Answer Explanations
SAT Practice Test #1®

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5KSA09

Answer Explanations

SAT Practice Test #1
Section 1: Reading Test
QUESTION 1.
Choice B is the best answer. In the passage, a young man (Akira) asks amother (Chie) for permission to marry her daughter (Naomi). The request
was certainly surprising to the mother, as can be seen from line 47, whichstates that prior to Akira’s question Chie “had no idea” the request was coming.
Choice A is incorrect because the passage depicts two characters engaged
in a civil conversation, with Chie being impressed with Akira’s “sincerity”
and finding herself “starting to like him.” Choice C is incorrect because
the passage is focused on the idea of Akira’s and Naomi’s present lives andpossible futures. Choice D is incorrect because the interactions between
Chie and Akira are polite, not critical; for example, Chie views Akira with“amusement,” not animosity.

QUESTION 2.
Choice B is the best answer. The passage centers on a night when a young

man tries to get approval to marry a woman’s daughter. The passage includes
detailed descriptions of setting (a “winter’s eve” and a “cold rain,” lines 5-6);
character (Akira’s “soft, refined” voice, line 33; Akira’s eyes “sh[ining] withsincerity,” line 35); and plot (“Naomi was silent. She stood a full half minutelooking straight into Chie’s eyes. Finally, she spoke,” lines 88-89).
Choice A is incorrect because the passage focuses on a nontraditional marriage proposal. Choice C is incorrect because the passage concludes without
resolution to the question of whether Akira and Naomi will receive permission to marry. Choice D is incorrect because the passage repeatedly makes
clear that for Chie, her encounter with Akira is momentous and unsettling,
as when Akira acknowledges in line 73 that he has “startled” her.

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QUESTION 3.
Choice C is the best answer. Akira “came directly, breaking all tradition,”(line 1) when he approached Chie and asked to marry her daughter, and he“ask[ed] directly,” without “a go-between” (line 65) or “mediation,” because
doing otherwise would have taken too much time.
Choices A, B, and D are incorrect because in these contexts, “directly” does
not mean in a frank, confident, or precise manner.

QUESTION 4.
Choice A is the best answer. Akira is very concerned Chie will find his mar-riage proposal inappropriate because he did not follow traditional protocol anduse a “go-between” (line 65). This is clear in lines 63-64, when Akira says toChie “Please don’t judge my candidacy by the unseemliness of this proposal.”
Choice B is incorrect because there is no evidence in the passage that Akira
worries that Chie will mistake his earnestness for immaturity. Choice C is incorrect because while Akira recognizes that his unscheduled visit is a nuisance, hislarger concern is that Chie will reject him due to the inappropriateness of his
proposal. Choice D is incorrect because there is no evidence in the passage that
Akira worries Chie will underestimate the sincerity of his emotions.

QUESTION 5.
Choice C is the best answer. In lines 63-64, Akira says to Chie, “Please

don’t judge my candidacy by the unseemliness of this proposal.” This reveals
Akira’s concern that Chie may say no to the proposal simply because Akira
did not follow traditional practices.
Choices A, B, and D do not provide the best evidence for the answer to theprevious question. Choice A is incorrect because line 33 merely describes
Akira’s voice as “soft, refined.” Choice B is incorrect because lines 49-51
reflect Chie’s perspective, not Akira’s. Choice D is incorrect because lines
71-72 indicate only that Akira was speaking in an eager and forthright matter.

QUESTION 6.
Choice D is the best answer because Akira clearly treats Chie with respect,

including “bow[ing]” (line 26) to her, calling her “Madame” (line 31), andlooking at her with “a deferential peek” (line 34). Akira does not offer Chieutter deference, though, as he asks to marry Naomi after he concedes that heis not following protocol and admits to being a “disruption” (line 31).
Choice A is incorrect because while Akira conveys respect to Chie, there isno evidence in the passage that he feels affection for her. Choice B is incorrect because neither objectivity nor impartiality accurately describes how
Akira addresses Chie. Choice C is incorrect because Akira conveys respect
to Chie and takes the conversation seriously.
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QUESTION 7.
Choice D is the best answer. The first paragraph (lines 1-4) reflects on how

Akira approached Chie to ask for her daughter’s hand in marriage. In theselines, the narrator is wondering whether Chie would have been more likely
to say yes to Akira’s proposal if Akira had followed tradition: “Akira came
directly, breaking all tradition. Was that it? Had he followed form—had heasked his mother to speak to his father to approach a go-between—would
Chie have been more receptive?” Thus, the main purpose of the first paragraph is to examine why Chie reacted a certain way to Akira’s proposal.
Choice A is incorrect because the first paragraph describes only one aspect ofJapanese culture (marriage proposals) but not the culture as a whole. Choice B
is incorrect because the first paragraph implies a criticism of Akira’s individual
marriage proposal but not the entire tradition of Japanese marriage proposals.
Choice C is incorrect because the narrator does not question a suggestion.

QUESTION 8.
Choice B is the best answer. In line 1, the narrator suggests that Akira’s

direct approach broke “all tradition.” The narrator then wonders if Akira had“followed form,” or the tradition expected of him, would Chie have been
more receptive to his proposal. In this context, following “form” thus means
following a certain tradition or custom.
Choices A, C, and D are incorrect because in this context “form” does notmean the way something looks (appearance), the way it is built (structure),or its essence (nature).

QUESTION 9.
Choice C is the best answer. Akira states that his unexpected meeting with

Chie occurred only because of a “matter of urgency,” which he explains as “anopportunity to go to America, as dentist for Seattle’s Japanese community”(lines 41-42). Akira decides to directly speak to Chie because Chie’s response
to his marriage proposal affects whether Akira accepts the job offer.
Choice A is incorrect because there is no evidence in the passage that Akira isworried his parents will not approve of Naomi. Choice B is incorrect because
Akira has “an understanding” with Naomi (line 63). Choice D is incorrect;
while Akira may know that Chie is unaware of his feelings for Naomi, this is
not what he is referring to when he mentions “a matter of urgency.”

QUESTION 10.
Choice B is the best answer. In lines 39-42, Akira clarifies that the “mat-ter of urgency” is that he has “an opportunity to go to America, as dentist
for Seattle’s Japanese community.” Akira needs Chie’s answer to his marriage
proposal so he can decide whether to accept the job in Seattle.
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Choices A, C, and D do not provide the best evidence for the answer to theprevious question. Choice A is incorrect because in line 39 Akira apologizes
for interrupting Chie’s quiet evening. Choice C is incorrect because lines
58-59 address the seriousness of Akira’s request, not its urgency. Choice D
is incorrect because line 73 shows only that Akira’s proposal has “startled”
Chie and does not explain why his request is time-sensitive.

QUESTION 11.
Choice A is the best answer. Lines 1-9 include examples of how many

people shop (“millions of shoppers”), how much money they spend (“over$30 billion at retail stores in the month of December alone”), and the manyoccasions that lead to shopping for gifts (“including weddings, birthdays,
anniversaries, graduations, and baby showers.”). Combined, these examples
show how frequently people in the US shop for gifts.
Choice B is incorrect because even though the authors mention that“$30 billion” had been spent in retail stores in one month, that figure isnever discussed as an increase (or a decrease). Choice C is incorrect becauselines 1-9 provide a context for the amount of shopping that occurs in the US,
but the anxiety (or “dread”) it might cause is not introduced until later in thepassage. Choice D is incorrect because lines 1-9 do more than highlight the
number of different occasions that lead to gift-giving.

QUESTION 12.
Choice B is the best answer. Lines 9-10 state “This frequent experienceof gift-giving can engender ambivalent feelings in gift-givers.” In the subsequent sentences, those “ambivalent” feelings are further exemplified asconflicted feelings, as shopping is said to be something that “[m]any relish”(lines 10-11) and “many dread” (line 14).
Choices A, C, and D are incorrect because in this context, “ambivalent” does
not mean feelings that are unrealistic, apprehensive, or supportive.

QUESTION 13.
Choice D is the best answer. In lines 10-13, the authors clearly state thatsome people believe gift-giving can help a relationship because it “offers apowerful means to build stronger bonds with one’s closest peers.”
Choice A is incorrect because even though the authors state that some
shoppers make their choices based on “egocentrism,” (line 33) there isno evidence in the passage that people view shopping as a form of selfexpression. Choice B is incorrect because the passage implies that shopping
is an expensive habit. Choice C is incorrect because the passage states thatmost people have purchased and received gifts, but it never implies that people are required to reciprocate the gift-giving process.
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QUESTION 14.
Choice A is the best answer. In lines 10-13, the authors suggest that people

value gift-giving because it may strengthen their relationships with others:“Many relish the opportunity to buy presents because gift-giving offers apowerful means to build stronger bonds with one’s closest peers.”
Choices B, C, and D do not provide the best evidence for the answer to theprevious question. Choice B is incorrect because lines 22-23 discuss how
people often buy gifts that the recipients would not purchase. Choice C isincorrect because lines 31-32 explain how gift-givers often fail to consider
the recipients’ preferences. Choice D is incorrect because lines 44-47 suggestthat the cost of a gift may not correlate to a recipient’s appreciation of it.

QUESTION 15.
Choice A is the best answer. The “deadweight loss” mentioned in the second

paragraph is the significant monetary difference between what a gift-giverwould pay for something and what a gift-recipient would pay for the same
item. That difference would be predictable to social psychologists, whose
research “has found that people often struggle to take account of others’
perspectives—their insights are subject to egocentrism, social projection,and multiple attribution errors” (lines 31-34).
Choices B, C, and D are all incorrect because lines 31-34 make clear thatsocial psychologists would expect a disconnect between gift-givers and giftrecipients, not that they would question it, be disturbed by it, or find it surprising or unprecedented.

QUESTION 16.
Choice C is the best answer. Lines 41-44 suggest that gift-givers assume

a correlation between the cost of a gift and how well-received it will be:“. . . gift-givers equate how much they spend with how much recipients willappreciate the gift (the more expensive the gift, the stronger a gift-recipient’s
feelings of appreciation).” However, the authors suggest this assumption may
be incorrect or “unfounded” (line 47), as gift-recipients “may not construe
smaller and larger gifts as representing smaller and larger signals of thoughtfulness and consideration” (lines 63-65).
Choices A, B, and D are all incorrect because the passage neither states
nor implies that the gift-givers’ assumption is insincere, unreasonable, or
substantiated.

QUESTION 17.
Choice C is the best answer. Lines 63-65 suggest that the assumption madeby gift-givers in lines 41-44 may be incorrect. The gift-givers assume thatrecipients will have a greater appreciation for costly gifts than for less costly
5gifts, but the authors suggest this relationship may be incorrect, as giftrecipients “may not construe smaller and larger gifts as representing smaller
and larger signals of thoughtfulness and consideration” (lines 63-65).
Choices A and D are incorrect because lines 53-55 and 75-78 address thequestion of “why” gift-givers make specific assumptions rather than addressing the validity of these assumptions. Choice B is incorrect because lines
55-60 focus on the reasons people give gifts to others.

QUESTION 18.
Choice D is the best answer. Lines 53-55 state that “Perhaps givers believethat bigger (i.e., more expensive) gifts convey stronger signals of thoughtfulness and consideration.” In this context, saying that more expensive gifts“convey” stronger signals means the gifts send, or communicate, stronger
signals to the recipients.

Choices A, B, and C are incorrect because in this context, to “convey” something does not mean to transport it (physically move something), counteract it (act in opposition to something), or exchange it (trade one thing
for another).

