Verbal Reasoning

You have 40 minutes for this section.

Read each passage and answer the corresponding questions. 10 questions will follow each of the 4 passages, for a total of 40 questions. Choose your answer based on the evidence given in the passage; no outside knowledge is required.

The final two questions in each passage will be analogy questions. Use your knowledge of the passage and the relationships demonstrated within it to arrive at your answer and complete each analogy.

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This passage is adapted from Anne Brontë's Agnes Grey, first published in 1847.

I spare my readers the account of my delight on coming home, my happiness while there, and my sorrow on being obliged to bid them, once more, a long adieu.

I returned, however, with unabated vigor to my work—a more arduous task than anyone can imagine, who has not felt something like the misery of being charged with the care and direction of a set of mischievous, turbulent rebels, whom his utmost exertions cannot bind to their duty, while, at the same time, he is responsible for their conduct to a higher power, who exacts from him what cannot be achieved without the aid of the superior's more potent authority, which, either from indolence, or the fear of becoming unpopular with the said rebellious gang, the latter refuses to give. I can conceive few situations more harassing than that wherein, however you may long for success, however you may labor to fulfill your duty, your efforts are baffled and set at naught by those beneath you, and unjustly censured and misjudged by those above.

I have not enumerated half the vexatious propensities of my pupils, or half the troubles resulting from my heavy responsibilities, for fear of trespassing too much upon the reader's patience.

But I particularly remember one wild, snowy afternoon, soon after my return in January: the children had all come up from dinner, loudly declaring that they meant "to be naughty," and they had well kept their resolution, though I had talked myself hoarse, and wearied every muscle in my throat, in the vain attempt to reason them out of it. I had got Tom pinned up in a corner, whence, I told him, he should not escape till he had done his appointed task. Meantime, Fanny had possessed herself of my work-bag, and was rifling its contents—and spitting into it besides. I told her to let it alone, but to no purpose, of course.

"Burn it, Fanny!" cried Tom: and this command she hastened to obey. I sprang to snatch it from the fire, and Tom darted to the door. "Mary Ann, throw her desk out of the window!" cried he: and my precious desk, containing my letters and papers, my small amount of cash, and all my valuables, was about to be precipitated from the three-storey window. I flew to rescue it. Meanwhile Tom had left the room, and was rushing down the stairs, followed by Fanny. Having secured my desk, I ran to catch them, and Mary Ann came scampering after. All three escaped me, and ran out of the house into the garden, where they plunged about in the snow, shouting and screaming in exultant glee.

What must I do? If I followed them, I should probably be unable to capture one, and only drive them farther away. If I did not, how was I to get them in? While I stood in this perplexity, I heard a voice behind me, in harshly piercing tones, exclaiming—

"Miss Grey! Is it possible? What, in the devil's name, can you be thinking about?"

"I can't get them in, sir," said I, turning round, and beholding Mr. Bloomfield, with his hair on end, and his pale blue eyes bolting from their sockets.

"But I insist upon their being got in!" cried he.

"Then, sir, you must call them yourself, if you please, for they won't listen to me," I replied, stepping back.

  1. Based on the passage, the narrator feels that her job is
  2. The passage makes clear that one of the main difficulties of the narrator’s work is that she
  3. Which lines in the passage provide the best evidence in support of the answer to the previous question?
  4. In Paragraph 2, the “mischievous, turbulent rebels” the narrator mentions refer to her
  5. According to the passage, what is one method that the narrator used to try to control her charges?
  6. In Paragraph 3, Sentence 1, the phrase “vexatious propensities” most closely means
  7. The passage makes clear that Mr. Bloomfield is
  8. Which of the following best describes the movement of the passage?
  9. The following analogy refers to actions taking place in the passage.

    Mary Ann : desk ::

  10. obedient soldier : commanding general ::
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Scientific Thinker

This passage is adapted from Naureen Ghani's "Inside the Mind of an Octopus," first published in 2017 on PLOS Blogs.

Octopuses possess a rich behavioral repertoire and the largest nervous systems among invertebrates. Alongside squids and cuttlefish, octopuses are believed to have evolutionarily separated from humans more than 700 million years ago. Given that long divergence, we should be a very different species. And we are... in some ways.

