sat virtual reality iii explanations phần 1 pdf

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 moder

Section 1 (Verbal)

1 D Since the veteran boxer won most of his bouts by knockouts, you can assume that

he was pretty successful Unbroken is the only choice that describes his series of

wins in a way that suggests success; an unbroken 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), resplendent, 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 “everyday 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)

conciliatory, meaning “tending to pacify or accommodate.” Choice (B)

precarious means “uncertain or dangerous,” and choice (C) haughty means

“arrogant, snobby, huffy.”

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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)

apostrophesare 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

periodical

11 C The related prefixes CO-, COL-, and COM- mean “with” or “together.”

COLLABORATEcontains the prefix CO- and the root LABOR, so it means “to

WORKtogether.” 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

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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 dryness 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

purgativeis 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

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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

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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

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“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

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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

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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 x2 + 2xy + y2 Since x is 1 and y is –1, this expression becomes

x2+ 2xy + y2 = (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 x2 + 2xy + y2is

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

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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

, 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 1, choice (B)

4

20

 80

40

 100

320



800

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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 2x2– 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 2x2– 8x looks very similar to x2 – 4x In fact, 2x2– 8x = 2(x2 – 4x).

So, if x2 – 4x – 12 = 0, then x2– 4x = 12, and 2x2 – 8x = 2(x2– 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, 1and 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

4crosses 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 1is parallel to 2,

the angles that are formed where 4 and 1 meet are also right angles That means

that 1and 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)

3also 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

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