sat virtual reality ii explanations phần 2 doc

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section two
Section 2 (Verbal)
1. C The important idea in this sentence is that the woman “lost herself in her work,”
which means it must have been “inspiring” (A), “complex” (B) or “absorbing” (C), not
“exhausting” (D) or “repetitive” (E). If she were really involved in her work, she
would have been ignorant of the noise around her. This rules out (A) and (B); if the
work were “inspiring” or “complex” she wouldn’t be “annoyed by” or “involved in” the
noise. (C) works: her work was so “absorbing” that she was completely “oblivious
to” the noise.
2. C “In contrast to” is the signal; that there is the difference between the piranhas’
image and the reality that many species of piranha are vegetarian. The word in the
blank has to emphasize the piranha’s image as a carnivore. (C), “voracious,” or
“greedy, ravenous, having a huge appetite,” works best. “Nomadic” (A) means
“moving from place to place”; “lugubrious” (B) means “mournful”; (D) “covetous”
means “eagerly desiring something belonging to someone else.” (E) might have
been tempting, but the fact that piranhas seem “exotic” has nothing to do with their
diet.
3. A This sentence has quite a bit of verbiage that you can ignore. The important thing
to see is that there is a contrast between the “modern, subway stations” and
the “graceful curves” of the old buildings. The word in the blank, therefore, has to
be something like “rectangular.” (A), “rectilinear,” which means “characterized by
straight lines” is the only one of the choices that provides the necessary contrast.
4. B The structural clue “while” alerts you that vetiver does not have a disruptive impact
on the local ecology like kudzu does. A good prediction for th blank would then b
“negative,” because vetiver has “no negative effects.“ The only good match for this
prediction among the choices is (B), “adverse,” which means “unfavorable.” Vetiver
clearly has “foreseeable” (A) and “advantageous” (E) effects because it controls soil
erosion, so these choices are wrong. (C), “domestic,” doesn’t make sense in the

sentence. Since you don’t know whether kudzu’s impact on the ecology is
permanent, (D) doesn’t fit either.
5. E Concentrate on the second blank first. It stands to reason that Douglass would
pattern his autobiography after Equiano’s own “autobiography” or “life story.” The
only choice that has a second-blank word coming even close to this prediction is
(E), “consciously narrative,” “Consciously” fits well into the first blank, too; Gates
think that Douglass patterned his autobiography after Equiano’s narrative
“consciously,” or “on purpose.” (E) is the correct answer. “patronizingly” (A) means
“condescendingly.” An “epitaph” (D) is the “inscription on a tomb or grave.”
6. D The first blank has to be consistent with “lived a lonely life”; you can predict a word
like “uncommunicativeness.” This rules out (B) “career” and (E) “gregariousness,”
which means “sociability.” SInce Houseman did let a few close friends into his life,
these friends must have been able to “get past” the “uncommunicativeness.” The
choice that matches these predictions is (D), “reserve penetrate.” “Reserve” is
restraint in one”s words and actions.” (A) is out because close friends would not
“spurn,” or disdainfully reject,” Houseman. “Seclusion” works in (C), but “observe”
doesn’t make any sense in the second blank.
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7. B Narrowing your focus helps with this sentence. Look at the phrase “patriotic and
other cliches.” The first blank has to be a word for a category that “patriotic”
falls into, such as “ideological” (B). For the second blank, you can infer that in an
impersonal world, relief will come from occasional “displays” of emotion. (B),
“ideological manifestations,” has what you need to fill the blanks. “Pragmatic,”
which mens “practical,” doesn’t work in the first blank, and “absences” is the
opposite of what we want in the second blank. “Ephemeral” (D) means “lasting a
very short time,” while “vestiges” (E) means “trace or makes left by something.”
8. C The semi-colon in the middle of the sentence tells you that the two halves of the

