to 10. There’s a limited
number of integers that meet those requirements – a could be 9 and b could be 1, a
could be 8 and b could be 2, etc. If you list all the possible values of a and b you’ll

find that there are 9 pairs of numbers that could be the values for a and b. You
could plug each of these 9 pairs of numbers into the expression a – b to see which
turns out the smallest. If you do it that way you’ll find that a – b is smallest when a
is 1 and b is 9, so a – b = –8, choice (C).
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That method is a little time-consuming, however. You can make this problem very
short and quick if you just think about the expression a – b. Since a and b are both
positive, this expression will be as small as it can get when a is as small as possible
and b is as large as possible. Since the smallest possible value for a is 1, the
largest possible value for b is 10 – 1 or 9, and therefore the smallest possible value
for a – b must be 1 – 9, or –8, again choice (C).
3 3 3
section two
3
3
22. E To do this question, you have to know what the word “median” means. The median
of a group of numbers is the one in the middle when the numbers are placed in
ascending order. For example, the median of the numbers 3, 6, 7, 12 and 20 is 7.
Notice that the same number of terms are smaller than the median as are greater
than the median.
In this question you’re given that 73 is the median of a group of 7 numbers (one for
each day of the week). That means that 3 numbers must be less than 73 and 3
numbers must be greater than 73. 67, 71, and 72, the temperatures for Monday,
Tuesday, and Wednesday, respectively, are each less than 73. The other 3
temperatures must be greater than 73. The Friday temperature is 76, and among
the answer choices the only values for Saturday and Sunday which are both greater
than 73 are 74 and 77, choice (E).
23. D This question is a lot easier if you pick numbers for the variables. Let’s say that x is

1 and y is 2. Then it takes the printer 1 minute to print 2 pages. That’s a lot easier
to deal with, isn’t it? Then how long does it take the printer to print y + 2, or 4
pages? If it prints 2 pages in one minute, then to print 4 pages it must take 2
minutes. Now you can eliminate any answer choice which does not equal 2 when x
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is 1 and y is 2. (A) is 3, (B) is
3
, (C) is
2
1
, (D) is 2, and (E) is
2
1
. Since only
2
choice (D) resulted in the correct value of 2, choice (D) must be correct.
If you wanted to do it algebraically, you have to determine the rate of the printer in
minutes per page and then multiply that rate by the number of pages. The rate is x
minutes per y pages, or
x
y
minutes per page. Since there are y + 2 pages, the
number of minutes is
x
y
answer choice (D).
minutes per page × (y + 2) pages =
x(y + 2)

3
y
minutes,
24. D One important thing to remember about quadrilaterals is that the sum of the interior
angles is 360˚. That means that w + x + y + 70 = 360, and therefore w + x + y =
290. x must be a positive, but it can be a number very close to 0. If x actually were
0 then w + y would be 290. If x were very slightly larger than 0, w + y would be very
slightly smaller than 290. So, 290 must be the upper bound of the range of values
that w + y could have, so the correct answer must be choice (B) or choice (D). If x
were equal to 45, then w + 45 + y would be 290, and w + y would be 245. However,
x can’t equal 45, but its largest possible value could be a number very slightly
smaller than 45. That means that w + y would equal a number very slightly larger
than 245. So, 245 must be the lower bound of the range of values that w + y could
have. That means that the correct answer must be choice (D).
3
section two
25. A If each term is x more than the previous term, then each term must equal x plus the
previous term, in other words s = r + x and t = s + x. Combining those 2 equations
gives you t = (r + x) + x = r + 2x. The average of r, s and t is
r + s + t
. Substituting
3
r + x for s and r + 2x for t gives you
r + s + t
3
=
3
r + (r + x) + (r + 2x)
333
=

3
3r + 3x
3
=
3
3(r + x)
3
3
= r + x, answer choice (A).
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16
1.
D
This is about the philosopher Thomas Malthus’s predictions about population
growth — kind of an intimidating subject if you haven’t read much philosophy. But
don’t worry. This sentence is pretty simple once you take it apart and look for
clues. The biggest clue is the word famine. You’re told that population growth
does something to food production, resulting in famine. Well, you know that when
many people are hungry and there’s not enough food to go around, famine
happens. Or, to put it in terms of the sentence, population growth would exceed
food production, resulting in massive famine. The answer choice that best matches
this prediction is (D) surpass.
2.
C
The key to this sentence is that Dr. Brown “brooked no deviation from his ideas.” In
other words, he wouldn’t put up with anyone who disagreed, which through the use
of “while,’’ is contrasted with his supposed belief in discussing issues. Hence, (C):
Brown
p r ofess es

or claims to have such a belief, but he interrupts anyone who
doesn’t concur, or agree. (A) makes no sense: there’s no contrast between
regretting
a belief in discussion and cutting off those who don’t
agree
with you.
(B), (D) and (E) may be a bit confusing. They’re just the opposite of what’s needed
in the second blank. Since Brown doesn’t tolerate disagreement, he probably
would not cut off anyone who did not (B)
debate
, (D)
question
, or (E)
pr
otest
.
3.
E
Here you may find it easier to fill in the second blank first, because it contains the
catchy phrase “merely ----, not canceled.” Look for cliched phrases like these on
sentence completions — they can help you get the answer fast. What probably
pops into your head when you read “merely ----, not canceled” is “merely put off, not
canceled.” That’s logical. What you need in this second blank is something that
means the employees have put off their demands for now, but will bring them up
again in the future. So (E)
postponed
is correct. (E)’s first word works as well: it
makes sense that employers would try to
moderate
wage increases during

serious economic difficulties. (C)
redressed
means “set right or corrected.”
4.
C
This example is typical of Sentence Completions testing vocabulary. Getting the
answer hinges on knowing that virulent means “extremely poisonous.” The
sentence tells us that certain poisonous compounds in peach pits are “usually not
harmful.” But, the sentence continues, if you eat enough of them, they can be ----.
We need a word that means “poisonous” or “harmful.” V
ir

ulent
, like the related
word virus, comes from a root that means “poison.” What if you didn’t know the
word vir
ulent
? If you noticed the resemblance between virus and vir
ulent
, that
would have been a good clue. Otherwise, you could have tried eliminating answer
choices. Choices (A) and (D) are words that relate to things that taste bad, but
neither means “poisonous.” (A)
acerbic
means “sour or harsh.” (D)
unpalatable
means “unacceptably bad-tasting.” (B)
superfluous
means
“unnecessary,” and (E)

multifarious
means “diverse.”
5.
D
Here you’re looking for words that fit with the phrases “---- speeches to historical
figures” and “an impartial and ---- historian.” The only choice that fits is (D).
Though Thucydides used psychological insight rather than documented information
to
attribute
speeches to historical figures, he is still considered an impartial and
accurate
historian. (A) doesn’t work, because historians are never referred to as
section three
Section
3
(V
erbal)
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