Chapter 17

Practice Exam 1: Answers and Explanations

After taking the Practice Exam 1 in Chapter 16, use this chapter to check your answers and see how you did. Carefully review the explanations because doing so can help you understand why you missed the questions you did and also give you a better understanding of the thought process that helped you select the correct answers. If you’re in a hurry, flip to the end of the chapter for an abbreviated answer key.

Analytical Writing Sections

Give your essays to someone to read and evaluate for you. Refer that helpful person to Chapters 14 and 15 for scoring guidelines.

Section 1: Verbal Reasoning

1. D. Reticent means reluctant. Given the statement that many countries around the world are struggling financially, it makes sense that leaders would be reluctant to pledge money to help others. If you chose Choice (A), eager, you fell for a common trap — an answer choice with the opposite meaning of the correct answer. Choice (B), apt, means leaning toward — somewhere between eager and reticent. Choice (C), deleterious, means harmful, which obviously doesn’t make sense, and Choice (E), judicious, means using good judgment, which also doesn’t make much sense.

2. C. Defy means to challenge, which matches the first part of the sentence that implies a dark, mysterious world with creatures that challenge human imagination. Choice (A), elude, means to avoid, but a creature wouldn’t avoid imagination. Choice (B), adapt, doesn’t fit due to meaning and usage — for the choice to remain in the running, it would have to be “adapt to,” and even that makes little sense. Choice (D), explore, fits in the sentence but doesn’t match the meaning. Choice (E), renounce, means to give up something or disown it — a meaning that doesn’t fit in this context.

3. C, D. Impeccable means perfect, flawless, and atrocious means exceptionally bad. The sentence begins with the word although, which clues you in that the two correct answers have opposite meanings. Choice (C), impeccable, and Choice (D), atrocious, are the only two answer choices opposite in meaning. Mary could be creative in the way that she dressed, but there’s no word choice for the second blank that is opposite of creative. She could also be drab, which means dull, but again there’s no opposing word choice for Blank (ii). Bilious means angry or irritable, and sincere means open or genuine.

4. B, F. One meaning of independence is freedom from control, which would tend to make someone more adventuresome than apprehensive (anxious, fearful) or reserved (withholding one’s opinion). History obviously doesn’t fit well with any of the choices in the second column. Approbation (approval) sort of fits; approbation would tend to make someone more confident, but independence suggests both confidence and an ability to stand on one’s own two feet, making it the better choice.

5. A, D. Anomaly means non-standard, and eclectic means pieced together from several sources. The word numerous makes eclectic the best choice for the second column, and because of that, anomaly is the better choice for the first column. You can rule out Choice (B), specification, because a building or collection of buildings cannot be a specification. You can also rule out Choice (C), prototype (model), because the sentence implies that the Presidio is an existing architectural structure in San Francisco. Choices (E) and (F), similar and standard, don’t work, because the last part of the sentence points out a building style (cottage) that has a mansard roof not normally used in cottages.

6. A, E, G. Venomous means poisonous, innocuous means harmless, and irrational means not logical or based on facts. The first word of the first sentence is though, providing a clue that the two blanks in that sentence require antonyms (words opposite in meaning). The only words in the first two columns that are nearly opposite in meaning are venomous and innocuous. Tempestuous means agitated, like a storm or tempest. If you chose venomous and dangerous, you fell for the trap of choosing words similar in meaning. You can also rule out slimy for the first blank, because none of the choices in the second column is opposite in meaning. In the second column, you can rule out small and dangerous, because neither is opposite in meaning to any of the choices in the first column. The second sentence starts with the word despite, indicating that the fact stated in the first part of the sentence is going to receive a response that’s not in line with that fact. So regardless that the Northern Water Snake is harmless, some people often kill it based on irrational fears, or fears not supported by the fact. Because the water snake is harmless, such fears could not be reasonable or justifiable (supported by fact).

7. B, D, I. The key word in the first sentence is but, indicating that the missing word is going to undercut everything before but. This rules out Choice (A), confirmed, and Choice (C), reinforced, both of which convey a sense of support. The only choice left in the first column is Choice (B), belied (contradicted). In the second sentence, the word actually clues you in that the next two missing words are contrary to speaking softly. In the second column, you can rule out unobtrusive and modest, because both convey a sense of trying not to be noticed; so conspicuous (easily noticeable), is the word you want. In the third column, gentle isn’t the word you’re looking for, and complex doesn’t fit either. The only remaining choice is boisterous (rowdy, unruly).

8. B, E, G. If you read the sentence without filling in any words, it conveys a sense that the school board president is trying to negotiate something that everyone on the school board can live with. Using your own words to complete the sentence, you may fill in the blanks with please, compromises, and touchy. Then, all you need to do is to identify the word in each column that’s closest to the word you came up with: please ≈ appease, compromises ≈ concessions, and touchy ≈ contentious. For the first blank, provoke isn’t typically what school board presidents set out to do. Inspire may make a good second choice, but it doesn’t fit with the rest of the sentence, which deals more with issues than ideas. For the second blank, accusations would work if the school board president wanted to provoke, but because she’s trying to appease, it’s the opposite of what you need here. Considerations would make a good second choice, but concessions fits better with appeasement. For the third blank the issues must be something the members disagree about, so you can instantly rule out agreeable. You can also rule out seditious (rebellious), because it’s way too strong for this context.