QUESTION 19.
Choice A is the best answer. The paragraph examines how gift-givers

believe expensive gifts are more thoughtful than less expensive gifts andwill be more valued by recipients. The work of Camerer and others offers
an explanation for the gift-givers’ reasoning: “gift-givers attempt to signal
their positive attitudes toward the intended recipient and their willingness toinvest resources in a future relationship” (lines 57-60).
Choices B, C, and D are incorrect because the theory articulated by Camerer
and others is used to explain an idea put forward by the authors (“givers
believe that bigger . . . gifts convey stronger signals”), not to introduce anargument, question a motive, or support a conclusion.

QUESTION 20.
Choice B is the best answer. The graph clearly shows that gift-givers believethat a “more valuable” gift will be more appreciated than a “less valuablegift.” According to the graph, gift-givers believe the monetary value of a gift
will determine whether that gift is well received or not.
Choice A is incorrect because the graph does not suggest that gift-givers areaware of gift-recipients’ appreciation levels. Choices C and D are incorrect
because neither the gift-givers’ desire for the gifts they purchase nor the giftgivers’ relationship with the gift-recipients is addressed in the graph.
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QUESTION 21.
Choice A is the best answer. Lines 69-75 explain that while people are often

both gift-givers and gift-receivers, they struggle to apply information theylearned as a gift-giver to a time when they were a gift-receiver: “Yet, despite theextensive experience that people have as both givers and receivers, they often
struggle to transfer information gained from one role (e.g., as a giver) andapply it in another, complementary role (e.g., as a receiver).” The authors suggest that the disconnect between how much appreciation a gift-giver thinks agift merits and how much appreciation a gift-recipient displays for the gift may
be caused by both individuals’ inability to comprehend the other’s perspective.
Choices B and C are incorrect because neither the passage nor the graphaddresses the idea that society has become more materialistic or that there isa growing opposition to gift-giving. Choice D is incorrect because the passage emphasizes that gift-givers and gift-recipients fail to understand eachother’s perspective, but it offers no evidence that the disconnect results only
from a failure to understand the other’s intentions.

QUESTION 22.
Choice B is the best answer. Lines 2-4 of the passage describe DNA as“a very long chain, the backbone of which consists of a regular alternation ofsugar and phosphate groups.” The backbone of DNA, in other words, is themain structure of a chain made up of repeating units of sugar and phosphate.
Choice A is incorrect because the passage describes DNA on the molecularlevel only and never mentions the spinal column of organisms. Choice C isincorrect because the passage describes the backbone of the molecule as
having “a regular alternation” of sugar and phosphate, not one or the other.
Choice D is incorrect because the nitrogenous bases are not the main structural unit of DNA; rather, they are attached only to the repeating units of sugar.

QUESTION 23.
Choice D is the best answer. The authors explain that hydrogen bonds join
together pairs of nitrogenous bases, and that these bases have a specificstructure that leads to the pairing: “One member of a pair must be a purine
and the other a pyrimidine in order to bridge between the two chains” (lines
27-29). Given the specific chemical properties of a nitrogenous base, itwould be inaccurate to call the process random.

Choice A is incorrect because lines 5-6 describe how nitrogenous bases
attach to sugar but not how those bases pair with one another. Choice B isincorrect because lines 9-10 do not contradict the student’s claim. Choice C
is incorrect because lines 23-25 describe how the two molecules’ chains arelinked, not what the specific pairing between nitrogenous bases is.
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QUESTION 24.
Choice D is the best answer. In lines 12-14 the authors state: “the first fea-

ture of our structure which is of biological interest is that it consists not of
one chain, but of two.”
Choices A and B are incorrect because lines 12-14 explicitly state that it is
the two chains of DNA that are of “biological interest,” not the chemical
formula of DNA, nor the common fiber axis those two chains are wrappedaround. Choice C is incorrect because, while the X-ray evidence did help
Watson and Crick to discover that DNA consists of two chains, it was notclaimed to be the feature of biological interest.

QUESTION 25.
Choice C is the best answer. In lines 12-14 the authors claim that DNA mol-ecules appear to be comprised of two chains, even though “it has often been
assumed . . . there would be only one” (lines 15-17). The authors support thisclaim with evidence compiled from an X-ray: “the density, taken with the X-ray
evidence, suggests very strongly that there are two [chains]” (lines 18-19).
Choices A, B, and D are incorrect because the authors mention density and
X-ray evidence to support a claim, not to establish that DNA carries genetic
information, present a hypothesis about the composition of a nucleotide, or
confirm a relationship between the density and chemical formula of DNA.

QUESTION 26.
Choice B is the best answer. The authors explain that “only certain pairs ofbases will fit into the structure” (lines 25-26) of the DNA molecule. Thesepairs must contain “a purine and the other a pyrimidine in order to bridge
between the two chains” (lines 27-29), which implies that any other pairing
would not “fit into the structure” of the DNA molecule. Therefore, a pairof purines would be larger than the required purine/pyrimidine pair andwould not fit into the structure of the DNA molecule.
Choice A is incorrect because this section is not discussing the distance
between a sugar and phosphate group. Choice C is incorrect because thepassage never makes clear the size of the pyrimidines or purines in relation
to each other, only in relation to the space needed to bond the chains of
the DNA molecule. Choice D is incorrect because the lines do not make animplication about the size of a pair of pyrimidines in relation to the size of apair consisting of a purine and a pyrimidine.

QUESTION 27.
Choice D is the best answer. The authors explain how the DNA molecule8contains a “precise sequence of bases” (lines 43-44), and that the authors canuse the order of bases on one chain to determine the order of bases on theother chain: “If the actual order of the bases on one of the pair of chains weregiven, one could write down the exact order of the bases on the other one,because of the specific pairing. Thus one chain is, as it were, the complement of the other, and it is this feature which suggests how the deoxyribonucleic acid molecule might duplicate itself ” (lines 45-51). The authors use
the words “exact,” “specific,” and “complement” in these lines to suggest thatthe base pairings along a DNA chain is understood and predictable, and may
explain how DNA “duplicate[s] itself ” (line 51).
Choice A is incorrect because the passage does not suggest that most nucleotide sequences are known. Choice B is incorrect because these lines are notdiscussing the random nature of the base sequence along one chain of DNA.
Choice C is incorrect because the authors are describing the bases attachedonly to the sugar, not to the sugar-phosphate backbone.

QUESTION 28.
Choice C is the best answer. Lines 6-7 state that “Two of the possible bases—
adenine and guanine—are purines,” and on the table the percentages of adenine and guanine in yeast DNA are listed as 31.3% and 18.7% respectively.

Choices A, B, and D are incorrect because they do not state the percentagesof both purines, adenine and guanine, in yeast DNA.

QUESTION 29.
Choice A is the best answer. The authors state: “We believe that the bases

will be present almost entirely in their most probable forms. If this is true,
the conditions for forming hydrogen bonds are more restrictive, and the only
pairs of bases possible are: adenine with thymine, and guanine with cytosine”(lines 31-35). The table shows that the pairs adenine/thymine and guanine/cytosine have notably similar percentages in DNA for all organisms listed.
Choice B is incorrect. Although the choice of “Yes” is correct, the explanation for that choice misrepresents the data in the table. Choices C and D areincorrect because the table does support the authors’ proposed pairing of
nitrogenous bases in DNA molecules.

QUESTION 30.
Choice A is the best answer because it gives the percentage of cytosine(17.3%) in sea urchin DNA and the percentage of guanine (17.7%) in sea
urchin DNA. Their near similar pairing supports the authors’ proposal thatpossible pairings of nitrogenous bases are “adenine with thymine, and guanine with cytosine” (line 35).
Choices B, C, and D do not provide the best evidence for the answer to theprevious question. Choice B (cytosine and thymine), Choice C (cytosine andadenine), and Choice D (guanine and adenine) are incorrect because theyshow pairings of nitrogenous bases that do not compose a similar percentage of the bases in sea urchin DNA.

9QUESTION 31.
Choice D is the best answer. The table clearly shows that the percentage of ade-nine in each organism’s DNA is different, ranging from 24.7% in E.coli to 33.2%
in the octopus. That such a variability would exist is predicted in lines 41-43,
which states that “in a long molecule many different permutations are possible.”
Choices A and B are incorrect because the table shows that the percentage ofadenine varies between 24.7% and 33.2% in different organisms. Choice C isincorrect because lines 36-38 state that adenine pairs with thymine but does
not mention the variability of the base composition of DNA.

QUESTION 32.
Choice B is the best answer. In this passage, Woolf asks women a series ofquestions. Woolf wants women to consider joining “the procession of educated men” (lines 56-57) by becoming members of the workforce. Woolfstresses that this issue is urgent, as women “have very little time in which toanswer [these questions]” (lines 48-49).

Choice A is incorrect because Woolf argues against the tradition of only
“the sons of educated men” (lines 82-83) joining the workforce. Choice C isincorrect because Woolf is not highlighting the severity of social divisions
as much as she is explaining how those divisions might be reduced (withwomen joining the workforce). Choice D is incorrect because Woolf does
not question the feasibility of changing the workforce dynamic.

QUESTION 33.
Choice A is the best answer. Throughout the passage, Woolf advocates formore women to engage with existing institutions by joining the workforce:“We too can leave the house, can mount those steps [to an office], pass inand out of those doors, . . . make money, administer justice . . .” (lines 30-32).
Woolf tells educated women that they are at a “moment of transition” (line 51)
where they must consider their future role in the workforce.
Choice B is incorrect because even though Woolf mentions women’s traditional roles (lines 68-69: “while they stirred the pot, while they rocked thecradle”), she does not suggest that women will have to give up these traditionalroles to gain positions of influence. Choice C is incorrect because though
Woolf wonders how “the procession of the sons of educated men” impacts
women’s roles, she does not argue that this male-dominated society has had
grave and continuing effects. Choice D is incorrect because while Woolf suggests educated women can hold positions currently held by men, she does notsuggest that women’s entry into positions of power will change those positions.

QUESTION 34.
Choice C is the best answer. Woolf uses the word “we” to refer to herself
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and educated women in English society, the “daughters of educated men”

(line 64). Woolf wants these women to consider participating in a changing workforce: “For there, trapesing along at the tail end of the procession[to and from work], we go ourselves” (lines 23-24). In using the word “we”
throughout the passage, Woolf establishes a sense of solidarity among educated women.
Choice A is incorrect because Woolf does not use “we” to reflect on whether
people in a group are friendly to one another; she is concerned with generating solidarity among women. Choice B is incorrect because though Woolf
admits women have predominantly “done their thinking” within traditional
female roles (lines 64-69), she does not use “we” to advocate for more candor among women. Choice D is incorrect because Woolf does not use “we”
to emphasize a need for people in a group to respect one other; rather, shewants to establish a sense of solidarity among women.

QUESTION 35.
Choice B is the best answer. Woolf argues that the “bridge over the River

Thames, [has] an admirable vantage ground for us to make a survey” (lines 1-3).
The phrase “make a survey” means to carefully examine an event or activity.
Woolf wants educated women to “fix [their] eyes upon the procession—theprocession of the sons of educated men” (lines 9-11) walking to work.
Choice A is incorrect because while Woolf states the bridge “is a place tostand on by the hour dreaming,” she states that she is using the bridge “toconsider the facts” (lines 6-9). Woolf is not using the bridge for fanciful
reflection; she is analyzing “the procession of the sons of educated men”
(lines 10-11). Choice C is incorrect because Woolf does not compare thebridge to historic episodes. Choice D is incorrect because Woolf does notsuggest that the bridge is a symbol of a male-dominated past, but rather thatit serves as a good place to watch men proceed to work.

