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GRE
The sudden, vehement objections of the senator understandably <code>________</code> the other members of his party, considering that he had previously expressed few qualms about the proposed amendment.<br/><br/>[ Note: Select 2 answer choices ]
Correct — E. The sentence is about a change in the senator's opinion about the 'proposed amendment.' Previously, he did not express any 'qualms' (doubts, misgivings), but then he made sudden, vehement objections. The word in the blank describes the reaction of the other party members upon the senator's objections. Their reaction is not positive; hence a negative word is required for the blank. Words such as 'upset' or 'stunned' are good fill-ins for the blank.<br/><br/>Now, let's examine the meanings of the words in the options:<br/><br/>bewitched – to be affected by witchcraft or magic; enchanted or delighted<br/><br/>disenfranchised – deprived of the right to vote<br/><br/>discombobulated – confused and disconcerted<br/><br/>truncated – shortened by cutting off the top or the end<br/><br/>enervated – weakened, drained of energy<br/><br/>addled – unable to think clearly, confused<br/><br/>'Discombobulated' and 'addled' match the meaning of the sentence. 'Bewitched' is a positive word and would go against the context. 'Disenfranchised' and 'truncated' are unrelated to the sentence. There is no information in the sentence to support the word 'enervated'. -
GRE
The investigators made it clear that nothing they would unearth was <code>________</code>; every misdeed they learned about would be revealed to the public.
Correct — C. In this restatement structure, the second part of the sentence confirms that everything will be revealed because nothing would be sacrosanct, or "inviolable or sacred." In other words, with choice C, there would be no secrets.<br/><br/>Choice A does not fit the context since being incredulous means you are having trouble believing something.<br/><br/>Choice B, exposed, doesn't make sense. The investigators would be saying that what they unearthed was exposed, which is a contradiction. The word cynical, choice D, makes no sense because there is no mention of anyone not believing the promise to expose crimes. There is no mention of any information that is contradictory, or at odds with what has been promised, so choice E should be ignored. -
GRE
In the 1950s, the profusion of goods, televisions, and other factors led to an explosion of ads. Alert to the captivating power of these images, pop artists set out to shock the world and redefine art. The paragon of this movement was Andy Warhol, who marketed mechanically reproduced images ranging from celebrities to soup cans. <br/><br/>Outwardly he cultivated a passive, cool, eccentric detachment; in reality, he was a workaholic perfectionist who spent long hours making his work appear effortless. His intention was easily achieved—many did not understand his vision and thought it required no effort. "Anyone can paint a soup can and call it art," some said. <br/><br/><em>But not just "anyone" did; only Warhol, whose sensibility epitomized the notion that the essence of art lies in its conception, did</em>. <br/><br/>Warhol passed another artistic litmus test by encapsulating in tangible form the tenor of his times, a mechanical age of mass production and mass consumption. <br/><br/><em>Despite the hype and myth-making that continually infused his enterprise, Warhol earned the title of artist</em>.<br/><br/>Which of the following, if true, most seriously undermines the argument?
Correct — D. Because the passage as a whole is about how Warhol did see artistic relevance in his subject matter, as it was emblematic of the world of mass production and mass consumption that he inhabited. Therefore, these objects had relevance and resonance.<br/><br/>Choice A is incorrect because, while Warhol is referred to as the "paragon," or perfect example or model, of the Pop Art movement, there is nothing in the passage to suggest that his art was the best. And, even if others produced work just as good or greater, Warhol would not have been less of an artist.<br/><br/>Choice B should be eliminated because the passage suggests that the conceptualization of art is its essence; therefore, merely conceptualizing the art, instead of carrying it out to the last detail, is still the primary work of the artist.<br/><br/>Choice C is incorrect because it actually strengthens, through restatement, a premise of the argument, which is that Warhol saw the relevance in everyday objects that had already demonstrated their power to captivate audiences.<br/><br/>Choice E is incorrect because it has little relevance to the conclusion that Warhol earned, or deserved, the title of artist; instead of focusing on the essence of Warhol's art, choice E focuses on his popularity. -
GRE
<em>Unseen Characters</em> by Will Floyd<br/><br/>Many plays, films, and television shows use the storytelling device of the unseen character. As the name implies, this trope involves a character the audience never directly encounters, but instead only hears about through the words of other characters. A common assumption is that a character that never speaks or is visible to the viewers of a play or film would only be a minor element, left to be the butt of jokes or as a simple way to add depth to a major character. In fact, unseen characters are frequently quite important, and further the plot because of their absence. The most notable instance of such a character is Godot, in Samuel Beckett’s play <em>Waiting for Godot </em>(1953). The two main characters in the play, Vladimir and Estragon, sit patiently by a tree, expecting Godot to come by at any moment. Three other characters, Lucky, Pozzo, and a boy, all speak to Vladimir and Estragon, with Godot never alighting on the stage. Nonetheless, Godot’s machinations in making the men wait—along with his supposed intentions—drive the play’s narrative. Godot, never seen or heard from directly, becomes the largest force in the created world of the play. This use of an unseen character creates an added mystery and increases the tension between the two main characters. Beckett uses the unseen character not as a gimmick or cheap ploy, but instead as the central focus of his play.<br/><br/>The author would NOT agree with the statement that <code>________</code>.