9. C. First, use the verbs to help eliminate wrong answers. Passages are rarely negative and don’t ridicule anything (Choice [E]). This very factual passage doesn’t refute (deny or disprove) anything, which eliminates Choice (B). A strong word like prove (Choice [D]) is rarely correct. (And how much can be proven in two paragraphs, anyway?) Just by examining the verbs, you can narrow your answers to two, giving you a 50/50 shot at the right one.

Although Choice (A) is tempting, the author never makes the claim that the Fremont ­culture was the most advanced, so how can that claim be challenged? Choice (C) fits: Recurring motifs between cultures may indicate connections between those cultures.

On the GRE, you can return to a question within the section if time remains. If you’re down to two answer choices, pick one for now and write the question number down on your scratch paper. If time remains when you get to the end of the section, go back to that question. If time is running out, you’ve already answered the question and don’t have to worry about rushing back.

10. B. The word links in the question almost gives away the answer. “Fremont rock art has recurring motifs that link it to other cultures in that time period.”

11. A, C. These “choose all” questions are tough, because you can’t just eliminate wrong choices; you also need to confirm right choices. You may need to go back to the passage again and again and again to find support for each correct answer choice and to make sure any answer choices you believe are wrong really are.

12. A. The key to this question is to identify the purpose of the first paragraph. The main idea of the first paragraph was to discuss the names given to the Civil War. The material listed names that the South called the war, but didn’t mention any names used by the North. Supplying names used by the North would strengthen the point.

13. D. When something is implied, it’s stated indirectly, meaning that the author may not be making a very strong point. Choose a wishy-washy, “possibly” or “maybe” style of answer. The other choices go too far. Nothing was said about Southern troops going to the capital, about the protection of Lincoln (or threats made against him), or about a conspiracy by the Confederate government. Choice (C) is a logical answer, and it may be true, but the statement in the passage doesn’t imply it.

Just because a statement is true, doesn’t mean it’s a correct answer. Something in the ­passage must support the answer.

14. B. The theme of the paragraph is the new technology. The rest of the paragraph would probably discuss the impact of that technology on the war. Choices (A), (C), and (D), dealing with photography, are too specific. Choice (E) may be true but probably isn’t the point of the passage. Industrialization in general and its effect on the war are the important parts, not the photography or railroads per se.

15. A, D. Extravagant means excessive or unrestrained, the opposite of frugal (spending sparingly, in this case). Choice (D), profligate, means wasteful. Choice (B), impulsive (without caution), would be a good third choice, but it conveys more of a sense of being reckless rather than excessive. Choice (C), generous, doesn’t work in the context of making purchase decisions. Neither of the last two answer choices is a good fit, either: Enigmatic means mysterious, and erroneous means incorrect.

16. B, F. To answer this question correctly, you need to know what exculpatory means. If you’ve heard the Latin expression mea culpa or “my fault,” you can figure it out: Culpa means fault and ex- means not, so exculpa would mean not one’s fault. The two choices that fit are Choice (B), exonerate (to clear from blame), and Choice (F), vindicate (to prove right).

You can also answer this question, or at least improve your chances of answering correctly, by the process of elimination: Rule out Choice (A), incriminate (prove guilty), and Choice (C), castigate (scold), because a defense attorney is unlikely to do either of these to a client. You can also rule out Choice (D), legitimize (to make something legal or acceptable), because that’s not really something a lawyer does to a client, nor would a lawyer use evidence to forgive a client.

17. A, C. The key word in this question is surprised, telling you that the parts before and after that word are opposite or nearly opposite. Because the issue is referred to as complex, expect something simple at the end. Succinct means brief and to the point, which is contrary to complex, and laconic is another word for succinct or concise. Discursive means lengthy. Historic doesn’t fit. Sardonic is scornful. Euphemistic means indirect or understated.

18. D, F. Saturnine means melancholy or sad. The word though is a clue that what’s before though and what’s after are very different, so if Virginia Woolf was very prolific (productive), what kind of moods would she be struggling with to make her less productive? Choices (A) and (B), ebullient and effusive, both convey a sense of enthusiasm, so cross those off the list. Spasmodic means sporadic, which doesn’t really fit. Sinister conveys a sense of evil.

19. B, E. Acerbic means harsh, and sardonic means scornful or with disdain. If the mayor’s remarks insulted people, the remarks must have been negative in some way, which enables you to rule out enthusiastic, encouraging, and reassuring. Confident remarks can be negative or positive, so rule that one out, too.

20. B. The first sentence states that Latin America is the region between the southern border of the United States to Puerto Toro at the tip of Chile, which implies the southernmost point in Chile. Choices (A) and (E) are obviously wrong — Choice (A) because no land exists between Mexico and the United States, and Choice (E) because the passage says nothing about Guatemala. You could make a case for Choice (C), Canada and Chile, but the passage is more precise, specifying the southern border of the United States as the northern boundary.