QUESTION 36.
Choice D is the best answer. Woolf writes that the men who conduct theaffairs of the nation (lines 15-17: “ascending those pulpits, preaching, teaching, administering justice, practising medicine, transacting business, making money”) are the same men who go to and from work in a “procession”(line 10). Woolf notes that women are joining this procession, an act thatsuggests the workforce has become less exclusionary: “For there, trapesing
along at the tail end of the procession, we go ourselves” (lines 23-24).
Choice A is incorrect because the procession is described as “a solemn sightalways” (lines 17-18), which indicates that it has always been influential.
Choice B is incorrect because the passage does not indicate that this procession has become a celebrated feature of English life. Choice C is incorrect
because the passage states only that the procession is made up of “the sons ofeducated men” (lines 10-11).

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QUESTION 37.
Choice C is the best answer, as lines 23-24 suggest that the workforce has

become less exclusionary. In these lines Woolf describes how women are
joining the male-dominated procession that travels to and from the work
place: “For there, trapesing along at the tail end of the procession, we goourselves.”
Choices A, B, and D are incorrect because they do not provide the best evidence for the answer to the previous question. Choice A is incorrect becauselines 12-17 describe the positions predominantly held by men. Choice B isincorrect because lines 17-19 use a metaphor to describe how the procession physically looks. Choice D is incorrect because lines 30-34 hypothesize
about future jobs for women.

QUESTION 38.
Choice C is the best answer. Woolf characterizes the questions she asks inlines 53-57 as significant (“so important that they may well change the livesof all men and women for ever,” lines 52-53) and urgent (“we have very little
time in which to answer them,” lines 48-49). Therefore, Woolf considers thequestions posed in lines 53-57 as both momentous (significant) and pressing (urgent).
Choice A is incorrect because Woolf characterizes the questions as urgent
and important, not as something that would cause controversy or fear.
Choice B is incorrect because though Woolf considers the questions to beweighty (or “important”), she implies that they can be answered. Choice D
is incorrect because Woolf does not imply that the questions are mysterious.

QUESTION 39.
Choice B is the best answer. The answer to the previous question shows

how Woolf characterizes the questions posed in lines 53-57 as momentous
and pressing. In lines 48-49, Woolf describes these questions as “important,”
or momentous, and states that women “have very little time in which toanswer them,” which shows their urgency.
Choices A, C, and D do not provide the best evidence for the answer to theprevious question. Choices A and D are incorrect because lines 46-47 andline 62 suggest that women need to think about these questions and not offer
trivial objections to them. Choice C is incorrect because line 57 characterizes only the need for urgency and does not mention the significance of thequestions.

QUESTION 40.
Choice C is the best answer. Woolf writes that women “have thought”

while performing traditional roles such as cooking and caring for children
12(lines 67-69). Woolf argues that this “thought” has shifted women’s roles insociety and earned them a “brand-new sixpence” that they need to learn how
to “spend” (lines 70-71). The “sixpence” mentioned in these lines is not a literalcoin. Woolf is using the “sixpence” as a metaphor, as she is suggesting womentake advantage of the opportunity to join the male-dominated workforce.
Choices A, B, and D are incorrect because in this context, “sixpence” does
not refer to tolerance, knowledge, or perspective.

QUESTION 41.
Choice B is the best answer. In lines 72-76, Woolf repeats the phrase “letus think” to emphasize how important it is for women to critically reflect on
their role in society. Woolf states this reflection can occur at any time: “Letus think in offices; in omnibuses; while we are standing in the crowd watching Coronations and Lord Mayor’s Shows; let us think . . . in the gallery of
the House of Commons; in the Law Courts; let us think at baptisms andmarriages and funerals.”
Choices A, C, and D are incorrect because in lines 72-76 Woolf is not emphasizing the novelty of the challenge faced by women, the complexity of socialand political issues, or the enjoyable aspect of women’s career possibilities.

QUESTION 42.
Choice B is the best answer. The author of Passage 1 identifies specificcompanies such as the “Planetary Resources of Washington,” “Deep Space
Industries of Virginia,” and “Golden Spike of Colorado” to support his earlier assertion that there are many interested groups “working to make spacemining a reality” (line 8).

Choices A, C, and D are incorrect because the author of Passage 1 does not
mention these companies to profile the technological advances in spacemining, the profit margins from space mining, or the diverse approaches tospace mining.

QUESTION 43.
Choice A is the best answer. The author of Passage 1 explicitly states thatone benefit to space mining is access to precious metals and earth elements:“within a few decades, [space mining] may be meeting earthly demands for
precious metals, such as platinum and gold, and the rare earth elements vitalfor personal electronics, such as yttrium and lanthanum” (lines 18-22).
Choice B is incorrect because Passage 1 does not suggest that precious metals extracted from space may make metals more valuable on Earth. Choice C
and Choice D are incorrect because Passage 1 never mentions how spacemining could create unanticipated technological innovations or change scientists’ understanding of space resources.
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QUESTION 44.
Choice A is the best answer. Lines 18-22 suggest that space mining mayhelp meet “earthly demands for precious metals . . . and the rare earth elements vital for personal electronics.” In this statement, the author is stating materials (“metals,” “earth elements”) that may be gathered as a result of
space mining, and that these materials may be important to Earth’s economy.
Choices B, C, and D do not provide the best evidence for the answer tothe previous question. Choice B is incorrect because lines 24-28 focus onan “off-planet economy” but never address positive effects of space mining.
Choice C is incorrect because lines 29-30 suggest the relative value of water
found in space. Choice D is incorrect because lines 41-44 state that spacemining companies hope to find specific resources in lunar soil and asteroids
but do not address how these resources are important to Earth’s economy.

QUESTION 45.
Choice D is the best answer. The author suggests in lines 19-22 that spacemining may meet “earthly demands for precious metals, such as platinum
and gold, and the rare earth elements vital for personal electronics.” In thissentence, “earthly demands” suggests that people want, or desire, these precious metals and rare earth elements.
Choices A, B, and C are incorrect because in this context “demands” does
not mean offers, claims, or inquiries.

QUESTION 46.
Choice C is the best answer. Lines 29-30 introduce the idea that watermined in space may be very valuable: “water mined from other worlds could
become the most desired commodity.” Lines 35-40 support this assertion bysuggesting how mined space water could be used “for drinking or as a radiation shield” (lines 36-37) or to make “spacecraft fuel” (line 38).
Choice A is incorrect because the comparison in the previous paragraph (therelative value of gold and water to someone in the desert) is not expanded
upon in lines 35-40. Choice B is incorrect because the question asked in theprevious paragraph is also answered in that paragraph. Choice D is incorrect
because no specific proposals are made in the previous paragraph; rather, anassertion is made and a question is posed.

QUESTION 47.
Choice B is the best answer. The author of Passage 2 recognizes thatspace mining may prove beneficial to humanity, stating that “we all standto gain: the mineral bounty and spin-off technologies could enrich us all”
(lines 50-52). The author also repeatedly mentions that space mining should
be carefully considered before it is implemented: “But before the miners
14

start firing up their rockets, we should pause for thought” (lines 53-54); “But[space mining’s] consequences—both here on Earth and in space—meritcareful consideration” (lines 57-59).
Choice A is incorrect because the author of Passage 2 concedes that “spacemining seems to sidestep most environmental concerns” (lines 55-56) but
does not imply that space mining will recklessly harm the environment,
either on Earth or in space. Choice C is incorrect because the author of
Passage 2 does not address any key resources that may be disappearing on
Earth. Choice D is incorrect because the author of Passage 2 admits that
“resources that are valuable in orbit and beyond may be very different tothose we prize on Earth” (lines 74-76) but does not mention any disagreement about the commercial viabilities of space mining discoveries.

QUESTION 48.
Choice A is the best answer. In lines 60-66, the author presents some environmental arguments against space mining: “[space] is not ours to despoil”
and we should not “[glut] ourselves on space’s riches.” The author then suggests that these environmental arguments will be hard to “hold,” or maintain,
when faced with the possible monetary rewards of space mining: “History
suggests that those will be hard lines to hold . . .” (line 68).

Choices B, C, and D are incorrect because in this context, “hold” does notmean grip, restrain, or withstand.

QUESTION 49.
Choice D is the best answer. The author of Passage 1 is excited about thepossibilities of space mining and how it can yield valuable materials, suchas metals and elements (lines 19-20 and lines 41-42), water ice (line 35),and space dirt (line 44). The author of Passage 2, on the other hand, recognizes the possible benefits of space mining but also states that space mining
should be thoughtfully considered before being implemented. Therefore, theauthor of Passage 2 expresses some concerns about a concept discussed in
Passage 1.
Choice A is incorrect because the author of Passage 2 does not refute thecentral claim of Passage 1; both authors agree there are possible benefits tospace mining. Choice B is incorrect because the author of Passage 1 does
not describe space mining in more general terms than does the author of
Passage 2. Choice C is incorrect because the author of Passage 2 is not suggesting that the space mining proposals stated in Passage 1 are impractical.

QUESTION 50.
Choice B is the best answer. In lines 18-28, the author of Passage 1 describes

many of the possible economic benefits of space mining, including the15

building of “an off-planet economy” (line 25). The author of Passage 2 warns
that there may be ramifications to implementing space mining and building
an “emerging off-world economy” (line 73) without regulation: “But miners
have much to gain from a broad agreement on the for-profit exploitation of
space. Without consensus, claims will be disputed, investments risky, andthe gains made insecure” (lines 83-87).
Choices A, C, and D are incorrect because the author of Passage 2 does
not suggest that the benefits to space mining mentioned in lines 18-28 of
Passage 1 are unsustainable, unachievable, or will negatively affect Earth’s
economy. Rather, the author recognizes the benefits of space mining but
advocates for the development of regulation procedures.

QUESTION 51.
Choice D is the best answer. In lines 85-87, the author of Passage 2 statesthat the future of space mining will prove difficult without regulations
because “claims will be disputed, investments risky, and the gains madeinsecure.”
Choices A, B, and C are incorrect because they do not provide the best evidence for the answer to the previous question. Choice A is incorrect becauselines 60-63 present some environmental concerns toward space mining.
Choice B is incorrect because lines 74-76 focus on how space mining may
discover valuable resources that are different from the ones found on Earth.
Choice C is incorrect because lines 81-83 simply describe one person’s
objections to the regulation of the space mining industry.

QUESTION 52.
Choice A is the best answer because both Passage 1 and Passage 2 indicate a belief that the resources most valued in space may differ from thosemost valued on our planet. Passage 2 says this explicitly in lines 74-76: “Theresources that are valuable in orbit and beyond may be very different tothose we prize on Earth.” Meanwhile Passage 1 suggests that water minedfrom space may be more valuable than metals or other earth elements whencreating an “off-plant economy” (lines 25-30).

Choice B is incorrect because neither passage discusses, either implicitly or
explicitly, the need for space mining to be inexpensive. Choice C is incorrect because Passage 2 does not specifically identify precious metals or rareearth elements but instead focuses on theoretical problems with space mining. Choice D is incorrect because diminishing resources on Earth is notdiscussed in Passage 2.

16

Section 2: Writing and Language Test
QUESTION 1.
Choice D is the best answer because “outweigh” is the only choice thatappropriately reflects the relationship the sentence sets up between “advantages” and “drawbacks.”
Choices A, B, and C are incorrect because each implies a competitive relationship that is inappropriate in this context.

QUESTION 2.
Choice B is the best answer because it offers a second action that farmers

can undertake to address the problem of acid whey disposal, thus supporting the claim made in the previous sentence (“To address the problem ofdisposal, farmers have found a number of uses for acid whey”).
Choices A, C, and D are incorrect because they do not offer examples of how
farmers could make use of acid whey.

QUESTION 3.
Choice A is the best answer because it results in a sentence that is grammatically correct and coherent. In choice A, “waterways,” the correct pluralform of “waterway,” conveys the idea that acid whey could impact multiple
bodies of water. Additionally, the compound verb “can pollute” suggests thatacid whey presents an ongoing, potential problem.

