SAT prep

Reading1

100

The local library was vital to community life in small towns during the early 1900s because it provided the books and resources that residents needed for education and leisure. Additionally, the library was a _______ of inspiration. Visitors engaging in book clubs and community events would share ideas and help spread them throughout the town.

Which choice completes the text with the most logical and precise word or phrase?

Hub, Obstacle, Burden, Imitation

The sentence describes the library as an important place where people gathered, shared ideas, and spread inspiration. The word "hub" fits perfectly, as it represents a central place where activities or ideas are exchanged. The other options do not fit the context:

1. hub – a central place where activities or ideas are exchanged
2. obstacle – contradicts the idea of inspiration and community sharing
3. burden – does not match the positive impact described
4. imitation – is unrelated to the concept of spreading ideas

Therefore, hub is the most logical and precise word for the sentence.

200

The following text is from William Wordsworth's poem "I Wandered Lonely as a Cloud" (1807). In the poem, the speaker states that recalling the daffodils later, when he is alone, makes his heart fill with pleasure, writing, ______

Which quotation from the poem "I Wandered Lonely as a Cloud" most effectively illustrates the claim?

A"They flash upon that inward eye / Which is the bliss of solitude;"

B"Ten thousand saw I at a glance; / Tossing their heads in sprightly dance."

C"Continuous as the stars that shine / And twinkle on the milky way,"

D"And then my heart with pleasure fills, / And dances with the daffodils."

Explanation

The prompt paraphrases Wordsworth's idea: the memory of the daffodils returns to him later, in solitude, and that recollection brings joy. The question asks for the line that most directly states this outcome. Therefore, the best evidence must explicitly say that his heart fills with pleasure when he recalls them, not merely describe the flowers’ number, movement, or his mental image.

Let's analyze each option one by one.

1. This line emphasizes recollection in solitude—"inward eye" and "bliss of solitude"—which supports the setting of the memory. However, it stops short of stating the specific resulting emotion: that his heart fills with pleasure.
2. These lines describe the daffodils’ multitude and lively motion at the original scene. They illustrate what he saw then, not the later emotional effect of remembering them while alone.
3. The comparison to countless stars conveys vastness and continuity, strengthening imagery of the scene. It does not mention later recollection or the joy the memory brings in solitude.
4. Correct, this couplet directly expresses the claim's outcome: when the daffodils return to his mind, "my heart with pleasure fills," and he "dances" with them—explicitly naming joy produced by remembered sight.

The correct answer is D.

300

Without significant advancements in marine exploration, scientists are unlikely to ever have _______ understanding of the creatures living in the deepest parts of the ocean, as these regions remain largely unexplored and inaccessible.

Which choice completes the text with the most logical and precise word or phrase?

A a fragmented

B an intuitive

C a comprehensive

D a biased

Explanation

The passage indicates that the deepest parts of the ocean are largely unexplored and difficult to access, making it hard for scientists to fully understand the creatures living there. The word comprehensive fits best because it means "complete and thorough," aligning with the idea of full understanding, which is challenging without further exploration.

1. a fragmented – suggests something incomplete and scattered, which is not the main idea. The passage speaks about achieving a full understanding, not pieces of it.
2. an intuitive – implies understanding through instinct rather than exploration and research, which is inappropriate in the context of scientific study.
3. a comprehensive – means complete and thorough, which matches the idea of fully understanding these unexplored regions.
4. a biased – suggests prejudice or partiality, which is not relevant to the concept of exploration and understanding.

Therefore, a comprehensive is the most logical and precise choice for completing the sentence.

The correct answer is C.

400

The following text is adapted from a public health article discussing vaccination outreach strategies.

To improve vaccine uptake in rural areas, public health officials tested various messaging approaches, including door-to-door campaigns and text reminders. The text-based messages led to only modest increases in vaccination rates. Still, the authors recommended continuing the use of text messaging because of its scalability and low cost.

Which choice best describes the function of the underlined portion in the text as a whole?