Section 2: Quantitative Reasoning

1. B. Plug in numbers. Suppose a = 1. Then Quantity A is , and then . Quantity B

requires you to square the 1 first, which is simply 1, and then multiply by to get . So far,

Quantity B is bigger. Try a different number. Suppose a = 2. Then Quantity A is half of 2, which is 1. You know that 12 = 1. Quantity B is half of 4 (because 22 = 4) and guess what — Quantity B is still greater. No matter what you plug in, Quantity B is larger.

With the type of problem in Question 1, always plug in more than one number. Otherwise, you never know whether the answer depends on what you plug in. Do you remember the

Sacred Six you need to plug in for variables? They are 1, 2, 0, –1, –2, and . Usually, just

plugging in 1 and 2 gets the job done. (Turn back to Chapter 13 for more info.)

2. A. Remember the tip from Chapter 13: Cancel quantities that are identical. Slash off the a in both quantities so that you’re left with – c and + b. Because c is negative, a negative c is a double negative, which is actually a positive. In Quantity B, b remains negative (because a positive times a negative is negative). Because any positive is greater than any negative, Quantity A is larger.

Did you look at all the variables and choose Choice (D), thinking the answer depended on what you plugged in? That’s a very good first reaction, but be sure to do the actual plugging in with numbers that fit the inequality, such as –1, –2, and –3. Be careful not to get messed up and put –3, –2, –1. With negatives, everything is backward: –1 is greater than –2.

Quantity A is –1 – (–3) = –1 +3 = 2. Quantity B is –1 + (–2) = –3.

3. B. If you chose Choice (D), you fell for the trap. You probably looked at the question, saw that only one side was given, and figured you didn’t have enough info to answer the question. Wrong. You should’ve reminded yourself of this tip: When a figure is given, the answer is rarely Choice (D). (This is the flip of the tip that when a QC geometry problem gives words but no pictures, the answer is usually Choice [D].)

Do you remember your common right triangles? Chapter 10 covers these. A 30:60:90 triangle has a side ratio of . The side opposite the 30-degree angle is the shortest side — the 5 in this case. The side opposite the 60-degree angle is the next shortest side, the “” side. With this question, that’s . Although you don’t need to know this fact to find the area of the triangle, the hypotenuse (the side opposite the 90-degree angle) is the longest side — the “2side” side. Here, it’s 10.

The area of a triangle is . The base is ; the height is 5. Therefore, the area

is . Don’t bother finding the exact number — it’s certainly less than .

If you chose Choice (C), you did all that work and, because you forgot the very last step, fell for a different trap: forgetting to divide the base × height by 2.

How can you prevent making a careless mistake like forgetting to multiply by in this

problem? Simple. Immediately write down the formula for the problem on the scratch paper. Writing the formula may seem amateurish or like extra work, but it only takes a second and can prevent careless errors. When you see the formula, you can more easily plug in the numbers and work it through.

4. C. It’s amazing how many QC questions that require you to actually do the work and solve the problem turn out to have Choice (C) answers. We’re not saying that you should choose Choice (C) as soon as you start shoving the pencil around, but the more calculations a question requires, the more often the answer seems to be Choice (C). (That’s the flip of the tip in Chapter 13 that if the quantities appear to be equal at first glance, without doing any work, a trap is probably lurking.) Here, set up the equations vertically:

16a + 5b = 37

–8a + 3b = –21

You want to either add or subtract to get the same numerical coefficient (the number that goes in front of the variable) for the a and the b. When you add the equations here, you get 8a + 8b = 16. (Notice how I moved the a to the front of the second equation to make the variables add up neatly?) Divide both sides by 8 to get a + b = 2.

5. B. The four sides of a square are equal, such that one side of Square RSTU is 12. If the points are midpoints, each one divides the large square’s sides into two parts, with each part consisting of 6 units. Connecting these midpoints gives you four isosceles right triangles (RAD, SAB, TCB, and UDC). The ratios of the sides of an isosceles right triangle are . That means the hypotenuse of Triangle RAD, for example, is . These hypotenuses are the sides of Square ABCD. Add the four sides to get , Choice (B).

If you chose Choice (A), you said that four “root 2s” equaled 8 and added 24 + 8 = 32. You can’t add square roots like that.

6. C. The key to this problem is knowing that Gigi and Neville work at the same rate. If they

finish the lawn in 12 hours, each did of the job in 12 hours. Therefore, Gigi working alone

would’ve taken 24 hours to finish the lawn. Because 3 hours is of 24 hours, she could’ve

done of the job in that time.

7. B. Think of a shaded area as a leftover: It’s what’s left over after you’ve subtracted the unshaded area from the figure as a whole. Because Quantity A tells you that the figure is a square, you find its area by multiplying side × side: 8 × 8 = 64. The diameter of the circle is the same as the length of the square, 8. The radius of a circle is half the diameter, or 4. The area of a circle is πradius2, or 16π. Find the shaded area by subtracting 64 – 16π.

Don’t bother figuring out how much 16π is. You know that π is slightly larger than 3.14, but don’t even make it that complicated. Just say that π is bigger than 3. Multiply 16 × 3 to get 48. Subtract 64 – 48 to get 16. The actual area will be even smaller than that because you’ll be subtracting some number larger than 48 (whatever you get when you multiply 3.14 × 16, which I’m not about to do, and neither should you). Because 16 is smaller than 20, and the real answer is even smaller than 16, Quantity B is bigger.