Choices B and D are incorrect because both use the possessive form of“waterway.” Choice C is incorrect because it creates an unnecessary shift inverb tense. The present tense verb “can pollute” should be used instead, as it
is consistent with the other verbs in the paragraph.

QUESTION 4.
Choice C is the best answer because it utilizes proper punctuation for items

listed in a series. In this case those items are nouns: “Yogurt manufacturers,
food scientists, and government officials.”
Choices A and B are incorrect because both fail to recognize that the items
are a part of a series. Since a comma is used after “manufacturers,” a semicolon or colon should not be used after “scientists.” Choice D is incorrect
because the comma after “and” is unnecessary and deviates from grammatical conventions for presenting items in a series.

QUESTION 5.
Choice C is the best answer because sentence 5 logically links sentence 2,

which explains why Greek yogurt production yields large amounts of acid17

whey, and sentence 3, which mentions the need to dispose of acid whey
properly.
Choices A, B, and D are incorrect because each would result in an illogicalprogression of sentences for this paragraph. If sentence 5 were left where it isor placed after sentence 3, it would appear illogically after the discussion of“the problem of disposal.” If sentence 5 were placed after sentence 1, it would
illogically discuss “acid-whey runoff ” before the mention of acid whey being“difficult to dispose of.”

QUESTION 6.
Choice D is the best answer because the paragraph includes several benefits of consuming Greek yogurt, particularly in regard to nutrition and satisfying hunger, to support the sentence’s claim that the conservation efforts
are “well worth the effort.” This transition echoes the passage’s earlier claimthat “the advantages of Greek yogurt outweigh the potential drawbacks of its
production.”

Choices A, B, and C are incorrect because they inaccurately describe thesentence in question.

QUESTION 7.
Choice B is the best answer because it provides a grammatically standard

preposition that connects the verb “serves” and noun “digestive aid” andaccurately depicts their relationship.
Choice A is incorrect because the infinitive form “to be” yields a grammatically incorrect verb construction: “serves to be.” Choices C and D are incorrect because both present options that deviate from standard English usage.

QUESTION 8.
Choice C is the best answer because it presents a verb tense that is consistentin the context of the sentence. The choice is also free of the redundant “it.”Choice A is incorrect because the subject “it” creates a redundancy. Choices
B and D are incorrect because they present verb tenses that are inconsistentin the context of the sentence.

QUESTION 9.
Choice A is the best answer because it properly introduces an additional

health benefit in a series of sentences that list health benefits. “Also” is thelogical and coherent choice to communicate an addition.
Choices B, C, and D are incorrect because none of the transitions they offer
logically fits the content that precedes or follows the proposed choice.
18

QUESTION 10.
Choice A is the best answer because “satiated” is the only choice that com-municates effectively that Greek yogurt will satisfy hunger for a longer
period of time.
Choices B, C, and D are incorrect because each is improper usage in this context. A person can be “fulfilled” spiritually or in other ways, but a person who
has eaten until he or she is no longer hungry cannot be described as fulfilled.
Neither can he or she be described as being “complacent” or “sufficient.”

QUESTION 11.
Choice B is the best answer because it provides a syntactically coherent andgrammatically correct sentence.
Choices A and C are incorrect because the adverbial conjunctions “therefore” and “so,” respectively, are unnecessary following “Because.” Choice D isincorrect because it results in a grammatically incomplete sentence (the partof the sentence before the colon must be an independent clause).

QUESTION 12.
Choice B is the best answer because the graph clearly indicates that, on March 5,

average low temperatures are at their lowest point: 12 degrees Fahrenheit.
Choice A is incorrect because the phrase “as low as” suggests that the temperature falls no lower than 20 degrees Fahrenheit, but the chart shows thatin January, February, and March, the temperature frequently falls below thatpoint. Choices C and D are incorrect because the information each provides
is inconsistent with the information on the chart.

QUESTION 13.
Choice A is the best answer because it concisely combines the two sen-tences while maintaining the original meaning.
Choices B, C, and D are incorrect because each is unnecessarily wordy, thus
undermining one purpose of combining two sentences: to make the phrasing more concise.

QUESTION 14.
Choice B is the best answer because it provides a conjunctive adverb that

accurately represents the relationship between the two sentences. “However”
signals an exception to a case stated in the preceding sentence.
Choices A, C, and D are incorrect because each provides a transition that
does not accurately represent the relationship between the two sentences,
and as a result each compromises the logical coherence of these sentences.
19

QUESTION 15.
Choice C is the best answer because it provides commas to offset the non-restrictive modifying clause “an associate professor of geology at Ohio State.”
Choices A, B, and D are incorrect because each provides punctuation that
does not adequately separate the nonrestrictive modifying clause about
Jason Box from the main clause.

QUESTION 16.
Choice C is the best answer because the colon signals that the other factor

that contributed to the early thaw is about to be provided.
Choice A is incorrect because it results in a sentence that deviates fromgrammatical standards: a semicolon should be used to separate two independent clauses, but in choice A the second clause only has a subject, nota verb. Choice B is incorrect because it is unnecessarily wordy. Choice D isincorrect because “being” is unnecessary and creates an incoherent clause.

QUESTION 17.
Choice C is the best answer because it provides the correct preposition(“of ”) and relative pronoun (“which”) that together create a dependent
clause following the comma.
Choices A, B, and D are incorrect because each results in a comma splice.
Two independent clauses cannot be joined with only a comma.

QUESTION 18.
Choice A is the best answer because the verb tense is consistent with thepreceding past tense verbs in the sentence, specifically “produced” and“drifted.”
Choices B, C, and D are incorrect because each utilizes a verb tense that is
not consistent with the preceding past tense verbs in the sentence.

QUESTION 19.
Choice D is the best answer because “their” is the possessive form of a plural noun. In this case, the noun is plural: “snow and ice.”

Choices A and B are incorrect because the possessive pronoun must referto a plural noun, “snow and ice,” rather than a singular noun. Choice C isincorrect because “there” would result in an incoherent sentence.

QUESTION 20.
Choice D is the best answer. The preceding sentences in the paragraph haveestablished that a darker surface of soot-covered snow leads to more melting
20

because this darker surface absorbs heat, whereas a whiter surface, free of soot,would deflect heat. As the passage points out, exposed land and water are also
dark and cannot deflect heat the way ice and snow can. Only choice D reflects
the self-reinforcing cycle that the preceding sentences already imply.
Choices A, B, and C are incorrect because the information each provides
fails to support the previous claim that the “result” of the soot “is a selfreinforcing cycle.”

QUESTION 21.
Choice B is the best answer because it is free of redundancies.

Choices A, C, and D are incorrect because each of the three presents a
redundancy: Choice A uses “repeat” and “again”; Choice C uses “damage”
and “harmful effects”; and Choice D uses “may” and “possibly.”

QUESTION 22.
Choice D is the best answer because sentence 5 describes the information

Box seeks: “to determine just how much the soot is contributing to the melting of the ice sheet.” Unless sentence 4 comes after sentence 5, readers will
not know what the phrase “this crucial information” in sentence 4 refers to.
Choices A, B, and C are incorrect because each results in an illogical sentence progression. None of the sentences that would precede sentence 4 provides details that could be referred to as “this crucial information.”

QUESTION 23.
Choice D is the best answer because it is free of redundancies and offers thecorrect form of the verb “wear” in this context.
Choices A, B, and C are incorrect because all three contain a redundancy.
Considering that “quickly” is a fixed part of the sentence, choice A’s “soon”
and choice B and C’s “promptly” all result in redundancies. Choices A and B
are also incorrect because each uses an incorrect form of the verb.

QUESTION 24.
Choice D is the best answer because it is the only choice that provides agrammatically standard and coherent sentence. The participial phrase“Having become frustrated. . .” functions as an adjective modifying “I,” thewriter.
Choices A, B, and C are incorrect because each results in a dangling modifier. The participial phrase “Having become frustrated . . .” does not referto choice A’s “no colleagues,” choice B’s “colleagues,” or choice C’s “ideas.”
As such, all three choices yield incoherent and grammatically incorrectsentences.
21

QUESTION 25.
Choice B is the best answer because it provides the correct preposition inthis context, “about.”
Choices A, C, and D are incorrect because each provides a preposition thatdeviates from correct usage. One might read an article “about” coworking
spaces but not an article “into,” “upon,” or “for” coworking spaces.

QUESTION 26.
Choice A is the best answer because it provides the correct punctuation forthe dependent clause that begins with the phrase “such as.”Choices B, C, and D are incorrect because each presents punctuation thatdeviates from the standard way of punctuating the phrase “such as.” When“such as” is a part of a nonrestrictive clause, as it is here, only one comma isneeded to separate it from the main independent clause.

QUESTION 27.
Choice B is the best answer because it provides a transitional phrase, “In

addition to equipment,” that accurately represents the relationship between
the two sentences connected by the transitional phrase. Together, the sentences describe the key features of coworking spaces, focusing on what the
spaces offer (equipment and meeting rooms).
Choices A, C, and D are incorrect because each provides a transition that
does not accurately represent the relationship between the two sentences.

QUESTION 28.
Choice C is the best answer because the sentence is a distraction from theparagraph’s focus. Nothing in the paragraph suggests that the cost of setting
up a coworking business is relevant here.
Choices A and D are incorrect because neither accurately represents theinformation in the paragraph. Choice B is incorrect because it does notaccurately represent the information in the next paragraph.

QUESTION 29.
Choice B is the best answer because it logically follows the writer’s preceding statement about creativity and accurately represents the information in
the graph.

Choices A, C, and D are incorrect because they present inaccurate andunsupported interpretations of the information in the graph. In addition,none of these choices provides directly relevant support for the main topic
of the paragraph.
22

QUESTION 30.
Choice D is the best answer because it provides a relative pronoun and verb

that create a standard and coherent sentence. The relative pronoun “who”
refers to the subject “the people,” and the plural verb “use” corresponds
grammatically with the plural noun “people.”
Choices A and B are incorrect because “whom” is the relative pronoun used
to represent an object. The noun “people” is a subject performing an action(using the coworking space). Choices B and C are also incorrect because
they display a form of the verb “to use” that does not correspond to the plural noun “people.”

QUESTION 31.
Choice C is the best answer because the proposed sentence offers a neces-sary and logical transition between sentence 2, which introduces the facility
the writer chose, and sentence 3, which tells what happened at the facility“Throughout the morning.”
Choices A, B, and D are incorrect because each would result in an illogicalprogression of sentences.

QUESTION 32.
Choice A is the best answer because the punctuation it provides results ina grammatically standard and coherent sentence. When an independent
clause is followed by a list, a colon is used to link the two.

Choice B is incorrect because the punctuation creates a fragment (a semicolon should be used to link two independent clauses). Choice C is incorrect because its use of the comma creates a series in which “several of mycoworking colleagues” are distinguished from the “website developer” andothers, although the logic of the sentence would suggest that they are thesame. Choice D is incorrect because it lacks the punctuation necessary tolink the independent clause and the list.

QUESTION 33.
Choice A is the best answer because it provides a phrase that is consistent

with standard English usage and also maintains the tone and style of thepassage.
Choice B is incorrect because “give some wisdom” deviates from standard English usage and presents a somewhat colloquial phrase in a textthat is generally free of colloquialisms. Choices C and D are incorrect
because both are inconsistent with the tone of the passage as well as its
purpose. The focus of the paragraph is on sharing, not on proclaiming
opinions.
23

QUESTION 34.
Choice A is the best answer because it offers a phrase that introduces a basic

definition of philosophy and thereby fits the sentence.
Choices B, C, and D are incorrect because each offers a transition that does
not suit the purpose of the sentence.

