sat virtual reality iii explanations phần 2 pps

Therefore the correct answer choice is the one even number, again choice C.. Since you’re asked which answer choice must be true, one way to do it is to go look at each answer choice and

15 C Here you’re given that a and b are integers, but you don’t know whether they are

positive or negative, so there are a lot of possible values of a and b that fit the equation 2a + 5b = 15 One way to solve this one is to backsolve – to try each

answer choice Plug in the given value for b and see if the equation works If you start with choice (C), which is a good idea when backsolving, you’re in luck here If

b were equal to 2, the equation 2a + 5b = 15 would be 2a + 10 = 15, or 2a = 5, or a

= 2.5 But you’re given that a is an integer, so a cannot possibly be 2.5, so b = 2

doesn’t work and choice (C) is correct

You might have noticed that in the equation 2a + 5b = 15 you have an even number, 2a, plus another number, 5b, being equal to an odd number, 15 An even number

plus an even number equals an even number, and an even number plus an odd

number equals an odd number, so the expression 5b must be an odd number If 5b

is an odd number, then b must be an odd number (since odd × odd = odd and odd× even = even) Therefore the correct answer choice is the one even number, again choice (C)

16 B Since you’re given that y is between –1 and 0, why not pick an appropriate number

for y and plug it into each answer choice? Try y = – Then choice (A) is

y2=– 2

= ; (B) is 1 – y = 1 – –  = 1 ; (C) is 1 + y = 1 + –  = ; (D) is

2y = 2– = –1; and (E) is = = = Choice (B) is the greatest

17 C A good way to solve this question is by making yourself a little table Each

employee is described by two different things Each one is a woman or a man and each one either drives to work or takes public transportation So make this table:

In this table each box will contain the number of employees having the two appropriate attributes For example, the box in the lower right-hand corner is the number of men who take public transportation We can also put numbers in the

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margins For example, we can put the number of women in the company below the

box in the lower left-hand corner Now let’s begin to put numbers in the table from

the information in the question stem The question stem tells us that there are 25

women and 25 men, and that 29 employees drive to work Each of these three

pieces of information describes only one attribute of the employees, so these

numbers will go in the appropriate margins We’re told that 6 men take public

transportation This describes both attributes, so put a 6 in the lower right-hand box

Now your table should look like this:

What we want to find is the number of women who drive to work which is the

number that must go in the upper left-hand box So let’s fill in information in the

table, hoping that we can work our way to the upper left-hand box We know that

there are a total of 25 men in the company and that 6 men drive to work This

means that the remaining 25 – 6 or 19 men take public transportation So put a 19

in the upper right-hand box Now we’re going to be able to find the number of

women who drive to work Since 29 employees drive to work and 19 men drive to

work, 29 – 19 or 10 women drive to work If you also put a 10 in the upper left-hand

box, your table should look like this:

So 10 women drive to work

18 B Careful here! If you said to yourself: “This is simple, pages 10-25 are empty, that’s

25 – 10 = 15 pages at 4 photos a page, that’s 60 photos all together ,” then you fell

into a trap! NEVER pick an obvious answer on a hard problem The catch here is

that page 10 is empty, too, and if you count from 10 to 25 while including both 10

and 25 you’ll see that there is a total of 16 empty pages, not 15 Since 16 × 4 = 64,

the correct answer is (B)

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19 10

In general, if a and b are integers and a < b, the number of integers from a through

b inclusive (meaning that we’re including a and b) is b – a + 1.

19 E This is much more of a logic question than a math question, so you have to think it

through carefully Since you’re asked which answer choice must be true, one way to

do it is to go look at each answer choice and try to find a possible situation in which that choice is not true Let’s start with choice (A), which says that at least one stereo was sold on each day of the month That’s not necessarily true, maybe all 63 stereos were sold on one day and none the rest of the month Cross out choice (A)

Is it necessarily true that exactly 2 stereos were sold on a particular day? No, again it’s possible that all 63 stereos were sold on one day and none the other days You can eliminate choice (B) Do we know if a stereo was sold on a Monday,

Wednesday or a Friday? What if all 63 were sold on a particular Tuesday? So choice (C) is not necessarily true Our useful scenario with all 63 stereos being sold

on one particular day is good enough to eliminate choice (D) as well, which leaves

us with only choice (E), which must be correct Just to be sure, take a look at it It says that at least 3 stereos were sold on one day If all 63 were sold on one day, then on that day at least 3 stereos were sold If the sale of stereos was more evenly distributed, would there necessarily be a day in which 3 or more stereos were sold? Since a month has at most 31 days, if 2 or less stereos were sold each day of the month, then at most only 62 stereos would have been sold in that month In order for 63 stereos to be sold, there has to be at least one day where 3 or more stereos were sold, so choice (E) is correct