Correct — E. The author quite clearly views unseen characters as being effective literary devices when used well. This means that the description of unseen characters which is negative will be the correct answer. The description of them as "useless literary devices" is the best choice among the answers. -
GRE
Etiquette, which is sometimes unwritten, is a code that governs the expectations of social behavior of people. It usually reflects the cultures and traditions of countries. The Democratic Republic of the Congo is the second largest country in African. It is also known as Congo (Kinshasa) or DRC. With over 200 ethnic groups represented the people of the Congo have a wide variety of customs, traditions, and values. They vary from place to place and group to group, especially when it comes to living in urban areas and rural areas. Therefore the etiquette rules differs depending on where a person lives.<br/><br/>Congolese that live in urban areas tend to have more Western customs and traditions. It is important to greet each other, and inquire about each others situation before other matters are discussed. Greetings consists of speaking, shaking their hands, and smiling. In the rural areas, men and women do not shake hands. Men will shake the hands of other men. Some women will greet men by clapping their hands and bowing slightly.<br/><br/>When dining in the Congo hands should be washed before and after eating. People should only eat with their right hands, especially if they are eating with their fingers. Men and women use separate communal bowls; often, women may sit together. When eating out of a communal bowl, people eat from the space directly in front of them. When utensils are used, the left hand holds the fork and the right hand holds the knife.<br/><br/>Dressing in the Congo is greatly influenced by the Western world, however, they are mixed with traditional clothing such as kikwembe, abacos, or a dashiki. The nicer a person look, the more respect he or she will receive. Jewelry is often made from wood, ivory bones, or shells. Many people in rural areas walk barefoot, but sandals and slippers are commonly worn.<br/><br/>What does the author’s tone suggest about the customs in different parts of the country?
Correct — B. The author’s tone suggests that customs are different, but none are superior to others. The author does not use any biased or preferential language to describe the customs of a single area. For example in the second paragraph, the author describes different ways of greeting, but uses no words to indicate superiority or preference for one over another. -
GRE
Etiquette, which is sometimes unwritten, is a code that governs the expectations of social behavior of people. It usually reflects the cultures and traditions of countries. The Democratic Republic of the Congo is the second largest country in African. It is also known as Congo (Kinshasa) or DRC. With over 200 ethnic groups represented the people of the Congo have a wide variety of customs, traditions, and values. They vary from place to place and group to group, especially when it comes to living in urban areas and rural areas. Therefore the etiquette rules differs depending on where a person lives.<br/><br/>Congolese that live in urban areas tend to have more Western customs and traditions. It is important to greet each other, and inquire about each others situation before other matters are discussed. Greetings consists of speaking, shaking their hands, and smiling. In the rural areas, men and women do not shake hands. Men will shake the hands of other men. Some women will greet men by clapping their hands and bowing slightly.<br/><br/>When dining in the Congo hands should be washed before and after eating. People should only eat with their right hands, especially if they are eating with their fingers. Men and women use separate communal bowls; often, women may sit together. When eating out of a communal bowl, people eat from the space directly in front of them. When utensils are used, the left hand holds the fork and the right hand holds the knife.<br/><br/>Dressing in the Congo is greatly influenced by the Western world, however, they are mixed with traditional clothing such as kikwembe, abacos, or a dashiki. The nicer a person look, the more respect he or she will receive. Jewelry is often made from wood, ivory bones, or shells. Many people in rural areas walk barefoot, but sandals and slippers are commonly worn.<br/><br/>What assumption does the author make about the readers of this passage?
Correct — A. The author assumes the reader of this passage is familiar with Western clothing and etiquette. The notes, for example, that dressing in the Congo is influenced by the Western world, but does not explain what that means. The author also notes that urban areas have more Western customs and traditions, but, again, does not explain what that means. It is assumed the reader has prior knowledge of Western customs, traditions, and style of dress. -
GRE
Over the years, she was able to dupe countless men into giving her money by using her beauty and her <code>________</code> deceptions.