A It identifies a reason the authors support a strategy even though it produces only limited improvements in outcomes.

B It highlights a logistical obstacle that might prevent the broader use of the text-based messaging strategy.

C It compares two different methods for increasing vaccination rates and indicates which one is more cost-effective.

D It questions the reliability of the study's results by pointing out a potential bias related to rural access to technology.

Explanation

This passage explains how health officials tried to raise vaccination rates using different outreach methods. Text reminders only had a small effect, yet researchers still endorsed their use. The underlined portion explains why: text messaging is cheap and scalable, meaning it can be applied widely at low cost. This cost-efficiency justifies the strategy despite its modest impact.

1. Correct. This precisely matches the underlined portion's role—offering a reason to continue a minimally effective method due to its low cost and scalability.
2. The underlined phrase supports using the method, not warning about an obstacle to its use.
3. While the passage mentions two approaches, the underlined portion does not compare them—it only justifies the continued use of text messages.
4. The sentence does not question the validity of the study's results or introduce bias concerns—it supports the findings.

The correct answer is A.

500

Text 1

Anthropologist Maya Laird and colleagues measured carbon and nitrogen isotope ratios in bone collagen from burials in two river valleys. They reported δ13C and δ15N values consistent with heavy reliance on maize by about 500 CE. Laird's team argues that these signatures support a regionwide shift to intensive maize farming and storage, broadly similar to later historical accounts. The authors contend that isotopes provide the clearest line of evidence available for diet and land use at this time, implying that communities had already adopted field systems that could sustain large settlements.

Text 2

Archaeologists David Corbett and Lina Cho maintain that bulk collagen isotopes are often overinterpreted as markers of maize agriculture. Similar values can arise from marine fish consumption, arid-zone plants, or trophic-level changes in freshwater settings. They note that Laird's study did not incorporate compound-specific amino-acid analyses, enamel carbonate data, or plant microfossils from tools and dental calculus, which could separate these possibilities. Corbett and Cho conclude that without such complementary evidence, claims about an early, regionwide maize regime likely rest on an incomplete reading of the available signals.

Based on the texts, how would Corbett and Cho (Text 2) most likely characterize the conclusion presented in Text 1?

A As unexpected, because many scholars had believed maize was absent locally at that time, so the isotope-based claim sharply overturns prevailing views.

B As premature, because researchers in this region have only recently begun using isotope methods, leaving too little baseline information for firm dietary inferences.

C As questionable, because it relies on isotope signals that could reflect several alternative sources, and it omits complementary tests needed to distinguish among them.

D As puzzling, because it is rare to recover measurable collagen isotope values from burials of that age, making any dietary reconstruction unusually uncertain.

Explanation

Text 1 claims isotope ratios in human bones point to heavy maize use by about 500 CE, which would imply an early, regionwide turn to intensive farming and storage. Text 2 warns that bulk collagen isotopes can be ambiguous. Similar values may come from marine fish, arid-zone plants, or freshwater food-web shifts. It also notes that Laird's team did not add other tests that could separate these sources, such as compound-specific amino acids, enamel carbonate, or plant microfossils.

Let's analyze each option one by one.

1. This frames the finding as unexpected because it overturns prior beliefs. Text 2 does not focus on historical consensus. It questions interpretation methods and missing lines of evidence rather than surprise.
2. This says the conclusion is premature because isotope methods are new in the region. Text 2 does not argue a lack of baseline use. It argues that multiple sources can mimic maize and that key complementary tests are absent.
3. Correct, because Text 2 says bulk isotopes can reflect several alternative diets and that Laird's study omitted confirmatory analyses. Without those additional tests, a regionwide maize regime is an overinterpretation of ambiguous signals.
4. This calls the result puzzling due to rarity of measurable collagen. Text 2 does not claim poor preservation or data scarcity. Its critique is about ambiguity and the need for additional evidence.

The correct answer is C.