If you can’t recall how to find the remaining area of a shape that’s partially occluded by another shape, flip to Chapter 10, where I provide a simple, three-step approach.

8. $5,000. Latin American sales account for 30 percent of total income. The equation is thus $50,000 = 0.3x. Divide both sides through by 0.3 to get x (total income) = $166,667. European sales were 20 percent of total income, or $166,667 × 0.20 = $33,333. Sales to France were 15 percent of that figure: 0.15 × $33,333 = $5000.

Feel free to estimate, especially because the answer is rounded to the nearest thousand. Say that $50,000 is slightly less than a third of the total, making the total slightly more than $150,000. Call it $160,000. Then European sales are 20 percent, or a fifth of that, which is $32,000. Then French sales are 15 percent of that. Fifteen percent of $30,000 is $4,500, so 15 percent of $32,000 is greater than $4,500 and less than $5,000. The closest thousand is $5,000.

The dollar sign is already there, to the left of the answer box, so you don’t need to enter the $ symbol in the box. In fact, in the computer-based GRE, you can’t enter the dollar sign in the answer box — you can enter only numbers, a decimal point, and a negative sign. Also, the comma in 5,000 appears automatically.

9. E. Read the titles on the graphs: They show income and sales from 1980 through 1990. You can’t figure out sales for one particular year. If you picked Choice (C), you fell for the trap. Shame on you for being so credulous (gullible). You should’ve been more skeptical than that.

If something looks too good to be true, it’s probably a trap.

10. B, C. This question challenges your ability to read the graph and do basic addition. Because you need to choose two out of four correct answers, you can identify the two ­correct answers or the two wrong answers. Start with Choice (A): Sales to Italy and Germany combined = 40 percent. Sales to France = 15 percent, which is not quite half as much, so cross Choice (A) off the list. Choice (B) is correct because sales to England and Germany each stand at 35 percent; 35 – 15 = 20%. Choice (C) is correct because 35 – 15 = 20% and 15 – 5 = 10%. Choice (D) is wrong because half the sales to Italy is 35% ÷ 2 = 17.5%, while sales to France is less than that at 15 percent.

11. A. Because the first equation provides a value for y in terms of x, start by substituting the value for y in terms of x into the second equation:

Simplify the second fraction, multiplying it by :

Now rewrite the original equation using the new value and solve it:

12. A, C. Simplify and solve:

13. A. If ten plums cost a cents, then each plum costs , and two plums cost . If six

apples cost b cents, then each apple costs cents, and two apples cost cents.

Now use 15 as a common denominator for 5 and 3. Convert: , and . Now, add the two:

Though plugging in numbers may be useful at times, this can be a pitfall when the answer choices are in terms of letters, such as Question 13. Say you declare ten plums cost $1, making the plums $0.10 each, and six apples cost $0.30, making the apples $0.05 each. Two plums and two apples total $0.30. This, however, doesn’t match any of the answer choices. You need to keep the a and b in your equation, because that’s the only way to produce an answer that matches one of the choices.

14. E. Unlike the previous question, work through this one by plugging in numbers. Choose a number with an easy square root. Make x = 9 (because ). Now, solve the question:

Keep in mind that 5 is the answer to the problem. It isn’t the value of x. Jot down the 5 to remind yourself that the answer you want is 5. Better yet, make a chart to the side, simply writing down x = 9 and answer = 5. Now go through each answer choice and see which one comes out to be 5. Only Choice (E) works:

Be very, very careful not to put 3 in for x in the problem. Remember x = 9 — the square root of x equals 3.

You can also solve this problem with an algebraic approach: Simplify the denominator by multiplying each side through by :

The numerator is . Use FOIL (First, Outer, Inner, Last) to multiply these terms:

. Then . Next, . Finally, –2 × 2 = –4. Add: .

The denominator is . Use FOIL again to multiply these terms: .

Then . Next, . Finally, 2 × 2 = 4.

The and cancel each other out, leaving you with x – 4. Combine the numerator and denominator, and you get your answer:

Flip to Chapter 9 for more on basic FOIL problems and be sure to memorize the following:

(a + b)(a + b) = a2 + 2ab + b2

(a + b)(a – b) = a2 – b2

15. 1:4. The volume of any right circular cylinder (and every cylinder that you calculate for on the GRE is a right circular cylinder) is πr2h. (More on this in Chapter 10.) To find the volume of any cylinder, you need its height and radius. You have the heights of Cylinders A and B, but not the radii.

The circumference of any circle (or any cylinder) is 2πr. Cylinder A has a circumference of 10, so to find the radius, back-solve using the circumference formula: 10 = 2πr. Solve for r

to find Cylinder A’s radius of . Do the same thing with Cylinder B to find its radius of .

Now that you have the radii of the two cylinders, calculate their volumes. Plug the height

and radius of each into the formula πr2h. With a height of 10 and a radius of , Cylinder A

has a volume of . Cylinder B, with a height of 10 and a radius of , has a volume of

. The ratio, at this point, is .