20 E If the slope of a line is – , that means every time the y-coordinate decreases by 3,

the x-coordinate increases by 2 So, if the y-coordinate goes from 6 to 0, as it does

if you travel along line  from point A to point B, it decreases by 6, or 2 × 3

Therefore the x-coordinate must increase by 2 × 2, or 4 Since the x-coordinate of A

is 0, the x-coordinate of B must be 4, so point B ’s coordinates are (4, 0) That means that the length of OB is 4 Since the length of OA is 6, the area of the

triangle is × 4 × 6 = 12, choice (E)

21 C You’re given that a and b are positive integers that add up to 10 There’s a limited

number of integers that meet those requirements – a could be 9 and b could be 1, a could be 8 and b could be 2, etc If you list all the possible values of a and b you’ll find that there are 9 pairs of numbers that could be the values for a and b You could plug each of these 9 pairs of numbers into the expression a – b to see which turns out the smallest If you do it that way you’ll find that a – b is smallest when a

is 1 and b is 9, so a – b = –8, choice (C).

That method is a little time-consuming, however You can make this problem very

short and quick if you just think about the expression a – b Since a and b are both positive, this expression will be as small as it can get when a is as small as possible and b is as large as possible Since the smallest possible value for a is 1, the largest possible value for b is 10 – 1 or 9, and therefore the smallest possible value for a – b must be 1 – 9, or –8, again choice (C).

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22 E To do this question, you have to know what the word “median” means The median

of a group of numbers is the one in the middle when the numbers are placed in

ascending order For example, the median of the numbers 3, 6, 7, 12 and 20 is 7

Notice that the same number of terms are smaller than the median as are greater

than the median

In this question you’re given that 73 is the median of a group of 7 numbers (one for

each day of the week) That means that 3 numbers must be less than 73 and 3

numbers must be greater than 73 67, 71, and 72, the temperatures for Monday,

Tuesday, and Wednesday, respectively, are each less than 73 The other 3

temperatures must be greater than 73 The Friday temperature is 76, and among

the answer choices the only values for Saturday and Sunday which are both greater

than 73 are 74 and 77, choice (E)

23 D This question is a lot easier if you pick numbers for the variables Let’s say that x is

1 and y is 2 Then it takes the printer 1 minute to print 2 pages That’s a lot easier

to deal with, isn’t it? Then how long does it take the printer to print y + 2, or 4

pages? If it prints 2 pages in one minute, then to print 4 pages it must take 2

minutes Now you can eliminate any answer choice which does not equal 2 when x

is 1 and y is 2 (A) is 3, (B) is , (C) is , (D) is 2, and (E) is Since only

choice (D) resulted in the correct value of 2, choice (D) must be correct

If you wanted to do it algebraically, you have to determine the rate of the printer in

minutes per page and then multiply that rate by the number of pages The rate is x

minutes per y pages, or minutes per page Since there are y + 2 pages, the

number of minutes is minutes per page × (y + 2) pages = minutes,

answer choice (D)

24 D One important thing to remember about quadrilaterals is that the sum of the interior

angles is 360˚ That means that w + x + y + 70 = 360, and therefore w + x + y =

290 x must be a positive, but it can be a number very close to 0 If x actually were

0 then w + y would be 290 If x were very slightly larger than 0, w + y would be very

slightly smaller than 290 So, 290 must be the upper bound of the range of values

that w + y could have, so the correct answer must be choice (B) or choice (D) If x

were equal to 45, then w + 45 + y would be 290, and w + y would be 245 However,

x can’t equal 45, but its largest possible value could be a number very slightly

smaller than 45 That means that w + y would equal a number very slightly larger

than 245 So, 245 must be the lower bound of the range of values that w + y could

have That means that the correct answer must be choice (D)

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25 A If each term is x more than the previous term, then each term must equal x plus the

previous term, in other words s = r + x and t = s + x Combining those 2 equations gives you t = (r + x) + x = r + 2x The average of r, s and t is Substituting

= r + x, answer choice (A).