Octopuses have striking morphological features such as camera-like eyes, an incredibly adaptive coloration system, and eight arms with more suckers than we have fingers or thumbs. And yet—they are like us. Even though octopus brains and vertebrate brains have no common anatomy, they both support similar features such as forms of short and long-term memory, versions of sleep, and the abilities to recognize individual people and explore objects through play.

In an octopus, the majority of neurons are in the arms themselves—nearly twice as many as in the central brain. Each arm has about 300 suckers and each sucker contains up to 10,000 neurons. Octopus suckers attach to surfaces as a local reflex. Since chemoreceptors line the sucker rim, the octopus can taste surfaces as it moves. There are also mechanoreceptors and proprioceptors present: the former provide information on touch and pressure, while the latter supply information about muscle activity.

When contact is detected, the sucker will automatically contract and attach. The mechanoreceptors trigger the reflex to keep what is there from getting away. The taste buds on the sucker rim then more slowly provide information on whether or not the object should be repulsed or retained. In this way, octopuses can ensure that a food item like a crab cannot scuttle away.

With such versatile suckers, octopuses have shown that smart can be spineless. Their arms can maneuver without input from the brain. Even an arm that is surgically removed can reach and grasp objects. How an octopus coordinates eight such arms in locomotion is still unknown.

Octopuses are indeed masters of distributed control. Hyper-redundancy is what makes octopuses so intriguing to researchers. There's redundancy in the sensors of the suckers, in the information processing in the brain, and in the structure of the body. The strong yet flexible hyper-redundant arms of the octopus endow it with high maneuverability but also place a great burden on its control system. It must interface incoming sensory information with the issuing of motor commands. Since the octopus arm does not have fixed joints or fixed linkages, it has infinite degrees of freedom. In other words, each arm has virtually unlimited ways to achieve the same goal with no constraints.

It is undoubtedly difficult to build a soft robot with the mechanical properties of an octopus arm. Arriving at that degree of soft manipulator form and the complexity of an octopus is dually challenging. The Grasso lab at Brooklyn College, run by psychology professor Frank Grasso, studies octopus motion instead by creating simulations in silica of what an appendage or sucker would be like. The first step is to look to biology to characterize movement. The next step is to build a model that captures what biology is doing. To do so, the Grasso lab uses neural networks inspired by octopus neuroanatomy. There are sensory inputs, motor outputs, and interneurons that model what the nervous system should do. In other words, the neural networks connect sensing in the world to outputs of the world.

"We're testing how the structure of the nervous system and the information that flows through it realizes behavior input," he says.

Table 1: Total Neurons in Various Species

Table information adapted from Table and passage used under Creative Commons license. (

  1. The passage primarily suggests that octopuses have
  2. Which paragraph in the passage provides the best evidence in support of the answer to the previous question?
  3. The passage and figure offer statistics about all of the following EXCEPT
  4. According to the passage, both octopus brains and vertebrate brains can
  5. In Paragraph 2, Sentence 3, the phrase “common anatomy” most closely means
  6. Based on the passage, which of the following may octopuses struggle to do because of their unique body design?
  7. According to the passage, the Grasso lab’s task is especially
  8. Which of the following conclusions can be drawn based on the information in Table 1?
  9. octopus brain : vertebrate brain ::
  10. mechanoreceptors : proprioceptors ::
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This passage is adapted from John Paul II's On the Christian Meaning of Human Suffering, first published in 1984.

Even though in its subjective dimension, suffering seems almost inexpressible and not transferable, perhaps at the same time nothing else requires as much as does suffering, in its "objective reality," to be dealt with, meditated upon, and conceived as an explicit problem. Therefore, it also requires that basic questions be asked about it and the answers sought.

Medicine, as the science and also the art of healing, discovers in the vast field of human sufferings the best-known area, the one identified with greater precision and relatively more counterbalanced by the methods of "reaction" (that is, the methods of therapy). Nonetheless, this is only one area. The field of human suffering is much wider, more varied, and multi-dimensional. Man suffers in different ways, ways not always considered by medicine, not even in its most advanced specializations.