sentence have similar meanings. If a plan has “caused widespread resentment,”
then it has few elements that will “make the party popular” with the electorate. We
need a word that means “make popular.” “Ingratiate” )C) means “to gain favor or
acceptance”; it’s the only choice that has the predicted meaning. To “consolidate”
(B) is to “join together into one whole or to strengthen,” and the party doesn’t want
to merge with the electorate, so (B)’s out. “Involve” (A) gives you a strange
sentence when you plug it in. A political party is always involved with the
electorate. “Deprecate” (D), to “express disapproval,” doesn’t make sense in the
context of the sentence. (E) “impeach,” “to charge with a crime, especially the
crime of misconduct in a public office” might have tricked you because it’s a word
that fits in with the political subject matter of the sentence. But it doesn’t fit in with
the meaning of the sentence.
9. C This is particularly difficult question, which you can anticipate because it comes at
the end of the set. Several of the choices look good at first, which is why you have
to look carefully at the sentence. You need an adjective describing the students
who founded the literacy movement. They all had come from French-speaking
colonies to live in France; so they were “expatriate” students, (C), which means
“exiled from or living outside of one”s country.” The word “expatriate” derives from
the root PATER, or “father” which is also found in “paternal.” And the prefix “EX”
means “out.” So to move out from your “fatherland” or native country is to “EX-
patriate.” “Laconic” (B) means “not talkative” and doesn’t fit the context. The
students may have been “radical” (D) or “sophisticated” (E), but the evidence in the
sentence that they were “expatriated” is much stronger.
10. C The WRIST is the joint that attaches the HAND to the rest of the body, in the same
way that the ANKLE is the joint that attaches the FOOT to the rest of the body.
None of the other pairs of words int he choices fits into the stem bridge.
11. E A good stem bridge here is “to REVERE someone is to ADMIRE that person
intensely.” Analogously, to “scrutinize” something is to “examine” it intensely.
“Think” and “ponder,” in (C), are synonyms; there is no difference in degree of
intensity. In (B), to “delay” something a great deal is not to “cancel” it.

12. A A HEDONIST is primarily occupied with the pursuit of PLEASURE; a “philosopher”
is primarily occupied with the pursuit of “knowledge.” In (B), a “stenographer,”
knows “shorthand” and in (C), a “physicist” studies “energy,” but they are not, by
definition, primary occupied with these things. In (D) a “progressive” wants social
improvement through government action, not necessarily “liberty.”
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section two
13. E When something is being UNEARTHed, the process is called EXCAVATION
(digging something out and removing it). Similarly, “imprisoning” someone is the
process of INCARCERATION. In (A), the process of “addition” does not always
involve “constructing.” In (D), “imposition” is “the act of imposing.” “Demanding”
something is not imposing something on someone, so this pair of words doesn’t
work.
14. C Something that is ABSTRUSE is by definition difficult to UNDERSTAND. Likewise,
something that is OBSCURED is difficult to SEE. Things that are “unusable” (A)
can still be changed; things that are “faulty” are not always difficult to “fix” (B);
things that are “irrelevant” (D) may be easy to “prove.” None of these has a bridge
that matches the stem bridge. “Tepid” (A) means “lukewarm,” not “difficult to heat.”
15. B To SULLY is to damage a person's REPUTATION. Similarly, to MAR is to damage
an object's FINISH.
Leatherback Turtles Passage
If you are particularly averse to science, you could have gone on to the next
passage, the fiction piece, and then returned to this one after you got through the
questions there. But take a look at the introduction to this one: this passage is
about turtles, not quantum electrodynamics — not too tough. Just be sure that with
a passage like this one, you don’t let yourself get bogged down in the details.
The overall sense of the passage is that the author, a scientist who is fascinated by
the deep-diving of leatherback turtles, is reporting what he and his wife have