3(r + x)

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3

r + s + t

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r + s + t

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section three

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Section 3 (Verbal)

1 D This is about the philosopher Thomas Malthus’s predictions about population

growth — kind of an intimidating subject if you haven’t read much philosophy But

don’t worry This sentence is pretty simple once you take it apart and look for

clues The biggest clue is the word famine You’re told that population growth does

something to food production, resulting in famine Well, you know that when many

people are hungry and there’s not enough food to go around, famine happens Or,

to put it in terms of the sentence, population growth would exceed food production,

resulting in massive famine The answer choice that best matches this prediction is

(D) surpass

2 C The key to this sentence is that Dr Brown “brooked no deviation from his ideas.” In

other words, he wouldn’t put up with anyone who disagreed, which through the use

of “while,’’ is contrasted with his supposed belief in discussing issues Hence, (C):

Brown professes or claims to have such a belief, but he interrupts anyone who

doesn’t concur, or agree (A) makes no sense: there’s no contrast between

regretting a belief in discussion and cutting off those who don’t agree with you.

(B), (D) and (E) may be a bit confusing They’re just the opposite of what’s needed

in the second blank Since Brown doesn’t tolerate disagreement, he probably

would not cut off anyone who did not (B) debate, (D) question, or (E) protest

3 E Here you may find it easier to fill in the second blank first, because it contains the

catchy phrase “merely , not canceled.” Look for cliched phrases like these on

sentence completions — they can help you get the answer fast What probably

pops into your head when you read “merely , not canceled” is “merely put off, not

canceled.” That’s logical What you need in this second blank is something that

means the employees have put off their demands for now, but will bring them up

again in the future So (E) postponed is correct (E)’s first word works as well: it

makes sense that employers would try to moderate wage increases during

serious economic difficulties (C) redressed means “set right or corrected.”

4 C This example is typical of Sentence Completions testing vocabulary Getting the

answer hinges on knowing that virulent means “extremely poisonous.” The

sentence tells us that certain poisonous compounds in peach pits are “usually not

harmful.” But, the sentence continues, if you eat enough of them, they can be

We need a word that means “poisonous” or “harmful.” Virulent, like the related

word virus, comes from a root that means “poison.” What if you didn’t know the

word virulent? If you noticed the resemblance between virus and virulent, that

would have been a good clue Otherwise, you could have tried eliminating answer

choices Choices (A) and (D) are words that relate to things that taste bad, but

neither means “poisonous.” (A) acerbic means “sour or harsh.” (D)

unpalatable means “unacceptably bad-tasting.” (B) superfluous means

“unnecessary,” and (E) multifarious means “diverse.”

5 D Here you’re looking for words that fit with the phrases “ speeches to historical

figures” and “an impartial and historian.” The only choice that fits is (D)

Though Thucydides used psychological insight rather than documented information

to attribute speeches to historical figures, he is still considered an impartial and

accurate historian (A) doesn’t work, because historians are never referred to as

endless (B), (C), and (E) don’t work because the first word in each choice — (B) transmit (to send); (C) disseminate (to distribute), (E) promote (to

advance) — doesn’t fit with the phrase “speeches to historical figures.”

Thucydides is an author He’s describing historical figures in his writing, not writing speeches for them

6 D When you’re working on Sentence Completions, pick up clues that aren’t obvious

For instance, notice complexity here Complexity might not have jumped out at you, but it’s key to figuring out both blanks Whatever goes in the first blank has

to describe how readers would react to a novel’s complexity Would they be (A)

charmed by its complexity ? Probably not They probably wouldn’t be (B) rejected by its complexity either (C) inhibited, (D) daunted or (E) enlightened are possible, but only (D) fits in the second blank In (D), it makes sense to say that readers daunted, or intimidated, by the allusiveness, or

symbolic quality, of Joyce’s novel would find Gilbert’s study a helpful introduction

Don’t be daunted by hard words like allusiveness If you don’t know

vocabulary, you can still use logic to rule out most of the wrong choices

7 E The word in the blank has to have something to do with religion (E) is the only

choice that does An agnostic is someone who is uncertain about the existence of god (A) an archetype is an original pattern or model (B) a bibliophile is a book-lover or book collector (C) a martinet is a strict disciplinarian, one who rigidly follows rules (D) an aesthete is someone who

appreciates and cares about beauty or beautiful art The vocabulary is pretty hard here As always, if you can rule out one clearly wrong choice, it’s worth your while to guess, rather than skip, the question

8 C Wrath means “anger.” In the first blank here, you can predict that the project

managers were unwilling to risk arousing the anger of their superiors, or bosses

(C) is correct – incurring means bringing down on oneself, becoming liable or subject to (C)’s second word, maintain, also works Maintain here isn’t

being used to mean “to keep in repair,” as in “maintain a car.” It’s being used in its secondary meaning: “to assert or declare.’ Watch out for secondary meanings like these on the SAT

9 B The clue although tells us that the two missing words have to show contrast.

Also, the word in the first blank has to go along with the word “sweet,” and the second word has to describe something offensive We can predict something like

“pleasant unpleasant.” The only choice that fits is B, mild pungent.