Suffering is something which is still wider than sickness, more complex, and at the same time still more deeply rooted in humanity itself. A certain idea of this problem comes to us from the distinction between physical suffering and moral suffering. This distinction is based upon the double dimension of the human being and indicates the bodily and spiritual element as the immediate or direct subject of suffering. Insofar as the words "suffering" and "pain" can, up to a certain degree, be used as synonyms, physical suffering is present when "the body is hurting" in some way, whereas moral suffering is "pain of the soul." In fact, it is a question of pain of a spiritual nature, and not only of the "psychological" dimension of pain, that accompanies both moral and physical suffering. The vastness and the many forms of moral suffering are certainly no less in number than the forms of physical suffering. But at the same time, moral suffering seems as it were less identified and less reachable by therapy.

It can be said that man suffers whenever he experiences any kind of evil. Suffering expresses a situation in which man experiences evil and in doing so becomes the subject of suffering. Even when man brings suffering on himself, when he is its cause, this suffering remains something passive in its metaphysical essence.

This does not, however, mean that suffering in the psychological sense is not marked by a specific "activity." This is, in fact, that multiple and subjectively differentiated "activity" of pain, sadness, disappointment, discouragement or even despair, according to the intensity of the suffering subject and his or her specific sensitivity. In the midst of what constitutes the psychological form of suffering there is always an experience of evil, which causes the individual to suffer.

Thus the reality of suffering prompts the question about the essence of evil: what is evil? This question seems, in a certain sense, inseparable from the theme of suffering. Man suffers on account of evil, which is a certain lack, limitation, or distortion of good. We could say that man suffers because of a good in which he does not share, from which in a certain sense he is cut off, or of which he has deprived himself. He particularly suffers when he ought—in the normal order of things—to have a share in this good and does not have it.

  1. The passage addresses all of the following EXCEPT
  2. The passage most strongly suggests that medicine is
  3. Which lines in the passage provide the best evidence in support of the answer to the previous question?
  4. In the passage, the author emphasizes that suffering stems from
  5. In Paragraph 5, Sentence 3, the word “constitutes” most closely means
  6. According to the passage, what are two categories of suffering?
  7. According to the passage, evil is
  8. In the final paragraph, the author
  9. sickness : suffering ::
  10. physical suffering : body ::

Historical/Founding Documents

Passage 1 is adapted from Aristotle's A Treatise on Government, written around the 4th century BC and translated here by William Ellis, A.M.

Passage 2 is adapted from Benjamin Franklin's "On luxury, idleness, and industry," first published in 1806.
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Passage 1

Nature requires that we should not only be properly employed, but to be able to enjoy leisure honorably: for this (to repeat what I have already said) is of all things the principal.

But, though both labor and rest are necessary, yet the latter is preferable to the first, and by all means we ought to learn what we should do when at rest. For we ought not to employ that time at play, for then play would be the necessary business of our lives. But if this cannot be, play is more necessary for those who labor than those who are at rest, for he who labors requires relaxation, which play will supply. For as labor is attended with pain and continued exertion, it is necessary that play should be introduced, under proper regulations, as a medicine.

Now rest itself seems to partake of pleasure, of happiness, and an agreeable life: but this cannot be theirs who labor, but theirs who are at rest; for he who labors, labors for the sake of some end which he has not: but happiness is an end which all persons think is attended with pleasure and not with pain.

It is evident that to live a life of rest there are some things which a man must learn and be instructed in, and that the object of this learning and this instruction centers in their acquisition. But the learning and instruction which is given for labor has for its object other things, for which reason the ancients made music a part of education, not as a thing necessary, for it is not of that nature, nor as a thing useful, as reading, in the common course of life, or for managing of a family, or for learning anything as useful in public life.

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Passage 2

It has been computed by some political arithmetician, that if every man and woman would work for four hours each day on something useful, that labor would produce sufficient to procure all the necessaries and comforts of life, want and misery would be banished out of the world, and the rest of the twenty-four hours might be leisure and pleasure.

What creates, then, so much want and misery? It is the employment of men and women in works that produce neither the necessaries nor conveniences of life, who, with those who do nothing, consume necessaries raised by the laborious.