learned about the turtles’ behavior. He tells of recording—at least, partially—the
dive of a female leatherback in the first paragraph. In the second paragraph, the
author discusses the difficulty of studying leatherbacks: they can’t be kept in
captivity. An instrument known as the time-depth recorder has been designed to
measure turtle-diving at sea. Using this instrument, the author found that female
leatherbacks dive almost continuously. Why do the turtles dive? This is the question
the author attempts to answer in the final three paragraphs. It seems that the turtles
are following the movements of a group of organisms known as the deep scattering
layer; this is where jellyfish, the turtles’ food source, are. The author has two main
pieces of evidence for this hypothesis: 1) the turtles’ pattern of diving seems to
match the movement of the deep scattering layer, and 2) turtles do not lose weight
between bouts of nesting. Don’t worry about the details — you can always go back
to the passage to get the details you need when you’re answering the questions.
16. B When you go back to the passage and locate the lines cited in a question stem, be
sure to read for the context. The author says in lines 18-23 that it is impossible to
keep leatherbacks in captivity because they constantly swim against the walls of the
tank. Now, if you only read these lines, you’ll be tempted to select (E), keeping an
animal in captivity can have negative consequences, or perhaps (A), larger facilities
have to be constructed. Neither is, however, the point that the author is trying to
make in the context of the passage. The author is explaining why “researchers have
been developing methods of studying [the turtles] at sea.” The best paraphrase of
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this is (B). (C) is far too broad a generalization to be correct; furthermore, the
author doesn’t say anything about scientific understanding of the turtles being
“limited.” As for (D), the author never mentions other species of reptile in the
passage.
17. A The “specific behavior” that the author describes in the cited lines is the continuous

diving of the turtles. The author at this point is relating how astonished he and his
wife were when they first recorded the turtles’ diving. He is conveying a sense of
“how impressive the diving activity of the leatherbacks is” (A). The author has not
yet talked about the deep scattering layer, so (B) is out. Leatherback breeding (C) is
never even mentioned in the passage. (D) is wrong because the author is not
suggesting that the turtles’ behavior is “unpredictable.” It may be unexpected and
astonishing because the scientists didn’t know much about the turtles, but that
doesn’t mean the turtles behave unpredictably. Finally, you may get an insight into
the life of a marine biologist from this part of the passage, but the author’s purpose
is to describe the leatherbacks, not his lifestyle.
18. C Several of the choices are possible definitions of “gradual.” Remember that with all
Vocabulary-in-Context questions, you need to check how the word is used in the
context of the passage. Approach this question in the same way as you would a
Sentence Completion. Put a blank in the sentence in place of “gradual” and you see
that the word in the blank has to have a meaning opposite of “vertical.” In other
words, “gradual” and “vertical” have opposite meanings here. The only word among
the possible answers that has a meaning opposite of “vertical” is “sloping” (C).
19. B The question “Why the incessant diving?” serves to lead the reader into a
discussion of the author’s attempts to explain the turtles’ diving behavior. The author
is using the device of asking a question and then answering it in order “introduce a
new topic for discussion” (B). Although the turtles’ diving may be an area requiring
“further research” (A), the author does not pose the question to make this point. Nor
is he making a statement about the limitations of the time-depth recorder (C); you
already know from the previous paragraph what the instrument can and cannot do.
There is no suggestion here that the turtles were “behaving in a novel way” (D).
How would the researchers know if the behavior were novel or not? This was the
first time time they ever monitored the turtles. Finally, (E) is far too broad to be the
right answer — watch out for this common kind of wrong answer type.
20. C Read the lines surrounding lines 56-57. The deep scattering layer “migrates to the
surface at night to feed on phytoplankton, then gradually retreats from daylight A

leatherback’s dives seem to follow the movements of the deep scattering layer.” The
reason turtles make shallower dives as dusk approaches is that their food source is
getting closer to the surface (C). Clearly turtles can locate their prey at night, so (A)
is out. (B) can be eliminated because turtles feed on jellyfish, not phytoplankton. (D)
and (E) may seem to be reasonable choices, but they don’t work in the context of
the passage.
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section two
21. E You can answer this question without reading all of the final paragraph. The author
says that they “have not been able to directly observe leatherbacks feeding, but we
have collected some additional circumstantial evidence.” It stands to reason, then,
that the additional evidence will support what the author has been claiming in the
previous two paragraphs, that “female leatherbacks find most of their food in the
deep scattering layer” (E). Choices (A), (B) and (D) have little to do with the
information in the passage. (C) may have been distracting because the author does
mention that female leatherbacks come ashore repeatedly during each nesting
season, but this is not the circumstantial evidence the author uses nor is it what the
author is trying to prove.
22. D The author’s hypothesis is that “female leatherbacks feed between bouts of
nesting.” You also know from working through the last few questions that the
leatherbacks apparently get their food (jellyfish) by following the deep scattering
layer as it moves. The author admits, though, that he has not been able to observe
the leatherbacks feeding when they dive. This is what would support his hypothesis
the most—information about “the activity of diving female leatherbacks” (D). (E) is
a tricky wrong choice. The average weight of the turtles doesn’t matter at all; it’s
how much each individual turtle gains or loses that will show whether they are
feeding between bouts of nesting.
23. E The correct answer to this Big Picture question should jump right out at you now

