sat virtual reality iii explanations phần 1 pdf

Section 1 (Verbal)
1. D Since the veteran boxer won most of his bouts by knockouts, you can assume that
he was pretty successful. Unbr
oken is the only choice that describes his series of
wins in a way that suggests success; an unbr
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 observation. 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 resplendent 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

veryday 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)
conciliator
y, meaning “tending to pacify or accommodate.” Choice (B)
precarious means “uncertain or dangerous,” and choice (C) haughty means
“arrogant, snobby, huffy.”
section one
SAT
Virtual Reality III
1
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), reprove
(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.
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
SAT
Virtual Reality III
2
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 dr
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.
section one
SAT
Virtual Reality III
3
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.
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
SAT
Virtual Reality III

4
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
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
SAT
Virtual Reality III
5
“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.
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
SAT
Virtual Reality III
6
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.
section one
SAT
Virtual Reality III
7
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.
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
SAT
Virtual Reality III
8
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.
Yo u ’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
, or , 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 ,
or , choice (B).
1
ᎏ
4
20
ᎏ
80
40
ᎏ
100
320
ᎏ
800
section two
SAT
Virtual Reality III
9
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.
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
SAT
Virtual Reality III
10
11. D If there were 1200 books on sale and were sold on the first day of the sale, then
× 1200 = 400 were sold on the first day of the sale. That means there were 1200
– 400 = 800 books left after the first day. On the second day of the remaining
800 books were sold. Since × 800 = 400, 400 books were sold on the second
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).
1
ᎏ
2
1
ᎏ
2
1
ᎏ
3
1
ᎏ
3
section two
SAT
Virtual Reality III
11