To explain this: The first elements of wealth are obtained by labor from the earth and waters. I have land, and raise corn. With this, if I feed a family that does nothing, my corn will be consumed, and at the end of the year I shall be no richer than I was at the beginning. But if, while I feed them, I employ them, some in spinning, others in making bricks for building, the value of my corn will be arrested and remain with me, and at the end of the year we may all be better clothed and better lodged.

Almost all the parts of our bodies require some expense. The feet demand shoes, the legs stockings, the rest of the body clothing, and the belly a good deal of victuals. Our eyes, though exceedingly useful, ask, when reasonable, only the cheap assistance of spectacles, which could not much impair our finances. But the eyes of other people are the eyes that ruin us. If all but myself were blind, I should want neither fine clothes, fine houses, nor fine furniture.

  1. Passage 1 is primarily
  2. In Paragraph 3 of Passage 1, the phrase “is attended with” most closely means
  3. According to Passage 1, what is one similarity between a life of labor and a life of rest?
  4. The author of Passage 2 would likely agree that which of the following situations would lead to the most wealth and leisure over time?
  5. The author of Passage 2 suggests that which of the following is responsible for some of the want in the world?
  6. Which lines in Passage 2 provide the best evidence in support of the answer to the previous question?
  7. Both the authors of Passage 1 and Passage 2 touch on
  8. Both authors view leisure
  9. labor : exertion ::
  10. labor : comforts of life ::
Next Up - Grammar/Writing!


You have 35 minutes for this section.

Read each of the 4 passages in this section and answer the corresponding questions (40 total). Each question will ask you to either correct an error or suggest an improvement in the passage. If no change is necessary, select the option "NO CHANGE."

Note: Most questions correspond to a numbered portion of the passage. In these questions, answer choices represent alternatives that could be substituted for the numbered portion. Select the best answer choice out of the given options.


This passage is adapted from Adam Smith's An Inquiry into the Nature and Causes of the Wealth of Nations, first published in 1776.

When the division of labor has been [41] thorough once established, it is but a very small part of a man's wants which the produce of his own labor can supply. He supplies the far greater part of them by exchanging that surplus part of the produce [42] of his farmlands, which is over and above his own consumption, for such parts of the produce of other men's labor as he has occasion for. Every man thus lives by exchanging or becomes, in some measure, a merchant, and the society itself grows to be what is properly a commercial society.

But when the division of labor first began to take place, this power of exchanging must frequently [43] has been very much clogged and embarrassed in its operations. One man, we shall suppose, has more of a certain commodity than he himself has occasion for, while another has less. The former, consequently, would be glad to dispose of, and the latter to purchase, a part of this [44] supposition.

But if this latter should chance to have nothing that the former stands in need [45] of, no exchange can be made between them. The butcher has more meat in his shop than he himself can consume, and the brewer and the baker would each of them be willing to purchase a part of it. But they have nothing to offer in exchange, except the different productions of their respective trades, and the butcher is already provided with all the bread and beer which he has immediate occasion for. No exchange can, in this case, be made between them. [46] He cannot be their merchant, and they cannot be his customers, and so as a result they are, altogether, less serviceable from one to the other, considered as a whole.

In order to avoid the inconvenience of such situations, every prudent man in every period of [47] society, after the first establishment of the division of labor must naturally have endeavored to have at all times by him, besides the peculiar produce of his own industry, a certain quantity of some one commodity or other, such as he imagined few people would be likely to refuse in exchange for the produce of their industry. [48] Plenty of stuff was probably used for this purpose. In the rude ages of society, cattle are said to have been the common instrument of commerce; and, though they must have been a most inconvenient one, yet, in old times, we find things were frequently valued according to the number of cattle which had been given in exchange for them. The armor of Diomedes, says Homer, cost only nine oxen, but that of Glaucus cost a hundred oxen.

In all countries, [49] therefore, men seem at last to have been determined by irresistible reasons to give the preference, for this employment, to metals above every other commodity. Metals can not only be kept with as little loss as any other commodity, scarcely any thing being less perishable than they are, but they can likewise, without any loss, be divided into any number of parts, as by fusion those parts can easily be reunited again. This is a quality that no other equally durable commodities possess and that, more than any other quality, renders them fit [50] and being the instruments of commerce and circulation.