Multiply both sides by π to get rid of the denominators, for a new ratio of 250:1,000. Reduce this to 1:4 for your answer.

A ratio is like a fraction — you can multiply or divide both sides by the same thing without changing its value. For example, 2:5 is equivalent to 4:10.

The GRE doesn’t provide the formulas needed to solve the type of problem in Question 15, so be sure to memorize the geometry formulas from Chapter 10.

16. B. To find the average speed of a trip, place the total distance over the total time (as discussed in Chapter 11). You don’t have the actual distance, but anything you pick will work, because the answer is in the form of a fraction that you reduce.

Pick a number for the distance. To simplify the math, use the lowest common multiple of the two speeds, 600 and 400, which is 1,200.

If the plane flew to New York, a distance of 1,200 miles at 400 mph, it flew for three hours. If it flew back at 600 mph, it covered the 1,200 miles in two hours. Now you have the total distance and total time, which is 2,400 miles over 5 hours. Set it up as a fraction

and reduce to , or 480 mph.

17. D. The formula for calculating slope is rise over run or , so plug in the numbers and do the math:

If you chose Choice (A), you probably did run over rise, like so:

If you chose Choice (C), you probably got mixed up and did something like this:

If you chose Choices (B) or (E), I don’t have any idea how you came up with those answers.

18. 187. To answer this question, first jot down the prime numbers from 3 to 19:

3, 5, 7, 11, 13, 17, 19

Of those numbers, choose the smallest prime number greater than 7, which is 11, and the largest prime number less than 19, which is 17. Now, do the math: 11 × 17 = 187.

19. A, D, E. Because you’re looking at the absolute value of x, the easiest way to answer this question is to ignore the negative signs in the answer choices, because the absolute value of a number is always its positive value. Drop the negative signs, and you immediately see that 21, 20, and 32 are all greater than 17.

20. E. With a system of equations problem, you may add the equations and then solve for either of the variables: x or y. In this case, you can quickly see that if you add the equations, the 4y and –4y cancel each other out, leaving 16x = 48, so x = 3. Plug 3 into either equation to find y: 9(3) – 4y = –5, which simplifies to 27 – 4y = –5. Subtract 27 from both sides, and you get –4y = –32, so y = 8. So x × y, being 3 × 8, is 24.

Section 3: Verbal Reasoning

1. A. Zeal is an enthusiasm to do something. You can immediately rule out turpitude (immorality) and apathy (disinterest, the opposite of zeal). Guile means cunning, which sort of fits but would work better in a sentence about someone being cunning. Certainty (confidence) sort of fits, too, but zeal is still the better choice.

2. D. Irascible means irritable, cantankerous. Because the mayor’s irritability was well known, outbursts were probably to be expected. Inchoate (undeveloped, as in an idea or plan) doesn’t fit, nor does pedantic (overly focused on details and rules). Demented (wild, irrational) sort of fits, but an outburst isn’t necessarily irrational, nor would a demented individual likely be mayor. Incorrigible means hopeless, which the mayor may well be, but nothing in the sentence suggests that.

3. B, D. Stellar means excellent and emulate means to imitate. The second part of the sentence includes the key phrase rather than change it, meaning the new manager thought of the leadership style as something positive, so you know the two words are both going to be positive. This rules out lackadaisical (apathetic, careless) in the first column and obviate (remove) and preclude (prevent, exclude) from the second column. Enigmatic, in the first column, means mysterious or difficult to understand, which really doesn’t fit in the first blank, either.

4. C, F. You’re looking for two words that match. If the speaker was soporific (sleep inducing), the audience would lull into a torpor (state of sleepiness). Fastidious (finicky or picky) and lucidity (clarity or lack of confusion) would be a reasonable match, because a fastidious speaker is likely to be lucid, but soporific and torpor are a better match. In the first column, unassuming means humble, which has no suitable match from the second column. And interest doesn’t match peaceful.

5. B, F. If you fill in the blanks with your own words before looking at the answer choices, you may come up with something like, “One of the possum’s primary defense maneuvers is to fake death until a potential predator loses interest.” This makes picking the right choice from the first column a snap, because aggressive and avoidance obviously don’t fit. The second column is a little more challenging. If you selected Choice (D), play, you probably misread death as dead. Animals may play dead, but they don’t play death, except maybe at Halloween. Subjugate means to overcome, and that doesn’t quite fit, either.

6. B, D, G. “The instructions were so explicit (clear) that the possibility anyone could misconstrue (misunderstand) them was completely inconceivable (unable to believe).” You have to look at the answers to figure this out, because the sentence could go one way or another. By filling in your own words, you may come up with, “The instructions were so baffling that the possibility anyone could comprehend them was completely unbelievable.” or “The instructions were so clear that the possibility anyone could misunderstand them was completely unbelievable.” Because the first column has no word comparable to baffling, you have to go with the second sentence and find words in the answer choices that match up with your own words. For the first blank, sincere obviously doesn’t work, and instructions aren’t implicit (understood without being communicated), because if they were, people wouldn’t need them. In the second column, you can rule out comprehend (to understand), because the instructions are so clear. Also, scratch mistake off the list, because it leaves you wondering “mistake them from what?” In the last column, rule out understandable, which is pretty close to the opposite of what’s needed here, and rule out laughable (ridiculous), because it goes a little too far.