Reading2

100

For chef Antonio Gonsalves, being _______ was an essential part of his culinary mastery. Because he paid close attention to the flavors, textures, and presentation of each dish, Gonsalves' creations captured the essence of Mediterranean cuisine with remarkable authenticity and flair.

Which choice completes the text with the most logical and precise word or phrase?

A. inventive

B. meticulous

C. impatient

D. hesitant 

B. meticulous

200

Among animals that coordinate in groups, such as wolves, dolphins, and humans, newborns often show an innate attraction to rhythmic, beat-based sounds. Cognitive scientist Maya Patel and her colleagues played sequences of evenly spaced clicks (regular beat) and irregularly spaced clicks to test whether this bias also occurs in solitary desert rodents that neither live in groups nor engage in coordinated hunting. They found that rodent pups showed a significant preference for the regular-beat sequence, suggesting that _____________

Which choice most logically completes the text?

A rhythmic sounds are likely perceived as harmless by newborns of group-living species but as threatening by newborns of solitary species.

B researchers should not assume that an innate attraction to rhythmic regularity is necessarily an adaptation for group coordination.

C researchers can assume that the attraction to rhythmic sounds seen in group-living species is learned rather than innate.

D newly weaned desert rodents show a stronger preference for regular beats than newborn desert rodents do.

Explanation

The passage describes a common claim: infants of group-living species show an innate attraction to rhythmic, beat-based sounds, presumed to aid group coordination. Patel's team tested solitary desert rodents (no group living or coordinated hunting) with regular vs. irregular click sequences. Newborn pups still preferred the regular beat. If a nonsocial species exhibits the bias, its origin need not be specialized for group coordination.

Let's analyze each option one by one.

1. This invents a harmless-versus-threatening contrast, and a social-versus-solitary split not tested in the study. The experiment only measured preference for regular beats, not emotional valence or cross-species fear responses.
2. Correct, observing the same preference in a species without group living or coordinated behavior weakens the assumption that the bias evolved specifically for coordination; the attraction could arise from more general auditory processing.
3. This claims the bias in group-living species is learned. The study uses newborn pups and characterizes the preference as innate; nothing in the passage supports a learning-based explanation.
4. This compares newly weaned rodents to newborns, but no data on older pups are provided. The passage reports only newborn responses, so we cannot infer developmental differences.
   The correct answer is B.

300

The following text is adapted from Jane Austen's 1811 novel Sense and Sensibility. Elinor Dashwood and her sister Marianne are discussing their differing views on emotional restraint.

Elinor, this eldest daughter, whose advice was so effectual, possessed a strength of understanding, and coolness of judgment, which qualified her, though only nineteen, to be the counsellor of her mother. She had an excellent heart; her disposition was affectionate, and her feelings were strong—but she knew how to govern them: it was a knowledge which her mother had yet to learn.

As used in the passage, what does the word "govern" most nearly mean?

A limit

B understand

C suppress

D control

Explanation

Elinor Dashwood, though only nineteen, is portrayed as wise beyond her years. She combines strong emotions with clear judgment and self-restraint, making her a trusted advisor to her mother. Unlike her mother, Elinor knows how to manage her feelings without being overwhelmed by them. The passage highlights the contrast between emotional depth and emotional discipline, presenting Elinor as a model of composure and quiet strength.

1. Limit – This implies reducing or restricting something, which is close but not precise. Elinor doesn't just limit her emotions—she manages them.
2. Understand – The sentence makes it clear that Elinor acts on her emotions wisely, not just understands them.
3. Suppress – Too extreme. Elinor's feelings are strong and affectionate—she doesn't repress them entirely.
4. Control – Correct. Elinor has strong emotions but knows how to manage or regulate them—this aligns with "govern" in this context.

The correct answer is D.

400

Scholar and abolitionist Anna Julia Cooper is often remembered for her 1892 work A Voice from the South, widely considered one of the first major texts of Black feminist thought. Cooper argued that the uplift of Black communities depended not only on racial equality, but also on gender justice. She emphasized the intellectual and moral agency of Black women, insisting that they be seen as central participants in political and educational progress. Her essays, delivered in the form of lectures and rhetorical appeals, challenged the dominant ideologies of her time and called for an inclusive vision of American democracy shaped by the voices of Black women.

