PSAT Mixed Review: Practice Problems for Your Upcoming Exam

PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

Table of content English

pages 2 - 7

Math

pages 8 - 11

Answer key

pages 13 - 36

free practice exams

pages 37

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

ENGLISH 1. Birch trees, a type of deciduous hardwood, thrive in cooler climates and have historically been susceptible to the harsh winters of the northern hemisphere. When global warming led to milder winters, birch trees began to expand their range further north.

Concurrently, efforts by conservation groups to plant more birch trees in these new areas further __________ the trees' proliferation.

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

A. monitored B. facilitated C. observed D. documented

2. Leonardo da Vinci, a master of the Renaissance period, is best known for his artistic genius and scientific inquiries, yet his impact was not merely ______ the realm of art: engineers and anatomists have applied his studies and methodologies.

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

A. contained within B. limited to C. separated from D. derived from 3. The role of wireless communication in accelerating modern technological advancements is hardly ______; indeed, tech giants frequently highlight its critical impact on innovation. Nonetheless, some experts believe that developments in artificial intelligence have played a more central role in shaping technology’s future.

A. overestimated B. insignificant C. exaggerated D. acknowledged

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

4. Queen Elizabeth I reigned over England from 1558 to 1603. She is known for advancing the English Renaissance, which promoted the flourishing of the arts, the innovation of ______ the expansion of maritime explorations, and the stabilization of the Protestant church.

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

A. technology B. technology; C. technology: D. technology, 5. In oceanography, the term “Lazarus species” refers to marine organisms that reappear in the fossil record after a period of apparent extinction. Like a sunken treasure resurfacing from the ocean depths, a Lazarus species is unexpectedly rediscovered, ______ is not a newly evolved organism.

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

A. nonetheless it B. nonetheless; C. nonetheless, it D. nonetheless. It 6. In 2017, British physicist and environmental advocate Emily Richards left her consultancy role in sustainable development ______ to spearhead a new climate change initiative.

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

A. to lead B. is leading C. led D. leads

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

7. In 2018, architect Laura Thompson designed several community gardens across urban areas in Detroit, Michigan. By creating green spaces in densely populated areas, ______ Which choice completes the text so that it conforms to the conventions of Standard English?

A. the reduction of urban heat islands and improvement of air quality have been facilitated by these gardens.

B. these gardens have facilitated the reduction of urban heat islands and improved air quality.

C. the gardens’ facilitation of the reduction of urban heat islands and improvement of air quality has been noticed.

D. urban heat islands have been reduced and air quality has been improved by these gardens.

8. Nobel laureate Malala Yousafzai and Canadian Prime Minister Justin Trudeau have been vocal advocates for the International Fund for Educational Development, a program that ______ the importance of global education equality.

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

A. have emphasized B. has emphasized C. were emphasizing D. emphasize

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

9. The following text is adapted from Virginia Woolf’s 1925 novel Mrs. Dalloway. Clarissa and some of her friends have recently attended a grand party in London.

[Clarissa] felt a surge of excitement and an intense connection to everything around her at the lavish event. In the evening, she observed the elegantly dressed guests mingling, and she marveled at the rich conversations that flowed around her. Back home, social gatherings had been simple and rarely so stimulating.

Which choice best states the main purpose of the text?

A. It illustrates a character’s reaction to a new social setting.

B. It explains why a character prefers city life to country life.

C. It compares a character’s past and present social experiences.

D. It presents a character feeling overwhelmed by a change in surroundings.

10. In northern Scandinavia, the Sami people have long been recognized for their expertise in reindeer herding. This traditional practice has been central to their culture and livelihood. While modern advancements have influenced their techniques, the Sami maintain a deep connection to their heritage.

Which choice best states the main idea of the text?

A. Despite modern influences, the Sami continue to uphold their traditional reindeer herding practices.

B. The Sami have many roles in their community, but they prefer reindeer herding.

C. The Sami have been celebrated as entertainers in their communities for generations.

D. Modern technology has replaced many of the traditional practices of the Sami.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

11.

Text 1: Anthropologists researching ancient Greek society often examine statuary to infer aspects of daily life in classical Athens. These marble sculptures frequently depict gods and heroes in idealized forms—statues portraying athletes are so anatomically perfect that some scholars have used them to understand athletic training and physical ideals of the era.