that you’ve done the other questions and re-read quite a bit of the passage in the
process. The author doesn’t say much about leatherbacks’ nesting patterns (A) or
about “misconceptions” concerning the leatherback’s feeding activity (B). His
description of the time-depth recorder (C) is a detail, not his primary objective. (D)
is wrong because the author never encourages others to study leatherbacks.
Instead, he is “offer[ing] his own findings about the behavior of leatherbacks.” A
shortcut to answering this question would have been to take a look at the verbs in
the answer choices first. Does the author “dispute” anything or “encourage” in the
passage? No, so these two choices could have been eliminated right away, leaving
you with only three to examine more closely.
Marc and Camilla Passage
With this fiction passage, you really needed to read the introduction (something you
should always do, in any case). If you didn’t, you wouldn’t have had any idea what
caused the extremely uncomfortable situation to arise between Marc and his
friends, and you’d be confused throughout the passage because the author never
specifically mentions what has upset Camilla and Karen. The first paragraph
centers on Camilla’s reaction to Marc’s bragging and Marc’s realization that he has
offended her once again. In the second paragraph, the author airs Marc’s opinion
on Camilla’s tendency to “overreact.” She gets “emotional when it isn’t warranted,
from Marc’s point of view, as a consequence of her intelligence and the fact that
she cares strongly about certain things. Marc’s attention and thoughts turn to Karen
in the third paragraph when he sees that he has offended her also, even though
they’ve been friends for a long time. The final paragraph depicts Marc’s initial,
awkward attempts to smooth the situation over.
This is approximately the level of information you should retain from a good-enough
reading. The question stems will direct you to specific details you need to answer
the questions.
24. A In line 22, Marc’s view is that “you had to watch your mouth” around Camilla. The
author goes on to explain that there were “certain things she cared strongly about,”
things about which she would get emotional. ”The most innocuous (harmless)

remark would set her off ” (lines 27-8). Therefore, “to watch you mouth” in this
context means to “avoid sensitive topics” in conversation (A). It was clearly not
Marc’s failure to observe grammatical rules (B) or the fact that he used profanities
(D) (you don’t know if he did or not) that upset Camilla. (C) “behave in a polite
fashion” is too broad to be the correct answer. (E) is far-fetched; Camilla would not
demand that you have to “talk eloquently” in her presence.
25. D Marc thinks that Camilla has a tendency to get emotional when it isn’t “warranted.”
You get a clue about what “not warranted” means in the next sentence: “the most
innocuous remark would set her off.” In other words, she has no good reason, in
Mark’s eyes, to get so upset; she tends to get emotional when it isn’t “justified” (D).
It may be true that Camilla gets upset when she doesn’t “intend” (B) to or when
Marc doesn’t “expect” (E) it, but these are not possible meanings of the word
“warranted.”
26. C Marc compares having a conversation with Camilla to walking in a minefield: “one
minute you’d be strolling along admiring the view, and the next, you’d have tripped
her wire ” This analogy emphasizes “the unpredictability of Camilla’s reactions”
(C). The author never mentions “Marc’s fear of offending other people” (A),
“Camilla’s discomfort at upsetting others” (B) or “the close understanding between
Marc and Camilla” (D). As for (E), Marc may be annoyed at Camilla’s behavior—the
author says he suppresses a momentary impulse to get angry—but this doesn’t
have anything to do with the minefield analogy.
27. B Choices (B), (C) and (E) are all possible meanings of the word “dissecting,” so you
have to go back to the passage to find the meaning of the word in context. Karen
and Marc had spent whole summers “dissecting each other’s private lives.” So
“analyzing” (B) is the right meaning of dissecting here; “criticizing” (C) has too
sharp a connotation and “cutting” (E) is too literal (remember to watch out for the
most common meaning of the word — usually it’s not the correct choice).
28. B In the line immediately following the description of Marc’s summers with Karen, the
author says that “Marc couldn’t think of a single woman who knew him better.” The
summers spent with Karen show the “longstanding nature of their friendship” (B).