  1. thorough once
  2. Which of the following phrases best completes the phrase in the sentence below?

    He supplies the far greater part of them by exchanging that surplus part of the produce [42] of his farmlands, which is over and above his own consumption, for such parts of the produce of other men's labor as he has occasion for.

  3. has been
  4. supposition
  5. of
  6. He cannot be their merchant, and they cannot be his customers, and so as a result they are, altogether, less serviceable from one to the other, considered as a whole.
  7. society, after the first establishment of the division of labor must
  8. Plenty of stuff was probably used for this purpose.
  9. therefore
  10. and being

Historical Profile

This passage is adapted from Friedrich Nietzsche's The Case of Wagner, translated by Anthony M. Ludovici and first published in 1911.

Yesterday I heard Bizet's masterpiece for the twentieth time. Once more I attended with the same gentle [51] reverence once again I did not run away. This triumph over my impatience surprises me. How such a work completes one! Through it one almost becomes a "masterpiece" oneself. And, as a matter of fact, each time I heard Carmen it [52] will seem to me that I was more of a philosopher, a better philosopher than at other times.

To sit for five hours: the first step to holiness! [53] Can I just say that Bizet's tunes are the only ones I can basically stand? That other orchestration which is all the rage at present—the Wagnerian—is [54] brutal artificial and "unsophisticated." Hence its appeal to all the three senses of the modern soul at once. How terribly Wagnerian orchestration affects me! I call it the Sirocco. A disagreeable sweat breaks out all over me. All my fine weather vanishes.

Bizet's music seems to me perfect. It comes forward lightly, gracefully, stylishly. [55] It is lovable; and it does not sweat. This music is wicked, refined, fatalistic, and thus remains popular. It possesses the refinement of a people, not of an individual. It is rich. It is definite. It builds, organizes, completes, and in this sense it stands as a contrast to the polypus in music, to "endless melody." Have more painful, more tragic accents ever been heard on the stage before? And how are they obtained? Without grimaces! Without counterfeiting of any kind! Free from the lie of the grand style! [56] On the other side of the coin: this music assumes that the listener is intelligent even as a musician. [57] Thereby it is the opposite of Wagner, who, apart from everything else, was the most ill-mannered genius on earth. Wagner repeats a thing so often that we become desperate, and ultimately believe it.

I become a better man, a better musician, a better listener when Bizet speaks to me. Is it in any way possible to listen better? I even burrow behind this music with my ears. I hear its very cause. I seem to assist at its birth. I tremble before the dangers which this daring music runs. [58] I attend the orchestra show once a week, regardless of the featured composer.

And, strange to say, at bottom I do not give it a thought, or am not aware how much thought I really do give it. For quite other ideas are running through my head the while. Has anyone ever observed that music [59] eradicates the spirit? It gives wings to thought, and the more one becomes a musician the more one is also a philosopher. The grey sky of abstraction seems thrilled by flashes of lightning. The light is strong enough to reveal all the details of things, to enable one to grapple with problems, and the world is surveyed as if from a mountain top.

With this I have defined philosophical pathos, and unexpectedly answers drop into my lap, a small hailstorm of ice and wisdom, of problems solved. Bizet makes me productive. Everything that is good makes me productive. I have gratitude [60] beyond nothing else, nor have I any other touchstone for testing what is good.

  1. reverence once
  2. will seem
  3. Can I just say that Bizet's tunes are the only ones I can basically stand?
  4. brutal artificial and “unsophisticated.”
  5. It is lovable; and it does not sweat.
  6. On the other side of the coin
  7. Thereby it is the opposite of Wagner, who, apart from everything else, was the most ill-mannered genius on earth.
  8. I attend the orchestra show once a week, regardless of the featured composer.
  9. eradicates
  10. beyond

Natural Science

This passage is adapted from Avicenna's The Physics of the Healing, first published in 1027 and translated here by Jon McGinnis. Text copyright 2009 by Brigham Young University Press.