Which choice best describes the main idea of the text?

A Cooper's work stood out in the 19th century for positioning Black women's experiences and leadership as essential to achieving racial and social equality.

B Cooper's writings often took the form of personal reflections that focused on the challenges she faced as a Black educator and woman.

C Although Cooper was primarily known as a teacher, her influence in literary circles grew steadily during the early 20th century.

D Cooper's ideas were mostly ignored during her lifetime, but were rediscovered by later generations of feminist scholars and civil rights activists.

Explanation

The passage highlights Anna Julia Cooper's significance as an early Black feminist thinker, focusing on her 1892 work A Voice from the South. Cooper did not separate race and gender, but asserted that true social progress required recognizing Black women as central to both educational and political reform. Her public speeches and essays advanced a vision of democracy inclusive of Black female voices, defying the norms of the time. The passage makes it clear that her influence came from her ability to shift discourse toward an intersectional understanding of justice, rather than from personal memoir or later rediscovery.

Let's analyze each option one by one.

1. 
   
2. Correct. This directly reflects the passage's emphasis: Cooper's writing uniquely argued that Black women's leadership was essential to racial and gender equality. It summarizes both her contribution and her challenge to 19th-century thought.
3. While Cooper was a Black woman and educator, the passage says nothing about personal reflections or her own challenges. Her work was rhetorical and intellectual in scope, not memoir.
4. There is no discussion of Cooper's reputation in literary circles, nor is the 20th century emphasized. The passage is focused on her 19th-century arguments and influence.
5. This is historically untrue in this context and unsupported by the passage. The text says her work was long influential, not ignored and "rediscovered."

The correct answer is A.

500

The migratory patterns of certain bird species are remarkably coordinated, with entire flocks traveling thousands of miles to reach warmer climates during the winter months. Scientists have discovered that these birds achieve this _______ through subtle communication signals and environmental cues that help them maintain formation and timing during their long flights.

Which choice completes the text with the most logical and precise word or phrase?

A cooperation

B isolation

C disruption

D alignment

Explanation

The passage describes how birds maintain coordination and timing during migration over long distances. The best word to complete this idea is alignment, which means "being arranged in a straight line or in proper position," matching the concept of birds flying in formation.

1. cooperation – implies working together, which is somewhat related but does not specifically capture the idea of precise positioning and timing during flight.
2. isolation – suggests separation, which is the opposite of what is happening; the birds are moving together in coordinated groups.
3. disruption – implies interruption or disturbance, which contradicts the idea of smooth, organized migration.
4. alignment – matches the idea of coordinated movement and formation, making it the most logical choice.

Thus, alignment is the most logical and precise choice for completing the sentence.

The correct answer is D.

Math1

100

The total cost, in dollars, to make 10,000 units of a certain brand of a premium pen is given by, where is the per unit cost, in dollars. What is the total cost, in dollars, to make 10,000 units of the pen when the per unit cost is $1.20.

Solution:

We are given that the total cost to make 10,000 units of the pen is given by f(x)=40,000+10,000x.

Since the per unit cost x is $1.20, the total cost would be f(x=1.20)=40,000+10,000×1.20

f(1.20)=40,000+12,000

f(1.20)=$52,000

The correct answer is 52,000.

200

A list of nine data values is shown:
2, 3, 8, -10, -22, 0, 0, 6, 4
What is the mean of these data?

Solution:

The mean of a data set is calculated by dividing the sum of the data values by the number of data values in the data set. For this data set, the mean can be calculated as
(2+3+8−10−22+0+0+6+4)/9

which is equivalent to −9/9=−1.

The correct answer is -1.

300

Microorganisms are growing in a liquid growth medium. There were 400,000 organisms per microliter during an initial observation. The number of organisms per microliter triples every 4 hours. How many organisms per microliter will there be 16 hours after the initial observation?