This choice should have stood out because it’s the only one that fits in the context
of the third paragraph, which is all about the fact that Marc has offended Karen also
even though they’ve been friends for a long time. Nowhere does the author
mention that Marc has “few close women friends” (A), that Marc has to overcome
many obstacles in his private life (D), or that Marc regrets not having pursued a
relationship with Karen further (E). (C) is based on a misinterpretation of the line
that says “Marc used to justify the relationship to his father ” This does not mean
that Marc had to seek his father’s approval; “justify” means “rationalize” here.
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29. C Marc’s feeling that he’d “really done it now” comes right on the heels of his
realization that he has offended Karen, his closest friend, in addition to upsetting
Camilla. Reading a few lines up from the phrase quoted in the question stem makes
this clear. Marc doesn’t feel that he’s “really done it now” because he’s lost the
ability to talk (A)—it’s the other way around. (B) is wrong because there is no
reason to think that Karen is not loyal to him. She is simply annoyed at him right
now. (D) and (E) can be eliminated quickly because they don’t make sense in the
context of the passage.
30. C The author says that Marc was the “statesman of the class people joked about
how much money he was going to make ” However, Marc is “groping for his words
now ” You can make the inference that the author talks about Marc being the
statesman of the class in order to show that he is “generally an articulate speaker”
(C), but he’s floundering now. It’s true that being the statesman means that Marc is
also probably “noted for his diplomacy” (A) and a “a popular student on campus”
(D). These do not, however, touch upon the contrast the author is making between
Marc’s usual articulate self and his current awkwardness. There is no evidence in
the passage that people resent Marc’s success (B) or that his “ambitions are not
realistic” (E).

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section two
Section 3 (Math)
1. B In the QC section you’re supposed to compare, not calculate. Plugging all these
numbers into your calculator is too time-consuming. If you look carefully at the
numbers in the 2 columns, you’ll see that each number in Column B is slightly larger
than a number in Column A, so you can compare piece by piece. 2 is greater than
1.7, 3.1 is greater than 3, 4.5 is greater than 4.1, and 5.4 is greater than 5.2, so the
correct answer is choice (B).
2. A These angles lie on a straight line, so together they measure 180˚. You can turn
this into an algebraic equation and then solve it:
a + 20 + a + 10 + a = 180
3a + 30 = 180
3a = 150
a = 50
So a is greater than 45, Column A is greater than Column B, and the correct answer
choice is (A).
3. C In this question you’re given 2 equations. Since one equation contains one variable,
x, and the other equation contains 2 variables, x and y, let’s start with the easier
one, the one with only one variable. If = 3, you can multiply both sides of the
equation by 2 to get x = 6. Now you know the value of x and you can plug that into
the 2nd equation like this:
2x – y = 7 Plug in 6 for x.
2(6) – y = 7 Multiply 2 × 6.
12 – y = 7 Subtract 7 from both sides.
5 – y = 0 Add y to both sides.
5 = y Now you’re ready to compare the columns.
Since x = 6, Column A is 6 – 1, or 5, and since y = 5, Column B is also 5, so the