Text 2: Art historian and classical scholar Helen Voss has argued that the interpretation of Greek statues as realistic representations of human figures may overlook the artistic expression involved. Greek statuary, Voss contends, are masterpieces where sculptors could transcend reality, using idealized forms not just to mimic real life but to elevate human figures into symbolic representations.

Based on the texts, what would Helen Voss (Text 2) most likely say about the interpretation presented in the underlined portion of Text 1?

A. The perfection seen in statues of athletes suggests a high level of skill in ancient Greek sculpting techniques.

B. It is probable that statues of athletes were intended to represent specific historical figures known for their physical prowess.

C. Statues may have been altered or eroded over time, thus distorting the original artistic intent.

D. The anatomical perfection of statues does not necessarily reflect true physical proportions or training methods of historical athletes.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

12. While researching a topic, a student has taken the following notes: The Catawba are a Native American tribe primarily located in the southeastern United States.

Catawba culture is deeply influenced by the natural resources of the Appalachian region.

Jeremy Two-Trees is a Catawba historian, craftsman, and conservationist.

He founded the Catawba Cultural Center in Rock Hill, South Carolina, in 2005.

Anna Blue-Sky is a Catawba historian, artist, and conservationist.

She founded the Catawba Museum of Natural History in Columbia, South Carolina, in 2005.

The student wants to emphasize the duration and purpose of Two-Trees’s and Blue-Sky’s work.

Which choice most effectively uses relevant information from the notes to accomplish this goal?

A. At the Catawba Cultural Center and Museum of Natural History, visitors can explore the rich history of the Catawba people who have inhabited the region for centuries.

B. Jeremy Two-Trees and Anna Blue-Sky have dedicated their careers to showcasing Catawba culture, deeply rooted in the Appalachian region.

C. Since 2005, Jeremy Two-Trees and Anna Blue-Sky have worked to conserve and celebrate Catawba culture through their respective institutions.

D. Drawing on the Appalachian influences, Catawba culture has thrived in the southeastern United States since pre-colonial times.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

MATH

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

9

PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

10

PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

11

Answer key

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

ENGLISH Words in Context 1. Birch trees, a type of deciduous hardwood, thrive in cooler climates and have historically been susceptible to the harsh winters of the northern hemisphere. When global warming led to milder winters, birch trees began to expand their range further north. Concurrently, efforts by conservation groups to plant more birch trees in these new areas further __________ the trees' proliferation.

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

A. monitored B. facilitated C. observed D. documented Rationale: In this context, “facilitated” means made easier or helped along, which fits the scenario of conservation groups actively planting trees to support their northward spread. The efforts described do not merely involve monitoring, observing, or documenting the trees, but actively assisting their expansion.

Choices A, C, and D are incorrect because they imply passive roles. "Monitored" and "documented" suggest only observing or recording the changes without any active intervention, which does not align with the description of efforts to actively plant more trees. "Observed" similarly indicates merely watching the changes without participating in the proliferation process, which again is less applicable given the context of active support described in the passage.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

2. Leonardo da Vinci, a master of the Renaissance period, is best known for his artistic genius and scientific inquiries, yet his impact was not merely ______ the realm of art: engineers and anatomists have applied his studies and methodologies.

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

A. contained within B. limited to C. separated from D. derived from Rationale: As used here, “limited to” suggests that da Vinci’s contributions were not just confined to artistic achievements but also extended to other fields like engineering and anatomy, reflecting his broad influence and interdisciplinary approach. Choice A could be tempting as it similarly suggests a boundary but lacks the connotation of a breakthrough beyond that boundary which is implied by "limited to."

Choice A, "contained within," implies a restriction that is too confining, which does not reflect the broader influence described.

Choice C, "separated from," incorrectly suggests a disconnection from the realm of art, which does not fit the context of da Vinci's influence across multiple disciplines.

Choice D, "derived from," incorrectly implies that his impact in other fields originated solely from his artistic work, which understates the independent value and direct impact of his contributions in science and engineering.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

3. The role of wireless communication in accelerating modern technological advancements is hardly ______; indeed, tech giants frequently highlight its critical impact on innovation.

Nonetheless, some experts believe that developments in artificial intelligence have played a more central role in shaping technology’s future.