QUESTION 35.
Choice A is the best answer because it offers the most succinct comparison

between the basic definition of philosophy and the fact that students cangain specific, practical skills from the study of philosophy. There is no needto include the participle “speaking” in this sentence, as it is clear from context that the writer is offering a different perspective.
Choices B, C, and D are incorrect because they provide options that are
unnecessarily wordy.

QUESTION 36.
Choice B is the best answer because it provides a verb that creates a grammatically complete, standard, and coherent sentence.

Choices A, C, and D are incorrect because each results in a grammatically
incomplete and incoherent sentence.

QUESTION 37.
Choice D is the best answer because it most effectively sets up the informa-tion in the following sentences, which state that (according to informationfrom the 1990s) “only 18 percent of American colleges required at least one
philosophy course,” and “more than 400 independent philosophy departments were eliminated” from colleges. These details are most logically linked
to the claim that “colleges have not always supported the study of philosophy.”
Choices A, B, and C are incorrect because none of these effectively sets up
the information that follows, which is about colleges’ failure to support the
study of philosophy.

QUESTION 38.
Choice C is the best answer because it provides a transition that logicallyconnects the information in the previous sentence to the information in thisone. Both sentences provide evidence of colleges’ lack of support of philosophy programs, so the adverb “Moreover,” which means “In addition,” accurately captures the relationship between the two sentences.
Choices A, B, and D are incorrect because each presents a transition that
does not accurately depict or support the relationship between the two sentences. The second sentence is not a result of the first (“Therefore,” “Thus”),
and the sentences do not provide a contrast (“However”).
24

QUESTION 39.
Choice A is the best answer because it succinctly expresses the idea that“students who major in philosophy often do better . . . as measured by standardized test scores.”
Choices B and D are incorrect because they introduce a redundancy anda vague term, “results.” The first part of the sentence mentions a researchfinding or conclusion but does not directly address any “results,” so it isconfusing to refer to “these results” and indicate that they “can be” or “aremeasured by standardized test scores.” The best way to express the idea issimply to say that some students “often do better” than some other students“in both verbal reasoning and analytical writing as measured by standardized test scores.” Choice C is incorrect because there is no indication thatmultiple criteria are used to evaluate students’ “verbal reasoning and analytical writing”: test scores and something else. Only test scores are mentioned.

QUESTION 40.
Choice B is the best answer because it provides subject-verb agreement andthus creates a grammatically correct and coherent sentence.
Choice A is incorrect because the verb “has scored” does not correspondwith the plural subject “students.” Similarly, Choice C is incorrect because
the verb “scores” would correspond with a singular subject, but not the plural subject present in this sentence. Choice D is incorrect because it results
in a grammatically incomplete and incoherent sentence.

QUESTION 41.
Choice B is the best answer because it provides a coherent and grammati-

cally standard sentence.
Choices A and D are incorrect because both present “students” in the possessive form, whereas the sentence establishes “students” as the subject(“many students . . . have”). Choice C is incorrect because the verb form it
proposes results in an incomplete and incoherent sentence.

QUESTION 42.
Choice C is the best answer because it accurately depicts how inserting thissentence would affect the overall paragraph. The fact that Plato used the dialogue form has little relevance to the preceding claim about the usefulness ofa philosophy background.
Choices A and B are incorrect because the proposed sentence interrupts the
progression of reasoning in the paragraph. Choice D is incorrect because, aswith Choice A, Plato’s works have nothing to do with “the employability ofphilosophy majors.”
25

QUESTION 43.
Choice D is the best answer because it creates a complete and coherent

sentence.
Choices A, B, and C are incorrect because each inserts an unnecessary relative pronoun or conjunction, resulting in a sentence without a main verb.

QUESTION 44.
Choice D is the best answer because it provides a possessive pronoun that is

consistent with the sentence’s plural subject “students,” thus creating a grammatically sound sentence.
Choices A, B, and C are incorrect because each proposes a possessive pronoun that is inconsistent with the plural noun “students,” the establishedsubject of the sentence.

Section 3: Math Test — No Calculator
QUESTION 1.
Choice D is correct. Since k = 3, one can substitute 3 for k in the equa-

1 = k, which gives _1 = 3. Multiplying both sides of _1 =3tion _​ x − ​​ x − ​​ x − ​
3
3
3
by 3 gives x − 1 = 9 and then adding 1 to both sides of x − 1 = 9 gives x = 10.
Choices A, B, and C are incorrect because the result of subtracting 1 fromthe value and dividing by 3 is not the given value of k, which is 3.

QUESTION 2.
Choice A is correct. To calculate (7 + 3i) + (−8 + 9i), add the real parts ofeach complex number, 7 + (−8) = −1, and then add the imaginary parts,
3i + 9i = 12i. The result is −1 + 12i.
Choices B, C, and D are incorrect and likely result from common errors thatarise when adding complex numbers. For example, choice B is the result of
adding 3i and −9i, and choice C is the result of adding 7 and 8.

QUESTION 3.
Choice C is correct. The total number of messages sent by Armand

is the 5 hours he spent texting multiplied by his rate of texting:m texts/hour × 5 hours = 5m texts. Similarly, the total number of messages
sent by Tyrone is the 4 hours he spent texting multiplied by his rate of texting: p texts/hour × 4 hours = 4p texts. The total number of messages sent
by Armand and Tyrone is the sum of the total number of messages sent by
Armand and the total number of messages sent by Tyrone: 5m + 4p.
26

Choice A is incorrect and arises from adding the coefficients and multiplying
the variables of 5m and 4p. Choice B is incorrect and is the result of multiplying 5m and 4p. The total number of messages sent by Armand and Tyrone
should be the sum of 5m and 4p, not the product of these terms. Choice D isincorrect because it multiplies Armand’s number of hours spent texting by
Tyrone’s rate of texting, and vice versa. This mix-up results in an expressionthat does not equal the total number of messages sent by Armand and Tyrone.

QUESTION 4.
Choice B is correct. The value 108 in the equation is the value of P in

P = 108 − 23 d when d = 0. When d = 0, Kathy has worked 0 days that week.
In other words, 108 is the number of phones left before Kathy has started
work for the week. Therefore, the meaning of the value 108 in the equationis that Kathy starts each week with 108 phones to fix because she has worked
0 days and has 108 phones left to fix.
Choice A is incorrect because Kathy will complete the repairs when P = 0.
108
Since P = 108 − 23d, this will occur when 0 = 108 − 23d or when d = ​ _ ​,23
not when d = 108. Therefore, the value 108 in the equation does not represent the number of days it will take Kathy to complete the repairs. Choices C
and D are incorrect because the number 23 in P = 108 − 23P = 108 indicatesthat the number of phones left will decrease by 23 for each increase in thevalue of d by 1; in other words, that Kathy is repairing phones at a rate of
23 per day, not 108 per hour (choice C) or 108 per day (choice D).

QUESTION 5.
Choice C is correct. Only like terms, with the same variables and exponents,

can be combined to determine the answer as shown here:(x2y − 3y2 + 5xy2) − (−x2y + 3xy2 − 3y2)
= (x2y − (−x2y)) + (−3y2 − (−3y2)) + (5xy2 − 3xy2)= 2x2y + 0 + 2xy2
= 2x2y + 2xy2
Choices A, B, and D are incorrect and are the result of common calculation
errors or of incorrectly combining like and unlike terms.

QUESTION 6.
Choice A is correct. In the equation h = 3a + 28.6, if a, the age of theboy, increases by 1, then h becomes h = 3(a + 1) + 28.6 = 3a + 3 + 28.6 =(3a + 28.6) + 3. Therefore, the model estimates that the boy’s height increases
by 3 inches each year.
Alternatively: The height, h, is a linear function of the age, a, of the boy. The
coefficient 3 can be interpreted as the rate of change of the function; in this27

case, the rate of change can be described as a change of 3 inches in height forevery additional year in age.
Choices B, C, and D are incorrect and are likely to result from common
errors in calculating the value of h or in calculating the difference between
the values of h for different values of a.

QUESTION 7.
Choice B is correct. Since the right-hand side of the equation is P times the

(

)(

)

r
r N
​​ ​ _ ​  ​ ​ 1 + ​ _ ​  ​​ ​
1,200
1,200
, multiplying both sides of the equation by
expression
r N​​ 1 + ​ _ ​  ​​ ​ − 1
r N
1,200
​​ 1 + ​ _ ​  ​​ ​− 1
1,200
m = P.
the reciprocal of this expression results inrr N​ ​ _ ​  ​ ​ 1 + ​ _ ​  ​​ ​
1,200
1,200

(

)

(

(

)(

)

)

Choices A, C, and D are incorrect and are likely the result of conceptual orcomputation errors while trying to solve for P.

QUESTION 8.
b 1
a
Choice C is correct. Since ​ _​= 2, it follows that ​ _​ = ​ _ ​. Multiplying both sides
b

(a) a

b 4b
of the equation by 4 gives 4 ​ ​ _​  ​ = ​ _​= 2.

a

2

4b
a
_
Choice A is incorrect because if ​ _a ​= 0, then ​ b ​ would be undefined.
4ba_
Choice B is incorrect because if ​ _a ​= 1, then ​ b ​= 4. Choice D is incorrecta4bbecause if _​  a ​= 4, then ​ _​= 1.
b

QUESTION 9.
Choice B is correct. Adding x and 19 to both sides of 2y − x = −19

gives x = 2y + 19. Then, substituting 2y + 19 for x in 3x + 4y = −23 gives
3(2y + 19) + 4y = −23. This last equation is equivalent to 10y + 57 = −23.
Solving 10y + 57 = −23 gives y = −8. Finally, substituting −8 for y in
2y − x = −19 gives 2(−8) − x = −19, or x = 3. Therefore, the solution (x, y) to
the given system of equations is (3, −8).
Choices A, C, and D are incorrect because when the given values of x and y
are substituted in 2y − x = −19, the value of the left side of the equation does
not equal −19.

QUESTION 10.
Choice A is correct. Since g is an even function, g(−4) = g(4) = 8.

28

Alternatively: First find the value of a, and then find g(−4). Since g(4) = 8,
substituting 4 for x and 8 for g(x) gives 8 = a(4)2 + 24 = 16a + 24. Solving thislast equation gives a = −1. Thus g(x) = −x2 + 24, from which it follows thatg(−4) = −(−4)2 + 24; g(−4) = −16 + 24; and g(−4) = 8.
Choices B, C, and D are incorrect because g is a function and there can only
be one value of g(−4).

QUESTION 11.
Choice D is correct. To determine the price per pound of beef when it was

equal to the price per pound of chicken, determine the value of x (the number of weeks after July 1) when the two prices were equal. The prices wereequal when b = c; that is, when 2.35 + 0.25x = 1.75 + 0.40x. This last equation
0.60
is equivalent to 0.60 = 0.15x, and so x = ​ _ ​= 4. Then to determine b, the0.15
price per pound of beef, substitute 4 for x in b = 2.35 + 0.25x, which givesb = 2.35 + 0.25(4) = 3.35 dollars per pound.
Choice A is incorrect. It results from using the value 1, not 4, for x in
b = 2.35 + 0.25x. Choice B is incorrect. It results from using the value 2,
not 4, for x in b = 2.35 + 0.25x. Choice C is incorrect. It results from using
the value 3, not 4, for x in c = 1.75 + 0.40x.