A 1,400,000

B 4,800,000

C 32,400,000

D 129,600,000

 

Solution:

We are given that initially, there were 400,000 organisms per microliter, and that they triple every 4 hours. So,

• Number of organisms in 0 hour =400,000;
• Number of organisms in 4 hours =400,000×3;
• Number of organisms in 8 hours =400,000×3×3=400,000×32;
• Number of organisms in 12 hours =400,000×32×3=400,000×33;
• Number of organisms in 16 hours =400,000×33×3=400,000×34=400,000×81=32,400,000

The correct answer is C. 

400

The function f(x)=10,100(0.925)x models the value, in dollars, of a car by the end of each year from 2000 through 2015, where x is the number of years after 2000. Which of the following is the best interpretation of "f(7) is approximately equal to 5,852" in this context?

A The value of the car is estimated to be approximately 7 dollars greater in 2007 than in 2000.

B The value of the car is estimated to be approximately $5,852 in 2007.

C The value, in dollars, of the car is estimated to be approximately 7 times greater in 2007 than in 2000.  

D The value of the car is estimated to increase by approximately $5,852 every 7 years between 2000 and 2015.

Solution:

We are given that the function f(x)=10,100(0.925)x models the value, in dollars, of a car by the end of each year from 2000 through 2015, where x is the number of years after 2000.

Thus, the value of the car, after

• the end of 2001, i.e., at x=1, is given by f(x=1)=10,100(0.925)1
• the end of 2002, i.e., at x=2, is given by f(x=2)=10,100(0.925)2
• the end of 2003, i.e., at x=3, is given by f(x=3)=10,100(0.925)3
• ...
• the end of 2007, i.e., at x=7, is given by f(x=7)=10,100(0.925)7=$5,852; given

Thus, in words, we can say the approximate $5,852 is the value of the car at the end of 2007.

The correct answer is B. 

500

Line p is defined by 5x+6y=30. Line q is perpendicular to line p in the xy-plane. What is the slope of line q ?

Solution:

We know that if two lines in the xy-plane are perpendicular to each other, the product of their slopes equals −1.

Say the slope of line p is m1 and the slope of line q is m2.

Thus, m1m2=−1

Let's find out the slope (m1)of line p:5x+6y=30.

We know that an equation of the line in the form y=mx+c given the slope of the line, where m= slope.

Transforming 5x+6y=30 in y=mx+c form, we get

6y=−5x+30

y=-(5/6)x+5

Thus, slope =m1=−5/6

We know that m1m2=−1

=>−(5/6) × m2=−1

=>m2=65

The correct answer is 6/5 or 1.2.

Math2

100

Imran bought a few packets of chewing gum and donuts for $90. Each packet of chewing gum cost $4, and each donut cost $2. If Imran bought 15 packets of chewing gum, how many donuts did he buy?

So, we know that Imran bought a few packets of chewing gum and donuts for $90; each packet of chewing gum cost $4, each donut cost $2, and he bought 15 packets of chewing gum.

Say Imran bought x donuts; thus, the amount of money he spent on donuts =$2x; and the amount of money he spent on chewing gum =$4×15=$60

So, 2x+60 must be equal to $90.

2x+60=90

x=(90−60)/2=15 donuts

The correct answer is 15.

200

What percent of x is x² ?

A x

B x/100

C 100x

D x²/100

Solution:

Say y percent of x is x²?

Thus, y% of x=x²

=>(y/100) × x=x²

=>y=(100x²)/x=100x

The correct answer is C.

300

78x+15y=108

64x+29y=80

The solution to the given system of equations is (x,y). What is the value of x−y ?

Solution:

We have two linear equations: 78x+15y=108 and 64x+29y=80.

One way of getting the value of x−y is to solve the given pair of simultaneous equations, get the values of x and y, and then get the value of x−y. However, there's a smarter way of doing it.