From the part of The Healing where we concisely presented the science of demonstration, you have already learned that some sciences are universal and some are [61] earthly, and that some are related to others. So now what you need to learn is that the science we are engaged in explaining is physics, which is a particular science in relation to what comes later.

Since you have learned that each science [62] have a subject matter, the subject matter of physics is the sensible body insofar as it is subject to change. What is investigated is the necessary accidents belonging to the body subject to change as such—that is, the accidents that are termed essential—and also the attendant features that attach to the body, inasmuch as it is, whether [63] forms accidents or derivatives of the two.

Now, these bodies are considered natural things and so, too, is whatever is accidental to them. All of them are called natural in relation to that power called nature. [64] Some of them are subjects, for it, some of them effects, motions, and dispositions proceeding from nature. If, as was explained in the science of demonstration, natural things have principles, reasons, and causes without which the science of physics could not be attained, then the only way to acquire [65] generic knowledge of those things possessing principles is simple. First, one must know their principles and, from their principles, to know them, for this is the way to teach and learn that gives us access to the authentic knowledge of things that possess principles.

[66] Also, if natural things do possess certain principles, then either each and every one of them has those principles, or they do not hold any principles in common. In the latter case, it would not be unlikely that the science of physics establishes the existence of those principles and at the same time [67] identify their essence. If these natural things do share certain first principles in common?namely, those that are undoubtedly principles of their shared subjects and states?then the proof of these principles will not belong to the discipline of natural philosophers (as was shown in the part of The Healing dealing with the science of demonstrations), but to another science. The natural philosopher must simply accept their existence as a postulate and conceptualize their essence as [68] full real.

Moreover, natural things possess certain common principles and certain principles more specific to their group ([69] however, belonging to one of their genera, such as the principles of growth). Some principles are even more specific than these (for instance, within one species, the principles of humanity). In addition, they possess essential accidents common to them all all, common to their genus, or common to their species. Thus, the right course of intellectual teaching and learning consists in starting [70] for what is more common and proceeding to what is more specific.

  1. earthly
  2. have
  3. forms accidents or derivatives of the two.
  4. Some of them are subjects, for it, some of them effects, motions, and dispositions proceeding from nature.
  5. generic
  6. Also, if natural things do possess certain principles, then either each and every one of them has those principles, or they do not hold any principles in common.
  7. identify
  8. full
  9. however
  10. for

Modern/Influential Thinkers

This passage is adapted from Susan Rice's "Human Rights First Annual Summit Address," delivered on December 4, 2013, in Washington, D.C.

Sixty-five years ago this month, representatives to the United Nations General Assembly came together to adopt the Universal Declaration of Human Rights—a worldwide [71] reckoning that all members of our human family are born possessing certain equal and inalienable rights. These same rights are reflected in the founding documents of the [72] United States and, we cherish them as part of our national character.

[73] Therefore, as President Obama has said, just because some truths are self-evident doesn't mean they are self-executing. We have to work relentlessly to make them real. We must constantly question and challenge [74] themselves to be on the right side of history—to do our part so that more and more of our fellow human beings can enjoy the rights and freedoms that are the birthright of all mankind.

Our history is filled with champions who have fought to bring us closer to our ideals, from Dr. King and the thousands who marched on Washington fifty years ago to "Battling" Bella Abzug, from [75] the United States to the United Nations, and countless others. I know everyone in this room believes, as I do, that continuing their work at home and expanding it around the globe is our great commission as the inheritors of their legacy.

For me, the struggle for equal human rights is [76] deep personally. It's essential to who I am as an American. I can never forget that I am the daughter of proud citizens who suffered the indignities of Jim Crow. Nor can I forget that, in 1964, the year of my birth, in many parts of this great country, people who looked like me could not vote or marry someone who looks like my husband. The unfinished battle for equality and human dignity is not only what drives me as a public servant: it is my central duty as the mother of my two children to make sure they never [77] encountered any limitations on their dreams because of who they are or what they look like.