correct answer is choice (C).
4. B The only thing you’re given here is that x is positive. In Column A you’ve got a
percent, and in Column B you’ve got a fraction. Remember the strategy “Make one
column look like the other”? That strategy is very useful here. You should either
change the percent to look like a fraction or change the fraction to look like a
percent. 10% is the same as and since is less than , of x is less than
of x (as long as x is a positive number). If you wanted to change the fraction to a
percent, you’d have to remember (or use your calculator to figure out) that is
approximately 11%. Either way you do it, Column B is larger and choice (B) is
correct.
1
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1
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1
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section three
5. A If you subtract 13 from both sides of the equation that’s given to you the result is
a + b = c + d + 1. The average of a and b is and the average of c and d is
. You can make the equation a + b = c + d + 1 look more like the averages by
dividing both sides by 2, which gives you = , or =
+ . Another way of writing this equation is “the average of a and b is one-
half more than the average of c and d”. That means that the average of a and b is
greater than the average of c and d, so choice (A) is correct.
6. C The best way to do questions like this is just to pick a number for the variable.
Since y is a positive even integer, let’s say that y is 2. Then Column A becomes the
remainder when 3 is divided by 2, which would be 1, and Column B becomes the
remainder when 7 is divided by 2, which is also 1. (In fact, y + 1 and y + 5 must
both be odd since y is even, and an even number plus an odd number is an odd
number. Any odd number divided by 2 has a remainder of 1.) Since the columns
are equal, the correct answer is (C).
7. A Here you are told that a circle has radius 5. That means that its circumference is
2π(5) or 10π. You’re also given that angle AOC is 60˚. That means that it is ,
or of the entire circle. If you cut the circle into 6 identical wedges (pieces like pie
slices), each one would be 60˚. Each one would also have the same area, and the
same arc length. The 6 equal arcs make up the entire circumference of the circle.
So the length of arc ABC must be of the circumference. of the circumference
is of 10π, or ( )π, which is π. Now π is a little greater than 3, so π is a little
greater than 5. Column A is greater.
8. B The slope of a line is the change in y divided by the change in x. (If that doesn’t
sound familiar to you, you might want to check out your Math Reference Book.)
Point D’s y-coordinate is 1 and point E ’s y-coordinate is 6, so the change in y is

6 – 1, or 5. Point D’s x-coordinate is 0 and E ’s is 4, so the change in x is 4 – 0, or
4, and the slope is . Notice that you could have written the change in y as 1 – 6
and the change in x as 0 – 4. It doesn’t matter which point’s coordinate you put first,
5
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5
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5
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1
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1
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a + b
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section three
as long as you’re consistent and put the same point’s coordinate first when you do
both the change in y and the change in x. You can find the slope of the line passing
through D and F the same way. That slope is = . You have in Column
A and in Column B, so B is greater and the answer is choice (B).
9. D If there were less than 60 students at the lecture and 60% of them were female, how

many were female? It’s probably a good idea to try picking numbers here. There
might have been 50 students, in which case there were 60% 50 = .6 50 = 30
female students. On the other hand, there might have been only 20 students at the
lecture, in which case there were 60% 20 = .6 20 = 12 female students.
Since you get 2 different relationships depending on exactly how many students
were there, the correct answer must be choice (D).
10. A Compare, don’t calculate. If T is greater than S, the result of the subtraction problem
would be negative. Think about it logically. If T and S were 1 and 2, respectively
(they’re not), then ST – TS would be 12 – 21 = -9. Don’t do the math; just think
logically.
11. B Inequalities are easy to solve if you remember that you can usually treat them the
same as you do equations. Just be careful if you multiply or divide by a negative
number — in that case you have to switch the direction of the inequality sign.
There’s more information about inequalities in your Math Reference Book. Here you
can solve pretty easily:
3 + 2c < –5 Now just subtract 3 from both sides.
2c < –8 Divide both sides by 2.
c < –4 That’s what you need to answer the question!
Notice that you didn’t have to change the direction of the inequality sign because
you divided by a positive number. Since c < –4, Column A is less than Column B
and choice (B) is correct.
12. D If you got this one wrong, you did not read the question carefully. If apples cost 79
cents a pound, then the cost of one pound of apples is 79 cents, the cost of two
pounds of apples is $1.58, etc., but how do you figure out the cost of a certain
number of apples? Well, you have to know how big the apples are, in other words
how many apples are in a pound. If they’re really big apples, they could weigh half
a pound each, but if they’re really small apples there might be 4 or 5 or 6 or even
more per pound. Since you have no way of knowing how many apples there are in
a pound, the only possible answer to pick is (D).
13. D The only thing you’re given here is the inequality a > 0 > b; in other words a is