QUESTION 12.
Choice D is correct. Determine the equation of the line to find the relation-

ship between the x- and y-coordinates of points on the line. All lines through1 ​ x. A point lies on
the origin are of the form y = mx, so the equation is y = ​ _71 ​of its x-coordinate.
the line if and only if its y-coordinate is ​ _Of the given
7
1_
choices, only choice D, (14, 2), satisfies this condition: 2 =​   ​(14).
7
Choice A is incorrect because the line determined by the origin (0, 0) and (0, 7) is
the vertical line with equation x = 0; that is, the y-axis. The slope of the y-axis is
1 . Therefore, the point (0, 7) does not lie on the line that passes
undefined, not _7
1 . Choices B and C are incorrect because neither of thethe origin and has slope _7
1 ​ the value of the x-coordinate.
ordered pairs has a y-coordinate that is _7

QUESTION 13.
Choice B is correct. To rewrite

1, multiply by(x + 2)(x + 3).
(x + 2)(x + 3)

1  ​1  ​ + ​ _​ _x+2 x+3(x + 2)(x + 3)
This results in the expression, which is equivalent to the(x + 3) + (x + 2)
expression in choice B.

Choices A, C, and D are incorrect and could be the result of common algebraic errors that arise while manipulating a complex fraction.

QUESTION 14.
8
Choice A is correct. One approach is to express ​ _y ​ so that the numeratorx2
and denominator are expressed with the same base. Since 2 and 8 are both29

(23)x
8x
powers of 2, substituting 23 for 8 in the numerator of ​ _y ​ gives ​ _​, which22y3x23x​ havecan be rewritten as _​ 2 y ​. Since the numerator and denominator of ​ _2y2
a common base, this expression can be rewritten as 23x−y. It is given that
3x − y = 12, so one can substitute 12 for the exponent, 3x − y, giving that the
8x
expression _​ y ​ is equal to 212.
2
Choices B and C are incorrect because they are not equal to 212. Choice D is
8x
incorrect because the value of ​ _ ​can be determined.
2y

QUESTION 15.
Choice D is correct. One can find the possible values of a and b in(ax + 2)(bx + 7) by using the given equation a + b = 8 and finding another equation that relates the variables a and b. Since(ax + 2)(bx + 7) = 15x2 + cx + 14, one can expand the left side of the equation
to obtain abx2 + 7ax + 2bx + 14 = 15x2 + cx + 14. Since ab is the coefficient of
x2 on the left side of the equation and 15 is the coefficient of x2 on the rightside of the equation, it must be true that ab = 15. Since a + b = 8, it follows
that b = 8 − a. Thus, ab = 15 can be rewritten as a(8 − a) = 15, which in turncan be rewritten as a2 − 8a + 15 = 0. Factoring gives (a − 3)(a − 5) = 0. Thus,
either a = 3 and b = 5, or a = 5 and b = 3. If a = 3 and b = 5, then (ax + 2)
(bx + 7) = (3x + 2)(5x + 7) = 15x2 + 31x + 14. Thus, one of the possible values of c is 31. If a = 5 and b = 3, then (ax + 2)(bx + 7) = (5x + 2)(3x + 7) =15x2 + 41x + 14. Thus, another possible value for c is 41. Therefore, the two
possible values for c are 31 and 41.
Choice A is incorrect; the numbers 3 and 5 are possible values for a andb, but not possible values for c. Choice B is incorrect; if a = 5 and b = 3,
then 6 and 35 are the coefficients of x when the expression (5x + 2)(3x + 7)
is expanded as 15x2 + 35x + 6x + 14. However, when the coefficients of x
are 6 and 35, the value of c is 41 and not 6 and 35. Choice C is incorrect; if
a = 3 and b = 5, then 10 and 21 are the coefficients of x when the expression(3x + 2)(5x + 7) is expanded as 15x2 + 21x + 10x + 14. However, when thecoefficients of x are 10 and 21, the value of c is 31 and not 10 and 21.

QUESTION 16.
The correct answer is 2. To solve for t, factor the left side of t2 − 4 = 0, giv-ing (t − 2)(t + 2) = 0. Therefore, either t − 2 = 0 or t + 2 = 0. If t − 2 = 0, thent = 2, and if t + 2 = 0, then t = −2. Since it is given that t > 0, the value of t
must be 2.
Another way to solve for t is to add 4 to both sides of t2 − 4 = 0, giving t2 = 4.
Then, taking the square root of the left and the right side of the equation_
gives t = ±​√4 ​= ±2. Since it is given that t > 0, the value of t must be 2.
30

QUESTION 17.
The correct answer is 1600. It is given that ∠AEB and ∠CDB have thesame measure. Since ∠ABE and ∠CBD are vertical angles, they have thesame measure. Therefore, triangle EAB is similar to triangle DCB because
the triangles have two pairs of congruent corresponding angles (angleangle criterion for similarity of triangles). Since the triangles are similar, theCD BD​. Substituting
corresponding sides are in the same proportion; thus _​  x ​= ​ _
EB
CD _
BD
the given values of 800 for CD, 700 for BD, and 1400 for EB in ​ _x ​ = ​  EB  ​(800)(1400)
800 _
700
_
gives ​ _ ​= 1600.
x ​ = ​  1400 ​. Therefore, x = ​ 700

QUESTION 18.
The correct answer is 7. Subtracting the left and right sides of x + y = −9 fromthe corresponding sides of x + 2y = −25 gives (x + 2y) − (x + y) = −25 − (−9),
which is equivalent to y = −16. Substituting −16 for y in x + y = −9 givesx + (−16) = −9, which is equivalent to x = −9 − (−16) = 7.

QUESTION 19.
4
The correct answer is ​ _ ​ or 0.8. By the complementary angle relationship5
4  ​.
for sine and cosine, sin(x°) = cos(90° − x°). Therefore, cos(90° − x°) = ​ _54 ​or its decimal equivalent, 0.8, may be gridded as theEither the fraction ​ _5correct answer.
Alternatively, one can construct a right triangle that has an angle of measure
4 ​, as shown in the figure below, where sin(x°) is equal
x° such that sin(x°) = ​ _5
4 ​.
to the ratio of the opposite side to the hypotenuse, or ​ _5
90 – x5x4
90°Since two of the angles of the triangle are of measure x° and 90°, the third
angle must have the measure 180° − 90° − x° = 90° − x°. From the figure,cos(90° − x°), which is equal to the ratio of the adjacent side to the hypot4 ​.
enuse, is also ​ _5

QUESTION 20.

__

The correct answer is 100. Since a = 5​√2 ​, one can substitute 5​√2 ​ for a in
_

_

_

_

_

10​√2 ​= ​√2 ​x. Squaring_each sideof 10​√2 ​= ​√2 ​x gives
2a =_​√2 ​x, giving
_
_
gives
(10​√2 ​)2 = (​√2 ​x)2, which simplifies to (10)2 (​√2 ​)2 = (​√2 ​x)2, or 200_= 2x. This_,x = 100. Checking x = 100
in the_original_
equation gives
2(5​√2 ​) = ​√(2)(100) ​__ __​ (2)(100) ​= (​√2 ​)(​√100 ​) = 10​√2 ​.
which is true since 2(5​√2 ​) = 10​√2 ​ and √31

Section 4: Math Test — Calculator
QUESTION 1.
Choice B is correct. On the graph, a line segment with a positive slope rep-resents an interval over which the target heart rate is strictly increasing as
time passes. A horizontal line segment represents an interval over which
there is no change in the target heart rate as time passes, and a line segment with a negative slope represents an interval over which the target heart
rate is strictly decreasing as time passes. Over the interval between 40 and
60 minutes, the graph consists of a line segment with a positive slope followed by a line segment with a negative slope, with no horizontal line segment in between, indicating that the target heart rate is strictly increasing
then strictly decreasing.
Choice A is incorrect because the graph over the interval between 0 and
30 minutes contains a horizontal line segment, indicating a period inwhich there was no change in the target heart rate. Choice C is incorrect
because the graph over the interval between 50 and 65 minutes consists ofa line segment with a negative slope followed by a line segment with a positive slope, indicating that the target heart rate is strictly decreasing thenstrictly increasing. Choice D is incorrect because the graph over the interval
between 70 and 90 minutes contains horizontal line segments and no segment with a negative slope.

QUESTION 2.
Choice C is correct. Substituting 6 for x and 24 for y in y = kx gives 24 = (k)(6),

which gives k = 4. Hence, y = 4x. Therefore, when x = 5, the value of y is(4)(5) = 20. None of the other choices for y is correct because y is a function ofx, and so there is only one y-value for a given x-value.
Choices A, B, and D are incorrect. Choice A is the result of using 6 for yand 5 for x when solving for k. Choice B results from using a value of 3 for kwhen solving for y. Choice D results from using y = k + x instead of y = kx.

QUESTION 3.
Choice D is correct. Consider the measures of ∠3 and ∠4 in the figure below.

s

t
1

2 4

32

3

m



The measure of ∠3 is equal to the measure of ∠1 because they are corresponding angles for the parallel lines  and m intersected by the transversal
line t. Similarly, the measure of ∠3 is equal to the measure of ∠4 because
they are corresponding angles for the parallel lines s and t intersected by
the transversal line m. Since the measure of ∠1 is 35°, the measures of∠3 and ∠4 are also 35°. Since ∠4 and ∠2 are supplementary, the sum of
the measures of these two angles is 180°. Therefore, the measure of ∠2 is180° − 35° = 145°.
Choice A is incorrect because 35° is the measure of ∠1, and ∠1 is not congruent to ∠2. Choice B is incorrect because it is the measure of the complementary angle of ∠1, and ∠1 and ∠2 are not complementary angles.
Choice C is incorrect because it is double the measure of ∠1.

QUESTION 4.
Choice C is correct. The description “16 + 4x is 10 more than 14” can be

written as the equation 16 + 4x = 10 + 14, which is equivalent to 16 + 4x = 24.
Subtracting 16 from each side of 16 + 4x = 24 gives 4x = 8. Since 8x is 2 times
4x, multiplying both sides of 4x = 8 by 2 gives 8x = 16. Therefore, the valueof 8x is 16.
Choice A is incorrect because it is the value of x, not 8x. Choices B and D
are incorrect; those choices may be a result of errors in rewriting 16 + 4x =10 + 14. For example, choice D could be the result of subtracting 16 from theleft side of the equation and adding 16 to the right side of 16 + 4x = 10 + 14,
giving 4x = 40 and 8x = 80.

QUESTION 5.
Choice D is correct. A graph with a strong negative association between

d and t would have the points on the graph closely aligned with a line thathas a negative slope. The more closely the points on a graph are aligned witha line, the stronger the association between d and t, and a negative slope
indicates a negative association. Of the four graphs, the points on graph
D are most closely aligned with a line with a negative slope. Therefore, thegraph in choice D has the strongest negative association between d and t.
Choice A is incorrect because the points are more scattered than the
points in choice D, indicating a weak negative association between d and t.
Choice B is incorrect because the points are aligned to either a curve or possibly a line with a small positive slope. Choice C is incorrect because thepoints are aligned to a line with a positive slope, indicating a positive association between d and t.

33

QUESTION 6.
Choice D is correct. Since there are 10 grams in 1 decagram, there are

2 × 10 = 20 grams in 2 decagrams. Since there are 1,000 milligrams in
1 gram, there are 20 × 1,000 = 20,000 milligrams in 20 grams. Therefore,
20,000 1-milligram doses of the medicine can be stored in a 2-decagram
container.
Choice A is incorrect; 0.002 is the number of grams in 2 milligrams. Choice B isincorrect; it could result from multiplying by 1,000 and dividing by 10 insteadof multiplying by both 1,000 and 10 when converting from decagrams to milligrams. Choice C is incorrect; 2,000 is the number of milligrams in 2 grams, notthe number of milligrams in 2 decagrams.

QUESTION 7.
Choice C is correct. Let x represent the number of installations that each
unit on the y-axis represents. Then 9x, 5x, 6x, 4x, and 3.5x are the number of rooftops with solar panel installations in cities A, B, C, D, and E,
respectively. Since the total number of rooftops is 27,500, it follows that
9x + 5x + 6x + 4x + 3.5x = 27,500, which simplifies to 27.5x = 27,500. Thus,x = 1,000. Therefore, an appropriate label for the y-axis is “Number of installations (in thousands).”