Correct — D. The sentence states that the woman used beauty and deception to con men into giving her money. Deceptions are often cunning and clever; therefore, artful, which means clever or skillful in a crafty way, is correct. Lackluster, which means uninspired, is incorrect. Simian, which means ape-like, does not make sense. Ignominious, which means causing public disgrace, is incorrect. Transformative, which means causing change, is incorrect. -
GRE
In the context in which it appears in the third paragraph, "nature" most clearly means
Correct — E. Because the passage makes it clear that science describes phenomena that can be publicly experienced and shared, or the outer world, while literature looks into the inner "reactive" human world. Therefore, the workings of nature that science sheds light on most clearly relate to the entire world beyond the inner "reactive" human world.<br/><br/>Choice A should be eliminated because, according to the passage, this is the meaning of nature with which literature would be concerned.<br/><br/>Choice B is incorrect because it does not fit the context of what science "sheds light on," including the more public aspects of human experience.<br/><br/>Choice C, although close to the correct answer, should be eliminated. While science may well shed light on the universe's causal agent, according to the passage, science is concerned with far more than that.<br/><br/>Choice D is incorrect because it doesn't fit the context of what science "sheds light on," including the more public aspects of human experience. -
GRE
There are a group of islands located in the East China Sea that are the subject of a dispute between two nations. China calls the islands Diaoyu; in Japan, they are known as the Senkaku. Both nations claims sovereignty over the islands. China asserts that they discovered the eight uninhabited islands, and controlled them until the end of the Sino-Japanese War in 1895. Before the war, Japan incorporated the islands into their territory.<br/><br/>Japan control the disputed East China Sea islands until World War II. Following the war, a 1951 treaty with Japan gave the United States rights to administer the islands. That authority reverted back to Japan in 1971. China asserts that the 1951 treaty should have given them control over the islands. In 1969, the United Nations reported that there was a possibility of large oil reserves in the East China Sea near the islands location. China and Japan have been locked in a territorial dispute since the 1970s. Its conflict has escalated in recent times, with citizens from both nations protesting and raising flags on different islands. The countries have launched diplomatic efforts to resolve the issue.<br/><br/>In what year did the United Nations report there may be oil reserves in the China Sea?
Correct — D. In 1969 The United Nations reported that there was a possibility of large oil reserves in the East China Sea near the islands’ location. Since the 1970s China and Japan have been locked in a territorial dispute. The conflict has recently begun to escalate. -
GRE
A nightmare is a dream occurring during REM sleep characterized by feelings of anxiety, fear, distress, sadness, guilt, or terror. Nightmares are often confused with night terrors. These two types of disturbing dreams can be differentiated both biologically and psychologically. <br/><br/>Unlike nightmares, which usually wake the dreamer and are often clearly recalled upon waking, night terrors typically don't wake the dreamer and are most often not remembered in the morning. One who suffers a night terror usually experiences confusion and a pervasive feeling of fear or anxiety upon waking, but is not often able to recollect the substance of the episode or the vivid imagery typically associated with nightmares. <br/><br/>Unlike nightmares, which occur generally during REM stages in the second half of the night, night terrors occur during slow-wave non-REM periods, usually within the first few hours of sleep. <br/><br/>The passage highlights the ways in which night terrors differ from nightmares, except for the following:
Correct — A. Both nightmares and night terrors are characterized by strong negative feelings: "anxiety, fear, distress, sadness, guilt, or terror" for nightmares, and "a pervasive feeling of fear or anxiety" for night terrors.<br/><br/>Choice A identifies a difference between nightmares and night terrors discussed in the passage: Nightmares occur during REM stages late in the night, whereas night terrors typically occur during earlier non-REM periods.<br/><br/>Choice B is an incorrect answer because nightmares generally wake the dreamer up, whereas night terrors do not.<br/><br/>Choice D is incorrect because the author states that people generally remember the details of their nightmares, but usually don't remember the details of their night terrors.<br/><br/>Choice E highlights a difference between nightmares and night terrors discussed in the passage: Nightmares occur during REM stages late in the night, whereas night terrors typically occur during earlier non-REM periods. -
GRE
The passage indicates which of the following about the development of republics in Europe?
Correct — E. In the first sentence, the author notes the following: “It might be surprising to discover that Europe’s first republic pre-dated the turn of the 11th century, long before Europe would see the rise of another such system.” This statement clearly indicates that Iceland’s republic came well before another in Europe, so indeed it was “many years” before another republic emerged in Europe.<br/><br/>The author of the passage mentions a monarchy in Norway and Denmark, but this mention alone is not enough to assume that monarchy was the more common system–based only on the information in the passage.<br/><br/>The information in "The republic in Iceland ultimately was unable to withstand..." and "The republic that developed in Iceland lacked the stability it needed..." focuses solely on the republic in Iceland, and this counters the question with its focus on the development of republics in Europe.<br/><br/>Additionally, the author mentions that Iceland is currently a republic, but this mention alone is not enough to comment on modern republics in Europe or on the level of “sophistication” that defines them. -
GRE
He has frequently faced criticism for his business practices; nevertheless, Winston was recently recognized by the governor for his <code>________</code> endeavors.