A. overestimated B. insignificant C. exaggerated D. acknowledged Rationale: Choice B, "insignificant," is the best answer as it underscores that the role of wireless communication is far from being minor or negligible, especially given its frequent citation by tech leaders as a key driver of innovation. This choice effectively conveys the significant, yet possibly overshadowed, impact compared to AI developments.

Choice A, "overestimated," and Choice C, "exaggerated," might seem plausible but imply an undue emphasis that doesn't align with the acknowledgment described.

Choice D, "acknowledged," is incorrect as it suggests a lack of recognition, contrary to the "tech giants frequently highlight" part of the statement.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Boundaries 4. Queen Elizabeth I reigned over England from 1558 to 1603. She is known for advancing the English Renaissance, which promoted the flourishing of the arts, the innovation of ______ the expansion of maritime explorations, and the stabilization of the Protestant church.

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

A. technology B. technology; C. technology: D. technology Rationale: Choice D is the best answer. Notice that "the innovation of technology" is the first item in a list of three things. We must use a comma to separate the first two items in the list, just as a comma is used to separate "the expansion of maritime explorations" and "the stabilization of the Protestant church."

Choice A is incorrect. This choice creates a punctuation error. Notice that "the innovation of technology" is the first item in a list of three things. To appropriately format the list, we need punctuation to separate each item.

Choice B is incorrect. This choice creates a punctuation error. Notice that "the innovation of technology" is the first item in a list of three things. While semicolons are sometimes used to separate list items, this list uses commas to separate the other list items, and lists must use the same punctuation throughout.

Choice C is incorrect. This choice creates a punctuation error. Notice that "the innovation of technology" is the first item in a list of three things. While colons can be used to introduce lists, they can’t be used to separate items within a list.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

5. In oceanography, the term “Lazarus species” refers to marine organisms that reappear in the fossil record after a period of apparent extinction. Like a sunken treasure resurfacing from the ocean depths, a Lazarus species is unexpectedly rediscovered, ______ is not a newly evolved organism.

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

A. nonetheless it B. nonetheless; C. nonetheless, it D. nonetheless. It

Rationale: Choice D is the best answer. The clause “Like a sunken treasure…apparent extinction” and the clause “it is…not a newly evolved organism” are both independent clauses, thus making them into two separate sentences with a period is grammatically correct.

Choice B, "nonetheless;" may seem tempting because it uses a semicolon, which can correctly separate two independent clauses. However, it fails to include the necessary pronoun "it" that is required to complete the second clause, thus making the sentence incomplete and grammatically incorrect.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Form, Structure, and Sense 6. In 2017, British physicist and environmental advocate Emily Richards left her consultancy role in sustainable development ______ to spearhead a new climate change initiative.

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

A. to lead B. is leading C. led D. leads Rationale: Choice A is the best answer. The convention being tested is the use of nonfinite verb forms in a sentence. The nonfinite to-infinitive verb "to lead" is correctly used to form a subordinate clause that expresses why Richards left her position (to lead the initiative).

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

7. In 2018, architect Laura Thompson designed several community gardens across urban areas in Detroit, Michigan. By creating green spaces in densely populated areas, ______ Which choice completes the text so that it conforms to the conventions of Standard English?

A. the reduction of urban heat islands and improvement of air quality have been facilitated by these gardens.

B. these gardens have facilitated the reduction of urban heat islands and improved air quality.

C. the gardens’ facilitation of the reduction of urban heat islands and improvement of air quality has been noticed.

D. urban heat islands have been reduced and air quality has been improved by these gardens.

Rationale: Choice B is the best answer. The convention being tested is subject-modifier placement. This choice makes the noun phrase “these gardens” the subject of the sentence and places it immediately after the modifying phrase “By creating green spaces...,” clearly establishing that the gardens—and not another noun in the sentence—are responsible for the environmental benefits.

Choice A is incorrect because it results in a passive construction that buries the main subject ("these gardens") at the end of the sentence, which can lead to confusion about what exactly is causing the reduction and improvement.

Choice C is incorrect because it uses a cumbersome and convoluted construction with "the gardens’ facilitation" that distracts from the direct impact of the gardens themselves. This choice also includes unnecessary nominalization ("facilitation"), which complicates the sentence unnecessarily.