Choices A, B, and D are incorrect and may result from errors when setting
up and calculating the units for the y-axis.

QUESTION 8.
Choice D is correct. If the value of |n − 1| + 1 is equal to 0, then |n − 1| + 1 = 0.

Subtracting 1 from both sides of this equation gives |n − 1| = −1. The expression |n − 1| on the left side of the equation is the absolute value of n − 1,and the absolute value can never be a negative number. Thus |n − 1| = −1
has no solution. Therefore, there are no values for n for which the value of|n − 1| + 1 is equal to 0.
Choice A is incorrect because |0 − 1| + 1 = 1 + 1 = 2, not 0. Choice B is incorrect because |1 − 1| + 1 = 0 + 1 = 1, not 0. Choice C is incorrect because|2 − 1| + 1 = 1 + 1 = 2, not 0.

QUESTION 9.
Choice A is correct. Subtracting 1,052 from both sides of the equa-tion a = 1,052 + 1.08t gives a − 1,052 = 1.08t. Then dividing both sides ofa − 1,052 ​.
a − 1,052 = 1.08t by 1.08 gives t = _​ 1.08
Choices B, C, and D are incorrect and could arise from errors in rewritinga = 1,052 + 1.08t. For example, choice B could result if 1,052 is added to the34

left side of a = 1,052 + 1.08t and subtracted from the right side, and thenboth sides are divided by 1.08.

QUESTION 10.
Choice B is correct. Substituting 1,000 for a in the equation a = 1,052 + 1.08t−52
gives 1,000 = 1,052 + 1.08t, and thus t = ​ _ ​≈ − 48.15. Of the choices given,

1.08−48°F is closest to −48.15°F. Since the equation a = 1,052 + 1.08t is linear,
it follows that of the choices given, −48°F is the air temperature when the
speed of a sound wave is closest to 1,000 feet per second.
Choices A, C, and D are incorrect, and might arise from errors in−52
calculating ​  _  ​or in rounding the result to the nearest integer. For exam1.08
ple, choice C could be the result of rounding −48.15 to −49 instead of −48.

QUESTION 11.
Choice A is correct. Subtracting 3x and adding 3 to both sides of

3x − 5 ≥ 4x − 3 gives −2 ≥ x. Therefore, x is a solution to 3x − 5 ≥ 4x − 3 if andonly if x is less than or equal to −2 and x is NOT a solution to 3x − 5 ≥ 4x − 3 if
and only if x is greater than −2. Of the choices given, only −1 is greater than
−2 and, therefore, cannot be a value of x.
Choices B, C, and D are incorrect because each is a value of x that is less thanor equal to −2 and, therefore, could be a solution to the inequality.

QUESTION 12.
Choice C is correct. The average number of seeds per apple is the total

number of seeds in the 12 apples divided by the number of apples, which
is 12. On the graph, the horizontal axis is the number of seeds per apple
and the height of each bar is the number of apples with the corresponding number of seeds. The first bar on the left indicates that 2 apples have
3 seeds each, the second bar indicates that 4 apples have 5 seeds each,the third bar indicates that 1 apple has 6 seeds, the fourth bar indicatesthat 2 apples have 7 seeds each, and the fifth bar indicates that 3 apples
have 9 seeds each. Thus, the total number of seeds for the 12 apples
is (2 × 3) + (4 × 5) + (1 × 6) + (2 × 7) + (3 × 9) = 73, and the average
73
number of seeds per apple is ​ _ ​= 6.08. Of the choices given, 6 is closest
12
to 6.08.
Choice A is incorrect; it is the number of apples represented by the tallest
bar but is not the average number of seeds for the 12 apples. Choice B isincorrect; it is the number of seeds per apple corresponding to the tallest
bar, but is not the average number of seeds for the 12 apples. Choice D isincorrect; a student might choose this by correctly calculating the average
number of seeds, 6.08, but incorrectly rounding up to 7.
35

QUESTION 13.
Choice C is correct. From the table, there was a total of 310 survey respondents,
19
and 19% of all survey respondents is equivalent to _​   ​× 310 = 58.9 respon-

100
dents. Of the choices given, 59, the number of males taking geometry, is closest to 58.9 respondents.

Choices A, B, and D are incorrect because the number of males taking
geometry is closer to 58.9 than the number of respondents in each of thesecategories.

QUESTION 14.
Choice C is correct. The range of the 21 fish is 24 − 8 = 16 inches, andthe range of the 20 fish after the 24-inch measurement is removed is
16 − 8 = 8 inches. The change in range, 8 inches, is much greater than thechange in the mean or median.
Choice A is incorrect. Let m be the mean of the lengths, in inches, of the
21 fish. Then the sum of the lengths, in inches, of the 21 fish is 21m. Afterthe 24-inch measurement is removed, the sum of the lengths, in inches, ofthe remaining 20 fish is 21m − 24, and the mean length, in inches, of these−m− ​
24 , which is a change of ​ 24__ ​inches. Since m must be
20 fish is ​ 21m
20
20
between the smallest and largest measurements of the 21 fish, it follows that
8 < m < 24, from which it can be seen that the change in the mean, in inches,
24 − 8 _−  ​
24 = 0 and ​ __is between ​ 24 ​ = ​  4 ​, and so must be less than the change
520
20
in the range, 8 inches. Choice B is incorrect because the median lengthof the 21 fish is the length of the 11th fish, 12 inches. After removing the24-inch measurement, the median of the remaining 20 lengths is the averageof the 10th and 11th fish, which would be unchanged at 12 inches. Choice
D is incorrect because the changes in the mean, median, and range of themeasurements are different.

QUESTION 15.
Choice A is correct. The total cost C of renting a boat is the sum of the initialcost to rent the boat plus the product of the cost per hour and the number of hours, h, that the boat is rented. The C-intercept is the point on the
C-axis where h, the number of hours the boat is rented, is 0. Therefore, theC-intercept is the initial cost of renting the boat.
Choice B is incorrect because the graph represents the cost of renting only
one boat. Choice C is incorrect because the total number of hours of rental isrepresented by h-values, each of which corresponds to the first coordinate ofa point on the graph. Choice D is incorrect because the increase in cost foreach additional hour is given by the slope of the line, not by the C-intercept.
36

QUESTION 16.
Choice C is correct. The relationship between h and C is represented by any

equation of the given line. The C-intercept of the line is 5. Since the points38−5 _ ​ = ​   ​= 3. Therefore,(0, 5) and (1, 8) lie on the line, the slope of the line is _​ 1−0 1
the relationship between h and C can be represented by C = 3h + 5, theslope-intercept equation of the line.
Choices A and D are incorrect because each uses the wrong values for boththe slope and intercept. Choice B is incorrect; this choice would result fromcomputing the slope by counting the number of grid lines instead of using
the values represented by the axes.

QUESTION 17.
Choice B is correct. The minimum value of the function corresponds to they-coordinate of the point on the graph that is the lowest along the verticalor y-axis. Since the grid lines are spaced 1 unit apart on each axis, the lowest
point along the y-axis has coordinates (−3, −2). Therefore, the value of x at
the minimum of f(x) is −3.
Choice A is incorrect; −5 is the smallest value for an x-coordinate of a pointon the graph of f, not the lowest point on the graph of f. Choice C is incorrect; it is the minimum value of f, not the value of x that corresponds to theminimum of f. Choice D is incorrect; it is the value of x at the maximum
value of f, not at the minimum value of f.

QUESTION 18.
Choice A is correct. Since (0, 0) is a solution to the system of inequalities,

substituting 0 for x and 0 for y in the given system must result in two true
inequalities. After this substitution, y < −x + a becomes 0 < a, and y > x + b
becomes 0 > b. Hence, a is positive and b is negative. Therefore, a > b.
Choice B is incorrect because b > a cannot be true if b is negative and ais positive. Choice C is incorrect because it is possible to find an example
where (0, 0) is a solution to the system, but |a| < |b|; for example, if a = 6 andb = −7. Choice D is incorrect because the equation a = −b could be true, butdoesn’t have to be true; for example, if a = 1 and b = −2.

QUESTION 19.
Choice B is correct. To determine the number of salads sold, write and solvea system of two equations. Let x equal the number of salads sold and let yequal the number of drinks sold. Since the number of salads plus the number of drinks sold equals 209, the equation x + y = 209 must hold. Since each37

salad cost $6.50, each soda cost $2.00, and the total revenue was $836.50, theequation 6.50x + 2.00y = 836.50 must also hold. The equation x + y = 209 is
equivalent to 2x + 2y = 418, and subtracting each side of 2x + 2y = 418 fromthe respective side of 6.50x + 2.00y = 836.50 gives 4.5x = 418.50. Therefore,
418.50 ​= 93.
the number of salads sold, x, was x = ​ _4.50
Choices A, C, and D are incorrect and could result from errors in writing theequations and solving the system of equations. For example, choice C could
have been obtained by dividing the total revenue, $836.50, by the total priceof a salad and a soda, $8.50, and then rounding up.

QUESTION 20.
Choice D is correct. Let x be the original price of the computer, in dollars.

The discounted price is 20 percent off the original price, so x − 0.2x = 0.8x is
the discounted price, in dollars. The tax is 8 percent of the discounted price,
so 0.08(0.8x) is the tax on the purchase, in dollars. The price p, in dollars,that Alma paid the cashiers is the sum of the discounted price and the tax:
p = 0.8x + (0.08)(0.8x) which can be rewritten as p = 1.08(0.8x). Therefore,p ​the original price, x, of the computer, in dollars, can be written as _​ (0.8)(1.08)
in terms of p.
Choices A, B, and C are incorrect; each choice either switches the rolesof the original price and the amount Alma paid, or incorrectly combines the results of the discount and the tax as 0.8 + 0.08 = 0.88 instead ofas (0.8)(1.08).

QUESTION 21.
Choice C is correct. The probability that a person from Group Y who recalled38

at least 1 dream was chosen from the group of all people who recalled atleast 1 dream is equal to the number of people in Group Y who recalled atleast 1 dream divided by the total number of people in the two groups whorecalled at least 1 dream. The number of people in Group Y who recalledat least 1 dream is the sum of the 11 people in Group Y who recalled 1 to
4 dreams and the 68 people in Group Y who recalled 5 or more dreams:
11 + 68 = 79. The total number of people who recalled at least 1 dream is
the sum of the 79 people in Group Y who recalled at least 1 dream, the 28
people in Group X who recalled 1 to 4 dreams, and the 57 people in GroupX who recalled 5 or more dreams: 79 + 28 + 57 = 164. Therefore, the prob79
ability is ​ _ ​.
164
Choice A is incorrect; it is the number of people in Group Y who recalled
5 or more dreams divided by the total number of people in Group Y. Choice
B is incorrect; it uses the total number of people in Group Y as the denominator of the probability. Choice D is incorrect; it is the total number of people in the two groups who recalled at least 1 dream divided by the total number of people in the two groups.

QUESTION 22.
Choice B is correct. The average rate of change in the annual budget for

agriculture/natural resources from 2008 to 2010 is the total change from to2008 to 2010 divided by the number of years, which is 2. The total change
in the annual budget for agriculture/natural resources from 2008 to 2010 is488,106 − 358,708 = 129,398, in thousands of dollars, so the average change
in the annual budget for agriculture/natural resources from 2008 to 2010
$129,398,000 ​= $64,699,000 per year. Of the options given, this averageis ​  __
2
rate of change is closest to $65,000,000 per year.
Choices A and C are incorrect; they could result from errors in setting up or
calculating the average rate of change. Choice D is incorrect; $130,000,000 is
the approximate total change from 2008 to 2010, not the average change from2008 to 2010.