7. A, F, G. “The crowd’s exuberance was ephemeral. Soon after they dispersed, a riot ensued, and even some of the most docile of the group brandished weapons.” The easiest way to answer this question is to start by filling in words from the end. The phrase, even the most _____ of the group brandished weapons begs for a word like passive (peaceful). With that word filled in, you know that the riot started instead of ended, and if that happened, the exuberance (enthusiasm or good spirits) probably ended, too. You may come up with something like, “The crowd’s exuberance was short-lived. Soon after they dispersed, a riot began, and even some of the most passive of the group brandished weapons.”

Then, you just have to find the word in each column that matches the words you inserted. Ephemeral means short-lived, ensued means began, and docile means passive.

As for the other choices, rule out passive from the first blank, because it clashes with ­exuberance and rule out enduring, because if the crowd’s exuberance was enduring, a riot wouldn’t have broken out. For the second blank, cross off endured (continued) and dissipated (faded), because it would have had to start before it could do either of those. For the third blank, cross eager and pugnacious (aggressive) off the list, because it wouldn’t be a surprise if they brandished weapons.

8. C, E, G. “Unable to arrive at a consensus (agreement), attorneys for the two parties engaged in arbitration (negotiation) to resolve the dispute (disagreement).” Without looking at the answers, fill in the blanks with your own words, and you’re likely to get something like, “Unable to arrive at a deal, attorneys for the two parties engaged in discussions to resolve the issues.” Scan the columns for the possible answers, and the correct ones should jump out at you, but if you don’t know what some of the words mean, they may throw you off. In the first column, variance and disparity mean a discrepancy or difference, not something you arrive at. In the second column, provocation is a threat of some sort, while amelioration is an enhancement, neither of which two attorneys would engage in to resolve anything. In the third column, agreement is something positive not needing to be resolved, and concurrence is agreement, so it doesn’t work either.

9. D. The answer is in the final two sentences: “The increase is due largely to the availability of versatile, convenient energy. As controlled, or useable, energy became more prevalent, the population expansion accelerated.”

10. A, B. The passage links the availability of convenient energy to population growth and an improved quality of life for human beings. It doesn’t support the idea that population growth contributed to the availability of convenient energy, although the two trends may appear to be concurrent.

11. B. “The human ability to harness various sources of energy has improved the quality of life.” Choice (A) describes only one possible effect that may be caused by an inability to start a fire; I’m sure people living along the equator wouldn’t have this problem. Choice (C) is speculative and not supported by any evidence in the passage. Choice (D) is hypothetical, based on the assumption that a necessary component of civilization is an ability to harness different sources of energy. Choice (E) is an example of faulty reasoning; just because increased energy availability is linked to population growth does not mean that reducing energy usage would decrease population growth.

12. B. The first two sentences of the passage tell you that “. . . certain components of the immune system behave abnormally in people with chronic fatigue syndrome” and “. . . interleukin-2 and gamma interferon . . . may not be made in normal amounts.” This one is a simple detail or fact question.

Choice (C) is a trap answer. The author does in fact say that antibody levels are higher in depressed people; however, he doesn’t make that statement to support the theory that the immune system may be affected by chronic fatigue syndrome. Just because a statement is true doesn’t mean that it’s the correct answer. Always be sure to address what a question is asking.

Questions usually go in order through the passage — especially science passages (which require you to find specific facts rather than make inferences). For the first question to a passage, go back to the first sentence or two to support your answer.

13. A. This is a very simple detail or fact question. The passage tells you that the body produces chemicals such as interleukin-2 and gamma interferon during its battle against cancer.

As you’ve probably noticed by now, the questions on science passages are often easier than the questions on other types of passages. Even if the science passages themselves are boring or difficult to understand, the questions relating to them are usually quite straightforward. Frequently, you just need to skim for a specific fact or detail.

14. B. Choices (C) and (D) each focus on sub-themes in the passage but not the main idea. Copyright protection and technology are specific subjects covered in the passage, but they aren’t the main idea, which is that the music industry is trying to control distribution of music. You can eliminate Choice (A) because it’s not supported by any part of the passage. The passage clearly states that music has circulated freely in society for millennia. Choice (E) is wrong because it goes beyond what’s stated in the passage. The author may well imply that without the free flow of music, society will lose its identity, but this isn’t the passage’s main idea.

15. C. Examine the text and eliminate the answers you find there. The one that remains is your correct answer. In connection with technology, the passage mentions Choice (A), new locks on music distribution; Choice (B), newcomers competing in the market; Choice (D), democratization of creativity; and Choice (E), faster, cheaper distribution of music. The author certainly doesn’t mention better music.

16. A, B. Regulation and ordinance refer to rules. None of the other choices come close to being correct answers. A prognostication is a prediction. A restraining order is an injunction or command to stay clear of someone or some place. A tenet is a principle or belief. A verdict is a formal decision, typically issued by a judge or jury.

17. B, E. “The dancer’s movements were so smooth and fluid that she epitomized or embodied (represented) grace and elegance.” None of the other choices fit: Undermined means weakened, synthesized means combined, extirpated means demolished, and dissipated means ­dispersed.