Say 78x+15y=108 ——(1) and

64x+29y=80 ——(2)

Subtracting (2) from (1), we get

(78x+15y=108)−(64x+29y=80)

(78−64)x+(15−29)y=108−80

14x−14y=28

x−y=2; dividing the equation by 14

The correct answer is 2.

400

For a quadratic equation ax²+bx+c=0, where a,b, and c are constants, which choice must be correct?

A The equation has no solution for x.

B The equation has two solutions for x.

C The equation cannot have two solutions for x.

D The equation has at most two solutions for x.

Solution:

Note for a quadratic equation ax²+bx+c=0, for the equation's discriminant (b²−4ac) if

• (b²−4ac)=0, it has one solution;
• (b²−4ac)>0, it has two solutions; and
• (b²−4ac)<0, it has no solution

Note that this is a must be true question and not could be true. For a "must be true" question, the correct choice must be correct in all cases.

Let's discuss each choice.

• Since we do not know for sure that (b²−4ac)<0, we cannot state that the equation has no solution for x.
• Its explanation is the same as that of choice A. Since we do not know for sure that (b²−4ac)>0, we cannot state that the equation has two solutions for x.
• Its explanation is also the same as that of choices A and B. Since we do not know for sure that (b²−4ac)<0 or (b2−4ac)=0, we cannot state that the equation cannot have two solutions for x.
• Correct. The phrase "at most two solutions" means that x can have no solution, one solution, or two solutions, which is correct.

The correct answer is D. 

500

A model estimates that at the end of each year from 2017 to 2023, the number of rats in a population was 60% less than the number of rats in the population at the end of the previous year. The model estimates that at the end of 2018, there were 7,000 rats in the population. Which of the following equations represents this model, where n is the estimated number of rats in the population t years after the end of 2017 and t≤6 ?

An=17,500(0.6)^t

Bn=17,500(0.4)^t

Cn=1,400(0.6)^t

Dn=7,000(0.4)^t

Solution:

Since the model estimates that the number of rats in the population decreased by a fixed percentage, 60%, each year, the model can be represented by an exponential equation of the form n=a(1−(p/100))^t, where a is the estimated number of rats in the population at the end of 2017, and the model estimates that at the end of each year, the number is p% less than the number at the end of the previous year.

Since the model estimates that at the end of each year, the number was 60% less than the number at the end of the previous year, p=60. Substituting 60 for p in the equation n=a(1−(p/100))t yields n=a(1−(60/100))^t, which is equivalent to n=a(1−0.6)^t, or n=a(0.4)^t.

It's given that the estimated number of rats at the end of 2018 was 7,000. This means that when t=1 and n=7,000.

Substituting 1 for t and 7,000 for n in the equation n=a(0.4)^t yields 7,000=a(0.4)¹, or 7,000=0.4a.

Dividing each side of this equation by 0.4 yields a=17,500. Substituting 17,500 for a in the equation n=a(0.4)^t yields n=17,500(0.4)^t.

The correct answer is B.

Mixed

100

In the late 1800s, Jane Addams co-founded Hull House in Chicago, one of the first settlement houses in the United States. Hull House provided social services such as childcare, education, and legal aid to immigrants and the working poor. Addams' work at Hull House inspired broader efforts to address poverty, education, and women's rights. In 1931, she became the first American woman awarded the Nobel Peace Prize for her commitment to social reform and international peace efforts.

According to the text, what did Jane Addams co-found in Chicago?

A The first American law firm focused on immigration justice

B A settlement house offering support to immigrants and the poor

C The first public school to offer free meals to students

D A political party advocating for women's voting rights

Explanation

This passage outlines the accomplishments of Jane Addams, especially her co-founding of Hull House, which provided support to marginalized groups in Chicago. Her work helped lay the groundwork for social welfare programs and earned her international recognition. The key detail is that Hull House was a settlement house, offering services to immigrants and the working poor—this directly answers the question about what she co-founded.

Let's analyze each option one by one.