Pungent means “sharp or biting.” It’s the opposite of mild In (C), bland means “not stimulating.” In D, cloying means “sickeningly sweet.” Ephemeral means “fleeting or short-lived.” In (E), rancid means “rotten” and acrid means

“sharp or bitter.”

10 C The word in the blank describes what audiences see the stand-up comic do So

it’s a word like “act” or “entertain.” (C) extemporize is the only possible answer.

It means “to improvise, to speak (or appear to speak) on the spur of the moment.”

If you didn’t know this hard word, you could have ruled out some wrong answers

that clearly had nothing to do with acting, like (A) recruit (B) placate means

“to soothe or be conciliatory.” (D) extricate means “to free from entanglement, rescue or disengage.” (E) exult means “rejoice.”

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11 B A SCOWL is a face you make when you’re ANGRY In (B), a grin is a face you

make when you’re cheerful In (A) to amble is to walk in a leisurely way It’s

not a hasty way of walking at all In (D), to fret is to worry This word might

have reminded you of the stem pair, since negative emotions are involved in both

But even though (B) contains words relating to positive emotions, it’s right

because the relationship between the two words is right

12 B A CARDIOLOGIST studies, or works with the HEART The word cordial or

warm, hearty, shares the same root as CARDIOLOGIST The answer is (B)

because a linguist studies language (C) surgeon:scalpel was a same

subject temptation (D) was close, but an astrologist doesn’t actually study a

star in the same way that a heart specialist studies the heart Astrologists study

something more obscure: the movements of the planets and their effects on

human behavior

13 D A group of SOLDIERS is called a PLATOON In the same way, a group of

birds is called a flock This might have fooled you because correct choice (D)

is the only one that doesn’t involve humans But the important thing is the

relationship: whole to part Only (D) gets that right

14 C Something ASKEW is crooked or awry If you STRAIGHTEN it, it’s no longer

ASKEW Likewise, something obscure is unclear or indistinct, and if you

clarify it, it’s no longer obscure (A) gives us the opposite of what we want: if

you disinfect something, it becomes sterile There’s no clear bridge in (B)

between saline and preserve You might (D) haggle or bargain over some

item, but that doesn’t necessarily make it not expensive It doesn’t make sense

to say in (E) that if you trust someone, he or she won’t be suspicious.

15 C The top of a MOUNTAIN is the SUMMIT The top of a wave is the crest.

You might have been fooled by (D), but an attic is a room in a house or building

that’s directly under the roof That’s not the very top of a house, for one thing, and

for another, not all houses have attics

16 A A SKEIN is a quantity of YARN that has been rolled into a spiral In the same

way, in (A), a coil is a quantity of wire that has been rolled into a spiral The

word SKEIN may be new to you, in which case you can use other strategies to

help you find the right answer: first, eliminate the choices that have weak bridges;

secondly, see if the stem words make sense when plugged in to the bridges of the

choices that remain (C) and (E) have weak bridges: in (C) only some pipes are

made of lead, and distance and track, (E), have no necessary connection.

Let’s consider the remaining choices (A), (B) and (D) As we saw above, (A) has

a strong bridge which sounds sensible when used with the stem words; so (A) is a

definite possibility (B) also has a strong bridge: a thimble is used to protect the

finger that pushes a needle in sewing; could a skein be used to protect the

finger from yarn? It doesn’t make sense so (B) is out Finally, look at (D): a

tape is used for obtaining measurement This bridge does not sound sensible

with the stem words either, so we can eliminate (D) That leaves (A), which is the

correct answer

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17 D When you’re PERTURBED, or disturbed, you don’t experience TRANQUILITY.

When you’re reassured, you don’t feel anxiety Although these pairs seem opposites of each other, they have the same relationship In (B), dissension is

disagreement This choice may have reminded you of the stem pair (C) was close,

but the word weeping is too specific If you are consoled, you might stop

weeping, but you don’t have to be weeping in order to be consoled

18 C The word ANARCHIC comes from the simpler word “anarchy” which means

“chaos.” Something that’s ANARCHIC lacks ORDER If you didn’t know that (C) artless means free from deceit or guile, you could have eliminated weak bridges

and guessed (D) and (E) have very shaky bridges (A) isn’t great either You

could be insane and still have a motive for doing things (B) has a strong bridge:

if you’re tranquil, you experience peace That’s different than the stem pair, so you might have picked (C) even if you didn’t know what artless and guile meant