18. C, F. Independence means being able to act without having to consult others. Autonomy is along the same lines, meaning freedom to act on your own. Supremacy is a bit too strong, meaning something like all powerful. Choice (A), dependence, is the opposite of autonomy. Solvency means worthy of credit. Neutrality is the quality of being objective or impartial, which would be a possibility if the sentence was about negotiating agreements.

19. A, F. The sentence starts with although, so you know the first and second halves of the ­sentence are going to be nearly opposite. If the judge delivered a harsh verdict, you can expect the judge to lighten up at the end. Clemency means mercy, compassion. Leniency is also mercy or compassion. Austerity and stringency are nearly the opposite, conveying a sense of toughness and being strict. Affluence means wealth and magnanimity means generosity, neither of which quite fit.

20. C, E. Denigrate is to put someone down or treat as lacking in value. Stigmatize is to mark someone as disgraceful. Chastise means to reprimand or punish. Disaffect means to alienate, which may be a good second choice if it had a suitable match. Emulate means to try to be like someone, so that obviously doesn’t work. Characterize is sort of like stigmatize without the negative connotation that would make it a good match.

Section 4: Quantitative Reasoning

1. D. The areas depend on how the figures are drawn. A rectangle of perimeter 20 can have, for example, sides of 1 and 9 and 1 and 9, making the area 9. Or it can have sides of 6 and 4 and 6 and 4, making the area 24. (The area of a rectangle is length × width.) A triangle of perimeter 20 can have sides of 5.5 and 5.5 with a base of 9, giving it a small area, or sides of 6 and 6 with a base of 7, giving it a large area. Insufficient information is available to compare the quantities.

2. D. If a is a whole number, such as 2, then Quantity A is bigger. If a is a fraction, such as ,

then and Quantity B is bigger. Because you don’t know what a is, the answer is

Choice (D).

Remember the Sacred Six numbers for plugging in from Chapter 13? These numbers are 1,

2, 0, –1, –2, and . You don’t need to plug in all the numbers to find that Choice (D) is the answer.

3. C. Line the equations up vertically and either add or subtract them to get the same numerical coefficients (the numbers before the variables). In this case, you add.

Now divide both sides of the equation by 8 to get a + b = 5. So 3(a + b), or 3(5), = 15.

4. A. The volume of any 3D figure on the GRE is area of the base × height. Because the base of a cylinder is a circle, the volume of a cylinder is πr2 × height. Divide the volume, 200π, by the height, 8, to find that the area of the base is 25π. Because the base is a circle of area = πr2, the radius is 5. But don’t choose Choice (B); you’re not finished yet.

Circumference of a circle is 2πr, which here is 10π. If you chose Choice (C), you fell for the trap. You forgot π, which is a common mistake. The circumference of 10π is actually 10 × approximately 3.14, which is more than 10 (don’t bother to figure it out exactly).

5. A. Both are right triangles, so you can solve this one using Pythagorean’s theorem: The square of the hypotenuse is equal to the sum of the squares of the other two sides. If you recall your common right triangles from Chapter 10, this is a snap to solve. Quantity A has the 8, 15, 17 triple; whereas Quantity B has the 5, 12, 13 triple. Because 15 is more than 13, that’s the end of story. You could also solve this question by doing the math:

6. D. If is between 10 and 14, x must be a number between 102 = 100 and 142 = 196. Quantity A, 144, is also between 100 and 196, but without knowing the exact value of x, you don’t have enough information to determine whether x is more or less than 144.

7. A. Write down the possible combinations for rolling each number, and you instantly see that the odds of rolling a total of 6 are greater:

You can roll a 6 five different ways: 1 + 5, 2 + 4, 3 + 3, 5 + 1, and 4 + 2.

You can roll a 9 four different ways: 3 + 6, 4 + 5, 5 + 4, and 6 + 3.

Chapter 11 explains that probability is the number of events you want divided by the number of events possible. With 36 possible outcomes for this roll of the dice, the probability of a

total of 6 is and the probability of a total of 9 is . Don’t bother reducing the , because

the fractions are easier to compare if they have the same denominator.

8. C. The GRE always gives you the units of conversion, except for units of time. Because a gallon is four quarts, two gallons are eight quarts. If 16 ounces of mix make 8 quarts, then each quart requires 16 ÷ 8 = 2 ounces of mix. To make three quarts, you’d need 3 × 2 = 6 ounces of mix, so Quantities A and B are equal.

9. B. If Bob traveled the last half of his trip alone, then the 40 percent and the 20 miles are the first half, or 50 percent. Because 50% – 40% = 10%, 20 miles = 10%. Thinking in terms

of fractions may be easier: 10% = . If of something is 20, that something is 200.

(Arithmetically: . Multiply both sides by 10 to get x = 200.) This problem is

based more on reasoning than arithmetic.

10. E. This relatively simple problem takes two steps. The top graph shows that 50 new

employees were hired in May; therefore, Total; solve for Total = (50)(5) = 250

Employees. Next, the bottom graph shows that 50 employees were laid off in 1994;

therefore, .