Correct — C. The word "however" suggests that despite criticism of Winston's business practices, the governor has acknowledged him for accomplishing something valuable. <br/><br/>Therefore, the correct answer is "philanthropic," which means charitable. <br/><br/>The word "philandering," meaning committing adultery, does not fit the context. <br/><br/>"Misanthropic," meaning disliking humankind, does not make sense either. <br/><br/>"Unorganized" is also nonsensical. <br/><br/>Additionally, "whimsical," which means playfully quaint or fanciful, does not fit the context. -
GRE
<em>Choose one answer for each blank. Select from the appropriate column for each blank. Choose the answer that best completes the sense of the text.</em><br/><br/>Russian author Leo Tolstoy wrote <em>War and Peace</em> from an <code>________</code> point of view because he wanted to convey what each of his characters was thinking and feeling.
Correct — E. In literature, an omniscient point of view is one that features a narrator who has total knowledge of the feelings and thoughts of all characters in the story. <br/><br/>Accomplished (choice A) means "skillful," and while that word does make grammatical sense in this context, it is not as specific a choice as omniscient. <br/><br/>The novel in question may have an enormous number of characters, but there is no such thing as an "enormous point of view" in literature, so choice B is not the best answer. <br/><br/>Ensemble (choice C) seems to make sense in this context because the author could be dealing with an ensemble of characters, but a point of view that conveys the feelings and thoughts of all characters is called an omniscient point of view, not an "ensemble" point of view. <br/><br/>Acrimonious (choice E) means "bitter or spiteful" and does not make any sense in this context. -
GRE
<em>Consist of short passages containing two or three blanks. Choose one answer for each blank.</em><br/><br/>According to Frank, the (i)<code>________</code> for his part-time job would hardly cover his college expenses. Still, he was too (ii)<code>________</code> to ask for a raise, believing he would be turned down and maybe fired. <br/><br/><table><tbody><tr><td> Blank (i)</td><td> Blank (ii)</td></tr><tr><td> A. derivation</td><td> D. reticent</td></tr><tr><td> B. exploitation</td><td> E. tactile</td></tr><tr><td> C. remuneration</td><td> F. invigorated</td></tr></tbody></table>
Correct — A. For blank (i), Frank is referring to his wages, which is what remuneration means in this context. Derivation refers to the source of an idea or word and makes no sense in this context. While Frank may feel exploited or victimized working for a low wage he receives, exploitation doesn't make sense in the context of the sentence.<br/><br/>For blank (ii), Frank is reticent, or quiet, by nature, even without the fear of losing his job. Something tactile can be touched, which doesn't describe Frank's feelings. Invigorated, derived from the root vigor, means "enlivened." It's an antonym of reticent and doesn't describe Frank accurately. -
GRE
<em>For each blank, choose one answer from the appropriate column that best completes the sense of the text.</em><br/><br/>To sell their products, many companies are harnessing social networking as a marketing tool. However, it is crucial to use it <code>________</code> because the hard sell approach risks offending potential customers.
Correct — E. The context of the sentence suggests that the correct answer should indicate an opposite action to the phrase "hard sell." The word that matches this sense is "judiciously" (choice C), which means "showing good judgment, being prudent." <br/><br/>"With ease" (choice A) doesn't fit the sense as a hard sell can be done easily. The same issue occurs with "actively" (choice B). <br/><br/>"Expeditiously" (choice D), meaning "efficiently and quickly," is incorrect because doing a hard sell efficiently and quickly doesn't make it more palatable to the consumer. <br/><br/>Additionally, simply being efficient (choice E) doesn't address the issue. -
GRE
In what sense are "<b>census reports, church records, directories</b>" (sentence (15)) inadequate?
Correct — C. The “census reports, church records and directories” (sentence (15)) are representative of the “available sources” (sentence (15)) that the author finds inadequate specifically because they “cannot provide one of the essential dimensions of history, the full narrative of the human experience” (sentence (16)). That is, they do not tell the human side of the story. -
GRE
What is <tex>_{8}P_{4}</tex> equal to?