1. No law firm is mentioned. The passage focuses on social services, not legal institutions.
2. Correct. Hull House is clearly identified as a settlement house offering services to immigrants and the poor.
3. While Hull House may have supported education and childcare, there's no mention of a school with free meals.
4. Addams supported women's rights, but there's no mention of founding a political party.

The correct answer is B.

200

Venue waste-reduction campaigns can be successful, says researcher Maya Singh of Northshore University, when theaters give patrons a choice: for example, the Brookside Theater cut program-printing by 35 percent after the theater staff was instructed to ask patrons whether ______ wanted a paper program.

Which choice completes the text so that it conforms to the conventions of Standard English?

A They

B One

C You

D it

The sentence summarizes a theater policy: staff asks patrons whether they want a paper program. The missing pronoun must agree in number with patrons (plural), fit formal expository tone, and maintain consistent grammatical person within reported instructions.

Let's analyze each option one by one.

1. Correct. They is a gender-neutral plural pronoun that agrees with patrons and reads naturally in reported speech: "ask patrons whether they wanted a paper program." It preserves third-person perspective and appropriate tone.
2. One is an impersonal, singular pronoun. It doesn't clearly refer back to the specific group patrons and sounds stilted here, weakening clarity and cohesion in a sentence reporting a practical instruction.
3. You shifts to second person, creating a perspective mismatch: the policy addresses patrons in general, not the reader. In reported speech, "ask patrons whether you wanted" is awkward and undermines grammatical consistency.
4. It is singular and typically refers to things, not people. Using it to refer to patrons is ungrammatical and semantically inappropriate, breaking pronoun-antecedent agreement and clarity.

The correct answer is A.

300

7 more than 10 times a number x is equal to 104. Which equation represents this situation? 

A (7)(10)x=104

B 10x=104+7

C 7x+10=104

D 10x+7=104

Solution:

We are given that 7 more than 10 times a number x is equal to 104.

Let's turn the given information into math form.

• 10 times a number =10x;
• "7 more" more means that 10x is "10x plus 7";
• "equal to 104" means =104

Thus, the mathematical model is

10x+7=104

The correct answer is D. 

400

In 1986, in the days after the Chernobyl nuclear reactor explosion, Soviet officials issued public statements that emphasized stability while downplaying risks. The early reports, later shown to be incomplete, ______ that the reactor containment held, delaying evacuation decisions.

Which choice completes the text so that it conforms to the conventions of Standard English?

A suggested

B suggesting

C to suggest

D having suggested

Explanation

The sentence describes how initial official reports, which were later revealed to be incomplete, gave a certain impression about the reactor's status and thus delayed evacuations. The blank requires a finite past-tense verb that completes the main clause and accurately reflects what those reports did.

Let's analyze each option one by one.

1. suggested
   Correct, this simple past tense verb agrees with the subject "early reports" and accurately conveys that the reports gave the impression (later shown false) that containment held, causing delay. It completes the independent clause properly.
2. suggesting
   This present participle creates a dangling or incomplete structure; without an auxiliary, it cannot serve as the main verb of the clause. It would leave the sentence grammatically unsettled.
3. to suggest
   The infinitive form cannot function as the main verb following the subject. It would make the clause dependent or malformed, lacking the required subject–verb relationship.
4. having suggested
   This perfect participial phrase implies a prior, completed action relative to something else, which distorts the timeline and leaves the main clause without its necessary finite verb. It also creates a misplaced modifier feel.

The correct answer is A.

500

A shopkeeper increases the price of furniture by 25%, and the next day he decreases the price by 20%. The price after the decrease is what percent of the price before the increase?

A 5%  

B 95%  

C 100%  

D 105%

Solution:

Say the price of the furniture before the increase was $100.

After 25% increase, the increased price =100+100×25%=$125

After 20% decrease, the decreased price =125−125×20%=125−125×(20/100)=125−25=$100

We see that the price after the decrease ($100) is equal to the price before increase ($100), thus, the price after the decrease is 100% of the price before the increase.

The correct answer is C.