19 A To AMELIORATE means to make BETTER Bad effects or bad situations can

be ameliorated or improved The word weaker in (A) might have made it hard to see that this was the right answer, since weaker seems opposed to BETTER But the important thing is that the bridge is the same: to enfeeble means to make weaker (E) was close but not quite right If something disintegrates, it falls apart – it doesn’t just get smaller

20 B PUISSANT means strong or powerful Someone who’s PUISSANT has a lot of

POWER; someone who’s affluent has a lot of money In (A) an intelligent person may or may not have a lot of books In (C), cryptic means puzzling You can’t say that someone or something that’s cryptic has understanding In (D), someone who’s belligerent is quarrelsome or war-like A quarrelsome person doesn’t necessarily have strength In (E) latent ability hasn’t been expressed

or revealed That’s not the same as the bridge in the stem pair

21 C Have you ever paid RAPT attention to anything? If you did, you were RAPT — so

fascinated by what you were seeing or hearing that you were at your highest

possible state of ATTENTIVENESS Similarly, an innovative person is at the highest level of creativity Unscrupulous (A) means “having no scruples, i.e., morals or ethics.” Assertiveness (B) means “self-confidence”—not a quality we’d associate with being derisive or mocking Indolent (D) means “lazy”; it has no connection whatsoever with jealousy Impudence (E) means “insolence or

cockiness.”

22 A To STUTTER is to speak HALTINGLY; to lumber is to walk awkwardly.

None of the other choices has a true bridge: (B) blinking needn’t be done rapidly; (C) whispering doesn’t have to be done indiscreetly; (D) gossip isn’t malicious by definition; (E) you don’t necessarily push something forcefully.

23 E The last question is usually tough, and this one is no exception To PETRIFY

means to turn to STONE Have you ever heard of the Petrified Forest in Arizona?

It contains remnants from a prehistoric forest that became mineralized long ago

The word pulverize in (E) has a very specific meaning: to pulverize something

is to crush it completely, to turn it into dust or powder This word was the hardest

word among the answer choices, but that’s what we can expect on the last question

of a set

Cave Painting Passage

There are some disconcerting place-names and scientific terms in this passage,

but you don’t need to know any of them to get the points the author makes about

some of the earliest preserved art—cave paintings The first paragraph ends with

a few questions: what sort of people were the cave painters? Why did they paint

at all, and specifically why in caves? These questions outline the rest of the

passage for you Keep this in mind if you ever encounter a passage with a similar

format—it gives you a handle on the material

24 B If you figure out what big points the author makes in the lines you’re referred to,

you’ll probably have no trouble understanding why the author mentions

body-painting (or whatever specific detail a question asks about) To do this, you

usually have to read a line or two around the line reference you’ve been given

These lines tell us that if prehistoric humans made art, they haven’t left us any

trace of it Body-painting is mentioned as an example of the kind of art they may

have made, but which we can’t have any evidence of (B) None of the other

choices match the point the author makes in these lines The author is not

making a point about when people began using paint (A) Choices (C), (D) and

(E) bring up things not discussed until later in the passage

25 C Again, go back to the passage and read around the line reference The author

says the paintings “rivet our attention” because they are “great art,” and because

they raise questions about the people who painted them Now check the answer

choices (B) probably jumped out, because it starts, “raise questions about ”

But read carefully! The rest of the choice doesn’t make sense Choice (C),

although not as eye-catching, is correct (A) is from left-field We do know some

things about the people and animals depicted in cave paintings, so (D) is wrong

Finally, the point is that the paintings raise questions, not that they cast doubt, so

(E) is out

26 B Don’t let strange words throw you—in this or any question Even if you don’t

know where “Gargas and Rouffignac” are, or what stalactites or stalagmites are,

the point is in plain English: they “fill us with awe” and “stun us with their beauty.”

The author speculates that the cave painters must have felt the same way This

should lead you to choice (B) The other choices provide reasons that might

sound sensible, but they don’t come from the passage Don’t choose an answer

just because it makes sense to you; be sure there’s evidence in the passage

27 A Assuming you’ve already gone to the line where “riot” is used (as you should do

with all vocabulary-in-context questions), which choices can you eliminate?

Certainly (C) brawl and (E) violence, since the word is used to describe something

of great beauty The most common definitions of a word are usually wrong, so you

can also eliminate (B) That leaves (A) and (D) Only (A), profusion, makes

sense in context

28 D In the quoted lines, the author says the term “cavemen” evokes an image of

“hairy brutes,” but then says that the Cro-Mags actually had “needles, buttons,

parkas and trail signs” in their caves In other words, they’re misrepresented as

stupid brutes, when in fact they were quite sophisticated (D) sums this up, and is

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