QUESTION 23.
Choice B is correct. The human resources budget in 2007 was

4,051,050 thousand dollars, and the human resources budget in 2010
was 5,921,379 thousand dollars. Therefore, the ratio of the 2007 bud2 ​. Similar estimates for4  ​ = ​ _get to the 2010 budget is slightly greater than ​ _6 3
agriculture/natural resources give a ratio of the 2007 budget to the 20103
budget of slightly greater than ​ _ ​; for education, a ratio of slightly greater
452 ​; for highways and transportation,
than ​ _
a ratio of slightly less than ​ _ ​; and3
65
for public safety, a ratio of slightly greater than ​ _ ​. Therefore, of the given
9
choices, education’s ratio of the 2007 budget to the 2010 budget is closest tothat of human resources.
Choices A, C, and D are incorrect because the 2007 budget to 2010 budget
ratio for each of these programs in these choices is further from the corresponding ratio for human resources than the ratio for education.

QUESTION 24.
Choice A is correct. The equation of a circle can be written as (x − h)2 +(y − k)2 = r2 where (h, k) are the coordinates of the center of the circle andr is the radius of the circle. Since the coordinates of the center of the circle
are (0, 4), the equation is x2 + (y − 4)2 = r2, where r is the radius. The radiusof the circle is the distance from the center, (0, 4), to the given endpoint of a25
4 ​, 5 ​. By the distance formula, r2 = ​ ​ _4 ​− 0 2​ + (5 − 4)2 = ​ _ ​. Therefore,
radius, ​ ​ _33
925
an equation of the given circle is x2 + (y − 4)2 = ​ _ ​.
9
Choice B is incorrect; it results from the incorrect equation (x + h)2 +(y + k)2 = r2. Choice C is incorrect; it results from using r instead of r2 in theequation for the circle. Choice D is incorrect; it results from using the incor1 ​.
rect equation (x + h)2 + (y + k)2 = ​ _
r

( )

( )

39

QUESTION 25.
Choice D is correct. When the ball hits the ground, its height is 0 meters.

Substituting 0 for h in h = −4.9t2 + 25t gives 0 = −4.9t2 + 25t, which canbe rewritten as 0 = t(−4.9t + 25). Thus, the possible values of t are t = 0
25
and t = ​ _ ​ ≈ 5.1. The time t = 0 seconds corresponds to the time the ball
4.9
is launched from the ground, and the time t ≈ 5.1 seconds corresponds tothe time after launch that the ball hits the ground. Of the given choices,
5.0 seconds is closest to 5.1 seconds, so the ball returns to the groundapproximately 5.0 seconds after it is launched.
Choice A, B, and C are incorrect and could arise from conceptual or computation errors while solving 0 = −4.9t2 + 25t for t.

QUESTION 26.
Choice B is correct. Let x represent the number of pears produced by theType B trees. Then the Type A trees produce 20 percent more pears than x,
which is x + 0.20x = 1.20x pears. Since Type A trees produce 144 pears, the144  ​= 120. Therefore, the Type B trees
equation 1.20x = 144 holds. Thus x = ​ _1.20
produced 120 pears.
Choice A is incorrect because while 144 is reduced by approximately 20 percent, increasing 115 by 20 percent gives 138, not 144. Choice C is incorrect;
it results from subtracting 20 from the number of pears produced by theType A trees. Choice D is incorrect; it results from adding 20 percent of thenumber of pears produced by Type A trees to the number of pears produced
by Type A trees.

QUESTION 27.
Choice C is correct. The area of the field is 100 square meters. Each 1-meter-by-1-meter square has an area of 1 square meter. Thus, on average, the earthworm counts to a depth of 5 centimeters for each of the regions investigated1  ​of the total number of earthworms toby the students should be about ​ _100
a depth of 5 centimeters in the entire field. Since the counts for the smaller
regions are from 107 to 176, the estimate for the entire field should be
between 10,700 and 17,600. Therefore, of the given choices, 15,000 is a reasonable estimate for the number of earthworms to a depth of 5 centimetersin the entire field.
Choice A is incorrect; 150 is the approximate number of earthworms
in 1 square meter. Choice B is incorrect; it results from using 10 square
meters as the area of the field. Choice D is incorrect; it results from using
1,000 square meters as the area of the field.

40

QUESTION 28.
Choice C is correct. To determine which quadrant does not contain any solu-

tions to the system of inequalities, graph the inequalities. Graph the inequality y ≥ 2x + 1 by drawing a line through the y-intercept (0, 1) and the point
1 x − 1 by drawing a dashed line through(1, 3), and graph the inequality y > _2
the y-intercept (0, −1) and the point (2, 0), as shown in the figure below.
yIIy > 2x + 1

I1
y > x–1
2
x

III

IV

The solution to the system of inequalities is the intersection of the shaded regions
above the graphs of both lines. It can be seen that the solutions only include
points in quadrants I, II, and III and do not include any points in quadrant IV.
Choices A and B are incorrect because quadrants II and III contain solutions to the system of inequalities, as shown in the figure above. Choice D isincorrect because there are no solutions in quadrant IV.

QUESTION 29.
Choice D is correct. If the polynomial p(x) is divided by x − 3, the resultp(x)rcan be written as ​ _  ​ = q(x) + ​ _  ​, where q(x) is a polynomial and rx−3x−3
is the remainder. Since x − 3 is a degree 1 polynomial, the remainder
is a real number. Hence, p(x) can be written as p(x) = (x − 3)q(x) + r,
where r is a real number. It is given that p(3) = −2 so it must be true that
−2 = p(3) = (3 − 3)q(3) + r = (0)q(3) + r = r. Therefore, the remainder whenp(x) is divided by x − 3 is −2.
Choice A is incorrect because p(3) = −2 does not imply that p(5) = 0.
Choices B and C are incorrect because the remainder −2 or its negative, 2,need not be a root of p(x).

QUESTION 30.
Choice D is correct. Any quadratic function q can be written in the form

q(x) = a(x − h)2 + k, where a, h, and k are constants and (h, k) is the vertex of
the parabola when q is graphed in the coordinate plane. (Depending on the41

sign of a, the constant k must be the minimum or maximum value of q, andh is the value of x for which a(x − h)2 = 0 and q(x) has value k.) This form
can be reached by completing the square in the expression that defines q.
The given equation is y = x2 − 2x − 15, and since the coefficient of x is −2,
the equation can be written in terms of (x − 1)2 = x2 − 2x + 1 as follows:y = x2 − 2x − 15 = (x2 − 2x + 1) − 16 = (x − 1)2 − 16. From this form of theequation, the coefficients of the vertex can be read as (1, −16)
Choices A and C are incorrect because the coordinates of the vertex A do
not appear as constants in these equations. Choice B is incorrect because it is
not equivalent to the given equation.

QUESTION 31.
The correct answer is any number between 4 and 6, inclusive. Since Wyatt
can husk at least 12 dozen ears of corn per hour, it will take him no more72
than ​ _ ​ 5 6 hours to husk 72 dozen ears of corn. On the other hand, since12
Wyatt can husk at most 18 dozen ears of corn per hour, it will take him
72
at least ​ _ ​ 5 4 hours to husk 72 dozen ears of corn. Therefore, the possi18
ble times it could take Wyatt to husk 72 dozen ears of corn are 4 hours to
6 hours, inclusive. Any number between 4 and 6, inclusive, can be gridded as
the correct answer.

QUESTION 32.
The correct answer is 107. Since the weight of the empty truck and its driveris 4500 pounds and each box weighs 14 pounds, the weight, in pounds, ofthe delivery truck, its driver, and x boxes is 4500 + 14x. This weight is below
the bridge’s posted weight limit of 6000 pounds if 4500 + 14x < 6000. That
1500
1 ​. Since the number
inequality is equivalent to 14x ≤ 1500 or x < ​ _ ​ = 107 ​ _714
of packages must be an integer, the maximum possible value for x that willkeep the combined weight of the truck, its driver, and the x identical boxes
below the bridge’s posted weight limit is 107.

QUESTION 33.
5
The correct answer is ​ _ ​ or .625. Based on the line graph, the number of8

portable media players sold in 2008 was 100 million, and the number of

portable media players sold in 2011 was 160 million. Therefore, the number
100 millionof portable media players sold in 2008 is _​  ​of the portable media
160 million
55players sold in 2011. This fraction reduces to ​ _ ​. Either ​  _ ​or its decimal
88
equivalent, .625, may be gridded as the correct answer.

QUESTION 34.
The correct answer is 96. Since each day has a total of 24 hours of time
42

slots available for the station to sell, there is a total of 48 hours of time slots

available to sell on Tuesday and Wednesday. Each time slot is a 30-minute1  ​-hour interval. Therefore, there are a totalinterval, which is equal to a ​ _2
48 hours__of ​    ​= 96 time slots of 30 minutes for the station to sell on
1  ​hours/time slot​ _
2
Tuesday and Wednesday.

QUESTION 35.
The correct answer is 6. The volume of a cylinder is πr2h, where r is theradius of the base of the cylinder and h is the height of the cylinder. Since
the storage silo is a cylinder with volume 72π cubic yards and height 8 yards,
it is true that 72π = πr2(8), where r is the radius of the base of the cylinder,in yards. Dividing both sides of 72π = πr2(8) by 8π gives r2 = 9, and so theradius of base of the cylinder is 3 yards. Therefore, the diameter of the baseof the cylinder is 6 yards.

QUESTION 36.
The correct answer is 3. The function h(x) is undefined when the denomi1
nator of ​  __   ​ is equal to zero. The expression (x − 5)2 +(x − 5)2 + 4(x − 5) + 4
4(x − 5) + 4 is a perfect square: (x − 5)2 + 4(x − 5) + 4 = ((x − 5) + 2)2, which
can be rewritten as (x − 3)2. The expression (x − 3)2 is equal to zero if andonly if x = 3. Therefore, the value of x for which h(x) is undefined is 3.

QUESTION 37.
The correct answer is 1.02. The initial deposit earns 2 percent inter-est compounded annually. Thus at the end of 1 year, the new value of theaccount is the initial deposit of $100 plus 2 percent of the initial deposit:
2  ​($100) = $100(1.02). Since the interest is compounded annually,$100 + ​ _100
the value at the end of each succeeding year is the sum of the previous
year’s value plus 2 percent of the previous year’s value. This is again equivalent to multiplying the previous year’s value by 1.02. Thus, after 2 years, thevalue will be $100(1.02)(1.02) = $100(1.02)2; after 3 years, the value will be$100(1.02)3; and after t years, the value will be $100(1.02)t. Therefore, in theformula for the value for Jessica’s account after t years, $100(x)t, the value ofx must be 1.02.

QUESTION 38.
The correct answer is 6.11. Jessica made an initial deposit of $100 into her

account. The interest on her account is 2 percent compounded annually, so
after 10 years, the value of her initial deposit has been multiplied 10 times
by the factor 1 + 0.02 = 1.02. Hence, after 10 years, Jessica’s deposit is worth$100(1.02)10 = $121.899 to the nearest tenth of a cent. Tyshaun made an initial deposit of $100 into his account. The interest on his account is 2.5 percent compounded annually, so after 10 years, the value of his initial deposit

43

has been multiplied 10 times by the factor 1 + 0.025 = 1.025. Hence, after
10 years, Tyshaun’s deposit is worth $100(1.025)10 = $128.008 to the nearest
tenth of a cent. Hence, Jessica’s initial deposit earned $21.899 and Tyshaun’s
initial deposit earned $28.008. Therefore, to the nearest cent, Tyshaun’s initial deposit earned $6.11 more than Jessica’s initial deposit.

44