Choice D is incorrect because it also employs a passive construction, which places the effects (reduction of urban heat islands and improvement of air quality) before the cause (these gardens), thus weakening the impact of the gardens as the active agent in these processes and making the sentence structure less clear and direct.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

8. Nobel laureate Malala Yousafzai and Canadian Prime Minister Justin Trudeau have been vocal advocates for the International Fund for Educational Development, a program that ______ the importance of global education equality.

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

A. have emphasized B. has emphasized C. were emphasizing D. emphasize Rationale: Choice B is the best answer. The convention being tested is subject-verb agreement. The singular verb “has emphasized” correctly agrees in number with the singular subject “program.”

Choice A is incorrect because the plural verb “have emphasized” does not agree in number with the singular subject “program.”

Choice C is incorrect because the past progressive verb "were emphasizing" does not appropriately match the present tense needed here and also disagrees in number with the singular subject.

Choice D is incorrect because the plural verb "emphasize" does not agree in number with the singular subject “program.”

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Text Structure and Purpose 9.The following text is adapted from Virginia Woolf’s 1925 novel Mrs. Dalloway. Clarissa and some of her friends have recently attended a grand party in London.

[Clarissa] felt a surge of excitement and an intense connection to everything around her at the lavish event. In the evening, she observed the elegantly dressed guests mingling, and she marveled at the rich conversations that flowed around her. Back home, social gatherings had been simple and rarely so stimulating.

Which choice best states the main purpose of the text?

A. It illustrates a character’s reaction to a new social setting.

B. It explains why a character prefers city life to country life.

C. It compares a character’s past and present social experiences.

D. It presents a character feeling overwhelmed by a change in surroundings.

Rationale: Choice A is the best answer because it most accurately describes the main purpose of the text. The narrator describes how Clarissa responds to being at the party: she is excited and feels a deep connection to her surroundings. She also contrasts the vibrant party with the simpler gatherings she experienced at home, emphasizing her reaction to this new social setting.

Choice B is incorrect because the text does not directly address why Clarissa prefers city life; it focuses on her reactions during a specific event.

Choice C is incorrect as the text primarily illustrates Clarissa's experiences at the party without explicitly comparing these experiences to her past social interactions; it only provides a brief mention of her simpler gatherings at home without detailed comparison.

Choice D is incorrect because there is no indication that Clarissa feels overwhelmed; rather, she is portrayed as exhilarated and engaged by her new environment.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Central Ideas and Details 10.In northern Scandinavia, the Sami people have long been recognized for their expertise in reindeer herding. This traditional practice has been central to their culture and livelihood. While modern advancements have influenced their techniques, the Sami maintain a deep connection to their heritage.

Which choice best states the main idea of the text?

A. Despite modern influences, the Sami continue to uphold their traditional reindeer herding practices.

B. The Sami have many roles in their community, but they prefer reindeer herding.

C. The Sami have been celebrated as entertainers in their communities for generations.

D. Modern technology has replaced many of the traditional practices of the Sami.

Rationale: Choice A is the best answer because it captures the main idea of the text effectively. The text emphasizes that despite the impact of modern advancements, the Sami people continue to preserve and engage in their traditional practice of reindeer herding, highlighting their enduring connection to their cultural heritage.

Choice B is incorrect because there is no evidence in the text suggesting that the Sami prefer reindeer herding over other roles or that their preference is a key aspect of the text.

Choice C is incorrect as the text does not discuss the Sami as entertainers; it focuses on their skills and cultural practices related to reindeer herding.

Choice D is incorrect because it misrepresents the text's message; while modern techniques have influenced their practices, the text does not claim that technology has replaced traditional Sami practices.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Cross-Text Connections 11.

Text 1: Anthropologists researching ancient Greek society often examine statuary to infer aspects of daily life in classical Athens. These marble sculptures frequently depict gods and heroes in idealized forms—statues portraying athletes are so anatomically perfect that some scholars have used them to understand athletic training and physical ideals of the era.

Text 2: Art historian and classical scholar Helen Voss has argued that the interpretation of Greek statues as realistic representations of human figures may overlook the artistic expression involved.

Greek statuary, Voss contends, are masterpieces where sculptors could transcend reality, using idealized forms not just to mimic real life but to elevate human figures into symbolic representations.