positive and b is negative. That means that is a positive number divided by a
negative number, which is a negative number. It also means that is a negative
b
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a
a
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b
×
×
×
×
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ᎏ
2
5
ᎏ
4
5
ᎏ
2
6 – 1
ᎏ
2 – 0
SAT
Virtual Reality II
21
section three
number divided by a positive number, which is also a negative number. Do you
know anything else about the quantities in the 2 columns? No, all you know is that

they’re both negative so the correct answer choice must be (D).
14. B We want to compare the area of a right triangle in Column A with 18 in Column B.
The area of a right triangle is × Leg
1
× Leg
2
. We know the length of leg BC,
that’s 6. We still need to find the length of leg AC. Angle C of this triangle is
indicated to be a 90-degree angle. Angle A is indicated to be a 60-degree angle.
So angle B must be 180–90–60 or 30 degrees. We have a 30-60-90 right triangle
and we know that the ratio of the lengths of the sides in such a triangle is 1:͙3
ෆ
:2.
In particular, the ratio of the length of the shorter leg to the length of the longer leg
is 1:͙3
ෆ
. Here the longer leg is 6, so the shorter leg must be . Now that we
know the lengths of both legs we can say that the area of triangle ABC is × BC ×
AC = × 6 × = . Since ͙3
ෆ
> 1, < 18. So the area of the triangle in
Column A, which is , is less than 18 in Column B.
15. C This is the last QC and it’s a very difficult one. If you run into a question that you
can’t solve quickly, your best strategy is to move on to another question. The ratios
of side lengths in the two columns suggests that the solution to this question might
be found by working with similar triangles. Can we find a pair of similar triangles in
the figure? Well, triangles ABD, ABE, BCE, and CDE all have a 90-degree angle.
Does any pair of these triangles also have another equal angle? Angle D is
common to both triangles CDE and ABD. Since these two triangles have two equal
angles, the third angles of these triangles, angle CED in triangle CDE and angle

ABD in triangle ABD must also be equal because the sum of all three angles in any
triangle must be 180 degrees. So triangles ABD and CDE are similar. Looking at
Column A, is the ratio of two sides of triangle ABD. is the ratio of the leg
opposite angle D to the hypotenuse BD opposite the right angle at A. The ratio of
the corresponding sides in triangle CDE must also be equal to . In triangle
CDE, CE is opposite angle D and ED is opposite right angle DCE. So = .
The left side of this equation, is exactly what we have in Column A. The right
side of this equation is and this has the same numerator, CE, as Column B, but
a different denominator. How do AE and ED compare? Well AE = ED because the
CE
ᎏ
ED
AB
ᎏ
BD
CE
ᎏ
ED
AB
ᎏ
BD
AB
ᎏ
BD
AB
ᎏ
BD
AB
ᎏ
BD