Correct — A. <tex>_nP_k</tex> depicts the permutation of n total objects with k objects being arranged.<br/><br/>Thus,<br/><br/><tex>_{8}P_{4} = \frac{n!}{k!}=\frac{8!}{4!}</tex><br/><br/>The upper factorial is the upper index, and the lower factorial is the difference of the indices.<br/><br/><tex>\frac{8!}{4!} = \frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1}</tex><br/><br/>The <tex>4!</tex> or <tex>4\times3\times2\times1</tex> will cancel out.<br/><br/><tex>8\times7\times6\times5 = 56\times30 = 1,680</tex> -
GRE
<em>a</em> + b + <em>c</em>+ <em>d</em> + <em>e</em> = 0 <em>a</em> × <em>b</em> × <em>c</em> × <em>d</em> × <em>e</em> ≠ 0 Quantity A: <em>a</em><sup>2</sup> + <em>b</em><sup>2</sup> + <em>c</em><sup>2</sup> + <em>d</em><sup>2</sup> + <em>e</em><sup>2</sup> Quantity B: (<em>a</em> + <em>b</em> + <em>c</em> + <em>d</em> + <em>e</em>)<sup>3</sup>
Correct — D. Don't let the many variables and exponents scare you. As you might expect with a problem that looks this complicated, there is a slick solution.<br/><br/>First, note that since the product of the five variables does not equal zero, then none of the variables equals zero. Next, consider quantity B, which cubes the sum of all the variables. Since the sum of the variables is zero, its cube is also zero—that is, quantity B is zero. Quantity A adds the squares of all the variables. Since none of the variables is zero, the squares aren't zero, either—and, in fact, each of them is positive. As the sum of positive numbers, quantity A is also positive, and therefore greater than quantity B. -
GRE
A business has made the decision to renew the surface of a specific section within their warehouse. This section happens to be a perfect square, with each side measuring 15 feet. <br/><br/>What is the total area that requires resurfacing?
Correct — C. 15 x 15 is 225 square feet.<br/><br/><b>Key Takeaway:</b> Squaring numbers that end in 5 becomes easier with this trick.<br/><br/>To square any number that ends in 5, use this trick: Take the first digit of the number, in this case 1, and multiply it by itself and the next consecutive digit, which is 2. So, 1 x (1+1) = 1 x 2 = 2. Then, simply append 25 to the end, resulting in 225. This trick is effective for squaring any number that ends in 5. -
GRE
What is a potential value for 'y' after the points of intersection for the equations:<br/><tex>y= -x^2 + 3</tex> and <tex>y= x^2- 5</tex>?
Correct — D. To find the distance between two points, we need to equate the two equations, determine the points of intersection, and apply the distance between points formula.<br/><br/>By equating the two equations, we obtain:<br/><br/>x = 2 and x = -2, which correspond to y = 7 and y = -1, respectively.<br/><br/>Hence, we select option -1 as the correct answer. -
GRE
Rectangle B has a length of six units and a width of four units. Rectangle A, on the other hand, has twice the length and 1/2 the width of Rectangle B.<br/><br/>What is the perimeter of rectangle A?
Correct — B. Rectangle A has two sides measuring 12 units each (twice the length of Rectangle B) and two sides measuring 2 units each (half the width of Rectangle B). <br/><br/>Therefore, the perimeter of Rectangle A is calculated as 12 + 12 + 2 + 2, which equals 28 units. -
GRE
Let universal set <tex>U</tex> be the set of all people. Let <tex>b</tex> represent Brittany.<br/><br/>Let <tex>A</tex> be the set of people who like James Blunt, <tex>B</tex>, the set of people who like John Legend, and <tex>C</tex>, the set of people who like Pharrell Williams.<br/><br/>True or false: Brittany likes James Blunt, John Legend, and Pharrell Williams.<br/><br/>Statement 1: <tex>b \in A \cap B \cap C</tex><br/><br/>Statement 2: <tex>b \in A \cup B \cup C</tex>
Correct — D. Assume Statement 1 alone. <tex>A \cap B \cap C</tex> is the intersection of the sets <tex>A</tex>, <tex>B</tex>, and <tex>C</tex>. Since Brittany falls in this intersection, she falls in all three sets, and it follows that she likes all three of James Blunt, John Legend, and Pharrell Williams.<br/><br/>Assume Statement 2 alone. <tex>A \cup B \cup C</tex> is the union of the three sets. Since Brittany falls in this union, she falls in one, two, or all three sets, which means that she likes at least one of James Blunt, John Legend, and Pharrell Williams. However, more information is needed before it can be established whether or not she likes all three. -
GRE
Simplify: <tex>\sqrt{-243}</tex>
Correct — C. Step 1: Split the <tex>\sqrt{-243}</tex> into <tex>\sqrt{243}\cdot\sqrt{-1}</tex>.<br/><br/>Step 2: Recall that <tex>\sqrt{-1}=i</tex>, so let's replace it.<br/><br/>We now have: <tex>\sqrt{243}\cdot i</tex>.<br/><br/>Step 3: Simplify <tex>\sqrt{243}</tex>. To do this, we look at the number on the inside.<br/><br/><tex>243=3\cdot3\cdot3\cdot3\cdot3</tex>.<br/><br/>Step 4: Take the factorization of 243 and take out any pairs of numbers. For any pair of numbers that we find, we only take 1 of the numbers out.<br/><br/>We have a pair of <tex>3's</tex>, so a 3 is outside the radical.<br/>We have another pair of <tex>3's</tex>, so one more three is put outside the radical.<br/><br/>We need to multiply everything that we bring outside: <tex>3*3=9</tex><br/><br/>Step 5: The <tex>i</tex> goes with the 9...<tex>9i</tex><br/><br/>Step 6: The last 3 after taking out pairs gets put back into a square root and is written right after the <tex>i</tex><br/><br/>It will look something like this: <tex>9i\sqrt{3}</tex> -
GRE
Select the correct option.<br/><br/><img src="asset:assets/questions/36323c4644d97aa4.png"/>
Correct — A. We know that circumference of a circle equals 2πr.<br/><br/>Here, r= 3 so the circumference equals 18 approximately.<br/><br/>Now, Perimeter of a square is equal to sum of all its sides, which in this case is 16.<br/><br/>Therefore, quantity A is greater. -
GRE
<em>x</em> – <em>y</em> = 9 11 – <em>y</em> = 2 Quantity A: <em>x</em> Quantity B: 0
Correct — B. First solve the second equation:<br/><br/>11 − y = 2 y = 9<br/><br/>Next, substitute this value of y in the first equation:<br/><br/>x − 9 = 9 x = 18<br/><br/>Of the two quantities, x is greater. -
GRE
Master Chef Alan has written 3 recipe books, and each book contains 15 different recipes. As a result, he prepares a dish every day using a recipe from one of his books.<br/><br/>Today, what is the probability that Master Chef Alan will cook the 4th dish from the 3rd book?