Did you see the shortcut in this problem? The 50 in the top graph is the same as the 50 in the bottom graph. Therefore, whatever percent you have for the top graph is the same as the percent for the bottom graph. You don’t need to go through all that work.

11. E. First, figure out the percent increase in new hires between January and February. Twenty new employees were hired in January and 30 were hired in February. To find a percent increase or decrease, you use the formula: number increase or decrease divided by original

whole (the number you began with). Here, that’s .

According to the bottom graph, the number of employees laid off in 1994 was 50. The number

laid off in 1995 was 50 percent greater. Fifty percent of 50 is . Add 50 + 25 = 75.

Did you fall for Choice (D)? The increase in new hires between January and February was ten, but that doesn’t mean that the number of layoffs in 1995 was ten higher than the number in 1994. You must figure the percentage.

12. $35,000. Because Carlos received a 7 percent raise, he’s now earning 107 percent of what he was earning initially (what he was earning was 100 percent of his pay; if you add 7 percent, you get 107 percent). He’s earning $37,450 now, so 107 percent of what he was earning is equal to $37,450. And 107 percent = 1.07, so the equation looks like this: 1.07x = $37,450. To isolate the x, divide both sides by 1.07 and you get $35,000.

With the on-screen calculator available in the Math sections of the GRE, clicking Transfer Display will throw whatever’s in the calculator display window into the answer box.

13. B. First determine the distance Jerry drove: 30 × 2.5 = 75 miles. Because Susan drove the same distance, she drove 75 miles, too. Knowing this, and that Susan drove 40 miles per hour, you now have everything you need to solve the problem:

14. D. This is a combination problem in which order doesn’t matter, because to “choose 5” means students A, B, C, D, E are the same as students E, D, C, B, A (or any other mixture of these 5) so use the following formula to solve it:

where C is the number of combinations you’re trying to determine, n is the total number of objects or events (25 in this case), and r is the number of objects or events you’re choosing at one time (5 in this case). You don’t actually have to do the math — just set it up:

If you chose one of the other answers, you probably either didn’t know the equation or you tried to simplify the fraction. Remember that simplifying fractions that contain factorials is

tricky; for example, doesn’t equal . It actually equals 129,260,083,694,424,883,200,000.

However, you may cancel identical terms in the numerator and denominator. Here’s an example in which 7! is cancelled out:

15. A. To solve this problem, you need to remember the following equation:

Group 1 + Group 2 + Neither Group – Both Groups = Total

Plug in the numbers and do the math:

16. B, D, E. You could find all the common factors of 18 and 48, but instead, just try each answer choice. Choice (A), 9, doesn’t work, because the closest you can get to 48 is 5 × 9 = 45, and another 9 puts you over into 54. Choice (B), 3, works for 18: 3 × 3 × 2 = 18. It also works for 48, because 2 × 24 = 48 and 3 × 8 = 24. You can rule out Choice (C), 4, because the closest you can get to 18 using 4 is 4 × 4 = 16, and another 4 gives you 20. Choice (D), 6, works for 18, because 3 × 6 = 18. It also works for 48, because you already saw that 2 × 3 × 8 = 48. Choice (E), 1, is a gimme because 1 is a factor of all integers.

17. C. The sequence has three terms (–5, 0, and 5), and every third term is 5. Divide 250 by 3 to get 83 with a remainder of 1. That means that the 249th number is 5 (because 249 divides evenly by 3), the 250th number is –5, and the 251st number is 0. Add –5 + 0 = –5.

In this particular problem, you’re adding two consecutive terms in the series, so you’re adding –5 + 5, –5 + 0, or 0 + 5, so there’s no possible way you can end up with 10 or –10. You can eliminate Choices (B) and (E).

The people who devise the GRE put questions like Question 17 on the test to get you to waste your time. You could’ve counted on your fingers up to the 250th term, but who has that sort of time? Find the closest number that divides by 3 and then work from there.

18. B. Start with what you know and work toward what you don’t know. You know you have 75 ounces of a 10 percent salt solution, and you’re adding x ounces of a 40 percent salt solution, so (75 × 0.10) + 0.40x = what? Your final solution will consist of 75 ounces plus x ounces, and it’ll have a 35 percent salt concentration:

19. D. Multiply both sides by (x – 7) and you get x + 5 = xy – 7y. Subtract 5 from both sides, and you get x = xy – 7y – 5. Now, subtract xy from both sides to get x – xy = –7y – 5. You can factor the left side of the equation to get x – xy = x(1 – y). Finally, divide both sides of the equation by (1 – y), and you have your answer:

If you chose Choice (C), you fell for a trap. In the numerator, both 7y and 5 must be negative; in Choice (C), the 7y is positive.

20. A, B. If you quickly scan the answer choices, you can see that they’re all comparisons of either total sales or percentage increases, so you may as well figure out all the numbers before closely examining each choice:

Company A’s increase in sales is $80,000 – $72,000 = $8,000, representing a percentage

increase of .

Company B’s increase in sales is $59,000 – $50,000 = $9,000, representing a percentage

increase of .

Company C’s increase in sales is $73,000 – $65,000 = $8,000, representing a percentage

increase of .

Answer Key for Practice Exam 1