18
ᎏ
͙3
ෆ
18
ᎏ
͙3
ෆ
18
ᎏ
͙3
ෆ
6
ᎏ
͙3
ෆ
1
ᎏ
2
1
ᎏ
2
6
ᎏ
͙3
ෆ
1
ᎏ
2
SAT

Virtual Reality II
22
section three
centered information tells us that E is the midpoint of AD. So we can substitute AE
for ED in the equation = , resulting in = . The columns are equal.
16. or .5
You’re given that the whole line segment, AE, is 3. Since D is the midpoint of AE, D
must cut AE in half. That means that AD is 1 and DE is 1 . AD is made up of
three small line segments, all of which are equal in length. That means that each
one must measure one-third of 1 , which is . So AB has length , and you can
put or .5 into your grid.
17. 70
If you notice that there is a triangle on the right side of the figure with 2 labeled
angles, you can probably solve this one. The 2 labeled angles are 60˚ and 80˚, so
the third angle of the triangle must be 180 – 60 – 80 = 40˚. The 40˚ angle and the
two angles labeled d˚ make up a straight line, so 40 + d + d = 180. That means that
40 + 2d = 180, 2d = 140, and d = 70, so grid in the number 70.
18. , 1.88, or 1.89
Since 17 is prime, its only factors are 1 and 17. Therefore, a must be 17 and c must
be 1, since 1 is not prime. Substitute 1 for c in the equation = 9. = 9. b = .
ab = 17 × = or 1.88.
19. 0 < a <
This one requires some thought. If 2a + b = 1, what kind of numbers could the
variables a and b represent? Could they be negative? No, because you’re given
that a > 0 and that b > . Since a and b are both positive and 2a and b sum to 1,
a and b must both be fractions between 0 and 1. What possible values could they
represent? Well, suppose b were equal to . Then 2a would have to equal
since + = 1. You’re given that b is greater than , so 2a must be less than
in order for 2a and b to sum to 1. If 2a is less than then a is less than . a is
also a positive number, so any value for a that is greater than 0 and less than ,

such as , is correct.
1
ᎏ
10
1
ᎏ
8
1
ᎏ
8
1
ᎏ
4
1
ᎏ
4
3
ᎏ
4
3
ᎏ
4
1
ᎏ
4
1
ᎏ
4
3
ᎏ

4
3
ᎏ
4
1
ᎏ
8
17
ᎏ
9
1
ᎏ
9
1
ᎏ
9
1
ᎏ
b
c
ᎏ
b
17
ᎏ
9
1
ᎏ
2
1
ᎏ

2
1
ᎏ
2
1
ᎏ
2
1
ᎏ
2
1
ᎏ
2
1
ᎏ
2
CE
ᎏ
AE
AB
ᎏ
BD
CE
ᎏ
ED
AB
ᎏ
BD
SAT
Virtual Reality II

23
section three
You could also have picked numbers. Since b plus some positive number sum to 1,
b must be less than 1, but you’re given that b > . So pick a number for b that is
between and 1, such as . If b = , then 2a + = 1, 2a = , and a = ,
which is greater than 0 and therefore meets the only other requirement you’re given
for a.
20. or 5.5
If the area of a circle is 36π its radius is 6 and if the area of a circle is 25π its radius
is 5. Therefore if a circle’s area is less than 36π but greater than 25π its radius must
be less than 6 but greater than 5. Since the diameter of a circle is twice the radius,
that means that the diameter is less than 12 but greater than 10. There is only one
integer that is less than 12 and more than 10, 11, so the diameter must be 11. The
radius of the circle must be of this which is of 11 or .
21. or 1.33
This one seems confusing, since you’re given the value of x + y over x – y and
asked to find . The way to do it is to just try and solve the equation like you
normally would, but try to solve it for rather than for x or for y. Since you’re given
the value of a fraction, first multiply both sides of the equation by x – y to get rid of
the denominator. That gives you x + y = 7(x – y). Is there any way of getting rid of
the x’s and y’s and getting just ? Try dividing both sides by y:
x + y = 7(x – y) Divide both sides by y.
+ 1 = (x – y) Multiply out.
+ 1 = – 7 Add 7 to both sides.
+ 8 = Subtract from both sides.
8 = Divide both sides by 6.
= Switch & reduce the fraction.
= That’s the answer!
4
ᎏ

3
x
ᎏ
y
x
ᎏ
y
8
ᎏ
6
6x
ᎏ
y
x
ᎏ
y
7x
ᎏ
y
x
ᎏ
y
7x
ᎏ
y
x
ᎏ
y
7
ᎏ

y
x
ᎏ
y
x
ᎏ
y
x
ᎏ
y
x
ᎏ
y
4
ᎏ
3
11
ᎏ
2
1
ᎏ
2
1
ᎏ
2
11
ᎏ
2
1
ᎏ

16
1
ᎏ
8
7
ᎏ
8
7
ᎏ
8
7
ᎏ
8
3
ᎏ
4
3
ᎏ
4
SAT
Virtual Reality II
24
section three