Correct — C. There are a total of 45 recipes, with each book containing 15 recipes. <br/><br/>Therefore, the probability of Master Chef Alan cooking the 4th dish from the 3rd book today is 1/45. <br/><br/>It is important to focus on the relevant information and not get distracted. <br/><br/>Additionally, all the recipes are unique and different from each other. -
GRE
<img src="asset:assets/questions/ebde6d3b131864ec.png"> <br/><br/>The figure shown consists of four straight lines and 24 individual angles. <br/><br/>What is the smallest number of angles that need to be explicitly measured in order for the measurements of all the angles in the figure to be determined?
Correct — C. <img src="asset:assets/questions/e905b7fa025ae472.png"><br/><br/>The way to proceed is to label one angle at a time as 'measured,' and then fill in the angles that you can calculate based on the angles already 'known.' In the diagram above, the first angle measured is marked with an arc, and the other angles that you can infer are marked with dots. The three inferred angles can be known because of the fact that two angles that make up a straight line add up to 180°, and also because vertical angles are equal to each other.<br/><br/><img src="asset:assets/questions/41efc8b3efa9a539.png"><br/><br/>The second diagram shows a second angle measured, and the angles that can be inferred. The 3 other angles at the intersection of the lines making up the measured angle are known for the same reason as before. The other four angles on the lower left are known because the three angles that make up a triangle add up to 180°.<br/><br/><img src="asset:assets/questions/818e41dd8e7c42d5.png"><br/><br/>In the third diagram, a third angle is measured, and the angles surrounding it (in the cluster labeled 1 on the diagram) are determined, as before. Then, the angles near the label 2 can be calculated, because three out of four of the angles in the quadrilateral at bottom right are already known. Finally, the angles marked in the cluster marked 3 can be deduced because now two of the three angles of the smallest triangle are known. Therefore, the minimum number of angle measurements required is 3. -
GRE
For which values of p is <tex>\sum_{n=1}^\infty \frac{1}{n^p}</tex> convergent?
Correct — C. We can solve this problem quite simply with the integral test. We know that if<br/><br/><tex>\int_1^{\infty} \frac{1}{x^p} dx</tex><br/><br/>converges, then our series converges.<br/><br/>We can rewrite the integral as<br/><br/><tex>\int x^{-p} dx</tex><br/><br/>and then use our formula for the antiderivative of power functions to get that the integral equals<br/><br/><tex>\frac{x^{1-p}}{1-p} \Big|_{x=1}^\infty</tex>.<br/><br/>We know that this only goes to zero if <tex>1-p \lt 0</tex>. Subtracting p from both sides, we get<br/><br/><tex>1 \lt p</tex>. -
GRE
What happens to the difference in the areas of the parallelogram and the rectangle with sides <em>a</em> and <em>b</em>, as <em>α</em> and <em>β</em> in the parallelogram approach 90º? <br/><br/><img src="asset:assets/questions/8981a00e39c1aff7.jpg">
Correct — A. As <em>α</em> and <em>β</em> in the parallelogram approach 90º, the values of <em>sin α</em> and <em>sin β</em> approach 1. The formula for the area of the parallelogram, therefore, approximately equals that of the rectangle, as shown here: Area of rectangle: A = <tex>a \cdot b</tex> Area of parallelogram: A = <tex>a \cdot b \cdot (approx.\;1)= approx.\;a \cdot b</tex> The difference continues to decrease as the angles become closer to 90º, until they become equal at 90º; at which point, parallelogram <em>STUV</em> would have actually become a rectangle (or parallelogram with right angles). (Remember that the formulas for the area of a rectangle and parallelogram are not the same.). -
GRE
A brick wall contains 52 bricks in its bottom row and 49 bricks in the next row up from the bottom row. Each subsequent row contains 3 fewer bricks than the row immediately below it. If the wall contains 16 rows, how many bricks total make up the wall?