Based on the texts, what would Helen Voss (Text 2) most likely say about the interpretation presented in the underlined portion of Text 1?

A. The perfection seen in statues of athletes suggests a high level of skill in ancient Greek sculpting techniques.

B. It is probable that statues of athletes were intended to represent specific historical figures known for their physical prowess.

C. Statues may have been altered or eroded over time, thus distorting the original artistic intent.

D. The anatomical perfection of statues does not necessarily reflect true physical proportions or training methods of historical athletes.

Rationale: Choice D is the best answer because it aligns with Voss's view that Greek statues transcend mere realistic representation, suggesting instead that these idealized forms are not direct mimics of reality but artistic elevations. Voss would likely argue that the anatomical perfection is symbolic rather than an accurate depiction of actual athletes.

Choice A is incorrect because it focuses solely on the skill of sculpting rather than the symbolic representation Voss emphasizes.

Choice B is incorrect as it suggests a literal interpretation of the statues representing specific individuals, which contradicts Voss's argument about symbolic representation.

Choice C is incorrect because it introduces an idea about physical alteration that is not supported by the text, diverting from the discussion of artistic intent.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Rhetorical Synthesis 12. While researching a topic, a student has taken the following notes: The Catawba are a Native American tribe primarily located in the southeastern United States.

Catawba culture is deeply influenced by the natural resources of the Appalachian region.

Jeremy Two-Trees is a Catawba historian, craftsman, and conservationist.

He founded the Catawba Cultural Center in Rock Hill, South Carolina, in 2005.

Anna Blue-Sky is a Catawba historian, artist, and conservationist.

She founded the Catawba Museum of Natural History in Columbia, South Carolina, in 2005.

The student wants to emphasize the duration and purpose of Two-Trees’s and Blue-Sky’s work. Which choice most effectively uses relevant information from the notes to accomplish this goal?

A. At the Catawba Cultural Center and Museum of Natural History, visitors can explore the rich history of the Catawba people who have inhabited the region for centuries.

B. Jeremy Two-Trees and Anna Blue-Sky have dedicated their careers to showcasing Catawba culture, deeply rooted in the Appalachian region.

C. Since 2005, Jeremy Two-Trees and Anna Blue-Sky have worked to conserve and celebrate Catawba culture through their respective institutions.

D. Drawing on the Appalachian influences, Catawba culture has thrived in the southeastern United States since pre-colonial times.

Rationale: Choice C is the best answer. The sentence emphasizes both the duration (the length of time) and the purpose of Two-Trees’s and Blue-Sky’s work by noting that they have been working since 2005 to conserve and celebrate Catawba culture.

Choice A is incorrect because it primarily focuses on what visitors can learn from the museums, rather than explicitly addressing the duration or purpose of the founders' work.

Choice B mentions the dedication of Two-Trees and Blue-Sky to showcasing Catawba culture but lacks specifics about the duration of their efforts, which is essential for fulfilling the student's intent.

Lastly, Choice D provides a historical overview of Catawba culture without linking it to the efforts of Two-Trees and Blue-Sky, failing to address the specific question about the duration and purpose of their work.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

MATH Nonlinear Functions

Rationale: The function provided represents the value of a piece of machinery over time, where the value decreases annually by a percentage. The formula uses a base of 0.72, which indicates that each year, the machinery retains 72% of its value from the previous year. To find the annual percentage decrease, you subtract this retention rate from 100%.

Thus, the calculation would be: 100% - 72% = 28%.

This shows that the machinery loses 28% of its value each year, which corresponds to the value of 𝑝. Therefore, the correct answer is that 𝑝 equals 28.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Rationale: The initial investment is $50,000 in 2010, and it doubles every 5 years. After 5 years (2015), the investment would be worth $100,000. After another 5 years (2020), the value would double again to reach $200,000. Therefore, according to the model, the investment reaches $200,000 in the year 2020, making the correct answer B.

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Nonlinear equations in one variable and systems of equations in two variables

Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Linear equations in one variable

Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Linear inequalities in one or two variables

Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Equivalent expressions

Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Ratios, rates, proportional relationships, and units

Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Percentages

= 91 Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Probability and conditional probability

Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam–Answer key

Percentages

= 76 Rationale:

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PSAT/NMSQT Mixed Review: Practice Problems for Your Upcoming Exam

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