Make no [78] mistake; advancing democracy and respect for human rights is central to our foreign policy. It's what our history and our values demand, but it's also profoundly in our interests. That is why the United States remains firmly committed to promoting freedom, opportunity, and prosperity everywhere. We stand proudly for the rights of women, the LGBT community, and minorities. We defend the freedom for all people to worship as they choose, and we champion open government and civil society, freedom of assembly, and a free press.

[79] We sometimes face painful dilemmas as the immediate need to defend our national security clashes with our fundamental commitment to democracy and human rights, as we seek to secure these core interests. We make tough choices.

Still, over time, we know that our core interests are inseparable from our core values, [80] and that our avowal of dedication to democracy and the rights of Homo sapiens utterly buttresses the security of the nation. So, the fact is: American foreign policy must sometimes strike a difficult balance—not between our values and our interests, because these almost invariably converge with time, but more often between our short and long-term imperatives.

  1. reckoning
  2. United States and, we
  3. Therefore
  4. themselves
  5. the United States to the United Nations
  6. deep personally
  7. encountered
  8. mistake; advancing
  9. We sometimes face painful dilemmas as the immediate need to defend our national security clashes with our fundamental commitment to democracy and human rights, as we seek to secure these core interests.
  10. and that our avowal of dedication to democracy and the rights of Homo sapiens utterly buttresses the security of the nation.
Next Up - Quantitative Reasoning!

Quantitative Reasoning

You have 45 minutes for this section.

Answer each of the questions to your best ability (40 total).

You may not use a calculator for the math portion of this exam. Keep in mind that accompanying figures are NOT necessarily drawn to scale. You may use any of the following formulas to help you in your calculations.

  • Area of a circle = πr2, where r is the radius of the circle
  • Circumference of a circle = 2πr, where r is the radius of the circle
  • There are 360 degrees in a circle.
  • There are 2π radians in a circle.
  • Volume of a sphere = 43πr3, where r is the radius of the sphere
  • Surface area of a sphere = 4πr2, where r is the radius of the sphere
  • Area of a rectangle = length × width
  • Area of a triangle = 1 2 (base × height)
  • The sum of the measures of the interior angles of a triangle is 180°.
  • Pythagorean theorem (for a right triangle): If a, b, and c are the side lengths of the triangle, and c is the hypotenuse, then a2 + b2 = c2.
  • Trigonometry:
    • sin θ = opposite hypotenuse
    • cos θ = adjacent hypotenuse
    • tan θ = opposite adjacent
    • csc θ = 1 sin θ
    • sec θ = 1 cos θ
    • cot θ = 1 tan θ
    • tan θ = sin θ cos θ
    • sin2θ + cos2θ = 1
  1. What is the value of 3222?

  2. Triangle A is similar to Triangle B. If Triangle B has angles measuring 30° and 70°, which of the following is the measure of one of the angles of Triangle A?

  3. If a is an even positive integer, which of the following must be true?

  4. What is the area of a circle with a radius of 5 cm?

  5. Diego is a member of the football team and the basketball team at his school, but not a member of any other teams. Brian is a member of three teams at the same school, only one of which he shares with Diego. Which of the following must be true?

  6. Six circular game chips can fit inside each holding cylinder in a board game. If the game comes with seven cylinders, each filled halfway with chips, then how many game chips does it come with?

  7. Ms. Gutierrez asks her students to pick their favorite color. If four students pick blue, and she has twenty-four students in total, then what ratio of students in Ms. Gutierrez' class chose blue as their favorite color?

  8. Which of the following is the measure of Y in the isosceles triangle XYZ below?

  9. What is the x-intercept of y=2x8?

  10. The ratio of protons to neutrons in one atom of Element Z is 3: 4. If a cluster of atoms of Element Z contain 12 protons, how many neutrons are in that same cluster?

  11. A student studying triangles comes up with the following rule:

    The hypotenuse of a right triangle is always exactly two units longer than at least one leg of the right triangle.

    Which of the following is a counterexample that disproves the above statement?

  12. What is the slope of 3y6x=10?

  13. How many numbers between 1 and 80 (inclusive) meet both conditions below?

    Statement 1: The number has a factor of 4.
    Statement 2: The number is a multiple of 10.