Correct — E. We know the number of terms (16) and the first term (52) in this series, but to find the sum using the formula <tex>n/2(a_1+a_n)</tex>, we also need to know the final term <tex>(a_n)</tex>. Using the formula for a the last term of an arithmetic sequence <tex>(a_n = a_0+nd)</tex> with a common difference <tex>(d)</tex> of 3 and a zeroth term of 55 (3 greater than the first term) gives <tex>a_n = 55-3(16)</tex>, or <tex>a_n = 7</tex>. We can now use the sum formula: replacing n with 16, <tex>a_1</tex> with 52, and a_n with 7, the sum equals <tex>16/2 (52 + 7)</tex>, which simplifies to 472.
GRE sample questions
Tap any question below to reveal the answer and a plain-English explanation.
Verbal Reasoning The sudden, vehement objections of the senator understandably ________ the other members of his party, considering that he had previously expressed few qualms about the proposed amendment. [ Note: Select 2 answer choices ]
A. enervated
B. bewitched
C. disenfranchised
D. truncated
E. addled ✓
Correct — E. The sentence is about a change in the senator's opinion about the 'proposed amendment.' Previously, he did not express any 'qualms' (doubts, misgivings), but then he made sudden, vehement objections. The word in the blank describes the reaction of the other party members upon the senator's objections. Their reaction is not positive; hence a negative word is required for the blank. Words such as 'upset' or 'stunned' are good fill-ins for the blank. Now, let's examine the meanings of the words in the options: bewitched – to be affected by witchcraft or magic; enchanted or delighted disenfranchised – deprived of the right to vote discombobulated – confused and disconcerted truncated – shortened by cutting off the top or the end enervated – weakened, drained of energy addled – unable to think clearly, confused 'Discombobulated' and 'addled' match the meaning of the sentence. 'Bewitched' is a positive word and would go against the context. 'Disenfranchised' and 'truncated' are unrelated to the sentence. There is no information in the sentence to support the word 'enervated'.
Quantitative Reasoning What is ₈P₄ equal to?
A. 1,680 ✓
B. 1,600
C. 1,640
D. 1,580
Correct — A. ₙPk depicts the permutation of n total objects with k objects being arranged. Thus, ₈P₄ = n!/k!=8!/4! The upper factorial is the upper index, and the lower factorial is the difference of the indices. 8!/4! = (8× 7× 6× 5× 4× 3× 2× 1)/(4× 3× 2× 1) The 4! or 4\times3\times2\times1 will cancel out. 8\times7\times6\times5 = 56\times30 = 1,680
Verbal Reasoning The investigators made it clear that nothing they would unearth was ________; every misdeed they learned about would be revealed to the public.
A. cynical
B. exposed
C. sacrosanct ✓
D. contradictory
E. incredulous
Correct — C. In this restatement structure, the second part of the sentence confirms that everything will be revealed because nothing would be sacrosanct, or "inviolable or sacred." In other words, with choice C, there would be no secrets. Choice A does not fit the context since being incredulous means you are having trouble believing something. Choice B, exposed, doesn't make sense. The investigators would be saying that what they unearthed was exposed, which is a contradiction. The word cynical, choice D, makes no sense because there is no mention of anyone not believing the promise to expose crimes. There is no mention of any information that is contradictory, or at odds with what has been promised, so choice E should be ignored.
Quantitative Reasoning a + b + c+ d + e = 0 a × b × c × d × e ≠ 0 Quantity A: a² + b² + c² + d² + e² Quantity B: (a + b + c + d + e)³
A. The two quantities are equal.
B. Quantity B is greater.
C. The relationship cannot be determined from the information given.
D. Quantity A is greater. ✓
Correct — D. Don't let the many variables and exponents scare you. As you might expect with a problem that looks this complicated, there is a slick solution. First, note that since the product of the five variables does not equal zero, then none of the variables equals zero. Next, consider quantity B, which cubes the sum of all the variables. Since the sum of the variables is zero, its cube is also zero—that is, quantity B is zero. Quantity A adds the squares of all the variables. Since none of the variables is zero, the squares aren't zero, either—and, in fact, each of them is positive. As the sum of positive numbers, quantity A is also positive, and therefore greater than quantity B.
Verbal Reasoning In the 1950s, the profusion of goods, televisions, and other factors led to an explosion of ads. Alert to the captivating power of these images, pop artists set out to shock the world and redefine art. The paragon of this movement was Andy Warhol, who marketed mechanically reproduced images ranging from celebrities to soup cans. Outwardly he cultivated a passive, cool, eccentric detachment; in reality, he was a workaholic perfectionist who spent long hours making his work appear effortless. His intention was easily achieved—many did not understand his vision and thought it required no effort. "Anyone can paint a soup can and call it art," some said. But not just "anyone" did; only Warhol, whose sensibility epitomized the notion that the essence of art lies in its conception, did. Warhol passed another artistic litmus test by encapsulating in tangible form the tenor of his times, a mechanical age of mass production and mass consumption. Despite the hype and myth-making that continually infused his enterprise, Warhol earned the title of artist. Which of the following, if true, most seriously undermines the argument?
A. The images Warhol co-opted had already demonstrated their visually mesmerizing effect on audiences.
B. Other pop artists produced art that can be considered as good as or greater than Warhol's art.
C. In later years, Warhol often only conceptualized the art; assistants carried out the real work of making it.
D. Warhol actually saw little or no artistic relevance in the images he transformed into Pop Art. ✓
E. Warhol became the darling of the art world by virtue of his carefully cultivated image as well as through his art.
Correct — D. Because the passage as a whole is about how Warhol did see artistic relevance in his subject matter, as it was emblematic of the world of mass production and mass consumption that he inhabited. Therefore, these objects had relevance and resonance. Choice A is incorrect because, while Warhol is referred to as the "paragon," or perfect example or model, of the Pop Art movement, there is nothing in the passage to suggest that his art was the best. And, even if others produced work just as good or greater, Warhol would not have been less of an artist. Choice B should be eliminated because the passage suggests that the conceptualization of art is its essence; therefore, merely conceptualizing the art, instead of carrying it out to the last detail, is still the primary work of the artist. Choice C is incorrect because it actually strengthens, through restatement, a premise of the argument, which is that Warhol saw the relevance in everyday objects that had already demonstrated their power to captivate audiences. Choice E is incorrect because it has little relevance to the conclusion that Warhol earned, or deserved, the title of artist; instead of focusing on the essence of Warhol's art, choice E focuses on his popularity.
Quantitative Reasoning A business has made the decision to renew the surface of a specific section within their warehouse. This section happens to be a perfect square, with each side measuring 15 feet. What is the total area that requires resurfacing?
A. 30 square feet
B. 215 square feet
C. 225 square feet ✓
D. 250 square feet
E. 60 square feet
Correct — C. 15 x 15 is 225 square feet. Key Takeaway: Squaring numbers that end in 5 becomes easier with this trick. To square any number that ends in 5, use this trick: Take the first digit of the number, in this case 1, and multiply it by itself and the next consecutive digit, which is 2. So, 1 x (1+1) = 1 x 2 = 2. Then, simply append 25 to the end, resulting in 225. This trick is effective for squaring any number that ends in 5.
Verbal Reasoning Unseen Characters by Will Floyd Many plays, films, and television shows use the storytelling device of the unseen character. As the name implies, this trope involves a character the audience never directly encounters, but instead only hears about through the words of other characters. A common assumption is that a character that never speaks or is visible to the viewers of a play or film would only be a minor element, left to be the butt of jokes or as a simple way to add depth to a major character. In fact, unseen characters are frequently quite important, and further the plot because of their absence. The most notable instance of such a character is Godot, in Samuel Beckett’s play Waiting for Godot (1953). The two main characters in the play, Vladimir and Estragon, sit patiently by a tree, expecting Godot to come by at any moment. Three other characters, Lucky, Pozzo, and a boy, all speak to Vladimir and Estragon, with Godot never alighting on the stage. Nonetheless, Godot’s machinations in making the men wait—along with his supposed intentions—drive the play’s narrative. Godot, never seen or heard from directly, becomes the largest force in the created world of the play. This use of an unseen character creates an added mystery and increases the tension between the two main characters. Beckett uses the unseen character not as a gimmick or cheap ploy, but instead as the central focus of his play. The author would NOT agree with the statement that ________.
A. unseen characters are well represented by Godot in Waiting for Godot
B. unseen characters can be more than cheap ploys
C. unseen characters can effectively be used by a good writer
D. unseen characters can advance a plot quite well despite not being seen
E. unseen characters are worthless literary devices ✓
Correct — E. The author quite clearly views unseen characters as being effective literary devices when used well. This means that the description of unseen characters which is negative will be the correct answer. The description of them as "useless literary devices" is the best choice among the answers.
Quantitative Reasoning What is a potential value for 'y' after the points of intersection for the equations: y= -x² + 3 and y= x²- 5?
A. 4
B. √2
C. 3/2
D. -1 ✓
E. √8
Correct — D. To find the distance between two points, we need to equate the two equations, determine the points of intersection, and apply the distance between points formula. By equating the two equations, we obtain: x = 2 and x = -2, which correspond to y = 7 and y = -1, respectively. Hence, we select option -1 as the correct answer.
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