  14. What is the area of triangle ABC below? (All units are in centimeters.)

  15. The line y=x+5 undergoes a transformation such that every point ab is now ab+3 on the resulting line. What is the equation of the line after the transformation?

  16. An online candle business open five days a week (Monday through Friday) sells fifteen candles a day its first week. If each week, it sells three more candles a day, how many candles IN TOTAL does that business sell in Week 5?

  17. The annual growth rate of Population Z, a colony of penguins in Antarctica, is given by the equation below, where P is percent growth within a certain number of years and Y is the number of years.

    Annual growth rate=PY

    If the population's annual growth rate over 5 years was 1.3, what was the percent growth within that time period?

  18. A food truck sells sandwiches, pizzas, and milkshakes only. If 25% of the truck's sales are from its milkshakes, and the truck sells an equal percentage of sandwiches as it does pizza, which of the following is true?

    1. A greater percentage of the food truck's sales come from its sandwiches than its milkshakes.
    2. 75% of people who order food from the truck do not order a milkshake.
    3. The sandwiches and pizza that the food truck sells are more expensive than its milkshakes.

  19. a3a24=?

  20. Which of the following could be the missing term in the series below?


  21. Jill's family is packing up all of their cylindrical glasses into boxes for their move. Each of the boxes they are using is 9 inches high, 12 inches long, and 7 inches wide. Each glass is 1.5 inches in radius and 8 inches high. If the family is packing all of the glasses upright in the boxes, how many glasses can they fit into each box?

  22. A triangle has side lengths that measure 6 inches, 8 inches, and 10 inches. What is the cosine of the smallest angle of the triangle?

  23. Planet Z has an atmosphere of 40% nitrogen, 25% oxygen, and 5% carbon dioxide. The rest of the atmosphere is made up of argon, methane, and another gas, Gas Q, that is not found on earth. Planet Z's atmosphere contains twice as much of Gas Q as it does of argon and methane combined. Which of the following is FALSE?

  24. How many points of intersection do the following equations have?


  25. If 3x+7<16, which of the following must be true?

  26. What is the surface area of a sphere whose largest cross section has an area that measures 16πunits2?

  27. Anja decides to track how long it takes her to get to school each day. After tracking her drive five times, Anja finds that it takes her an average of 27 minutes to get to school each day. The quickest Anja can get to school, if she encounters no traffic, is in 23 minutes. If on the first day, Anja drove to school in 31 minutes, what is the longest possible time it took Anja to drive to school during those five days?

  28. The amount of Pollutant A in a lake increases linearly over time, at a rate given by the equation below, where x is time in days and y is units of Pollutant A. Pollutant B, on the other hand, is decreasing at the same rate that Pollutant A is increasing. If on Day 0, there were 108 units of Pollutant B in the lake, which equation represents the amount of Pollutant B in the lake after x days?


  29. What are the solutions to the equation below?


  30. If ab=2a2+3b, what is 42?

  31. Which of the following is equivalent to 2tan2xcos2x?

  32. How many numbers between 20 and 70 (inclusive) meet both conditions below?

    Statement 1: The number is prime.
    Statement 2: The product of the digits is six.

  33. Which of the following is NOT an x-intercept of y=x34x221x?

  34. A line is tangent to the circle 25=x+12+y+42 at 40. What is the slope of that line?

  35. A builder is working on a new fence for a house. He needs to buy 123 cans of paint for every panel, of the type shown below. Each panel is surrounded on either side by a single post, with only one post between adjacent panels. The fence will cover three sides of the backyard, and each panel will connect except for the two end panels. Each side will contain 5 panels. How many cans of paint in total will the builder need to buy if each separate post requires 1 can of paint?

  36. A right triangle's hypotenuse is twice as many inches long as one of its legs. Which of the following must be true?

  37. Triangle DFG below is equilateral. JG is 6 inches. HD is one third the length of DF. What is the length of FH?

  38. Which of the following is equivalent to the expression below?


  39. If yz=x and 8z=xy, then what is x+y+z if y is half the value of z?

  40. Triangle MNP is similar to Triangle RQP, and MN and QR are parallel. If the sine of R is 22, then what is the measure of N?