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Question 1 of 6

2024 Test B English, question 20
Passage Excerpt from “How Exercise Could Help You Learn a New Language”

Excerpt from “How Exercise Could Help You Learn a New Language”

by Gretchen Reynolds

Many scientists suspect that exercise alters the biology of the brain in ways that make it more malleable and receptive to new information, a process that scientists refer to as plasticity.

But many questions have remained unanswered about movement and learning, including whether exercise is most beneficial before, during or after instruction and how much and what types of exercise might be best.

So for a new study, which was published recently in PLOS One, researchers in China and Italy decided to home in on language learning and the adult brain.

Language learning is interesting. As young children, almost all of us picked up our first language easily. We didn’t have to be formally taught; we simply absorbed words and concepts.

But by early adulthood, the brain generally begins to lose some of its innate language capability. It displays less plasticity in areas of the brain related to language. As a result, for most of us, it becomes harder to learn a second language after childhood.

To see what effects exercise might have on this process, the researchers first recruited 40 college-age Chinese men and women who were trying to learn English. The students had some facility with this second language but were far from proficient.

The researchers then divided the students into two groups. Those in one group would continue to learn English as they had before, primarily while seated in rote vocabulary-memorization sessions.

The others would supplement these sessions with exercise.

Specifically, the students would ride exercise bikes at a gentle pace (about 60 percent of their maximum aerobic capacity) beginning 20 minutes before the start of the lessons and continuing throughout the 15 minutes or so of instruction.

Both groups learned their new vocabulary by watching words projected onto large screens, together with comparable pictures, such as “apple” and a Red Delicious. They were shown 40 words per session, with the sequence repeated several times.

Afterward, the students all rested briefly and then completed a vocabulary quiz, using computer keys to note as quickly as possible whether a word was with its correct picture. They also responded to sentences using the new words, marking whether the sentences were accurate or, in the case of “The apple is a dentist,” nonsensical. Most linguists1 feel that understanding sentences shows greater mastery of a new language than does simple vocabulary improvement.

The students completed eight vocabulary sessions over the course of two months.

And at the end of each lesson, the students who had ridden bikes performed better on the subsequent vocabulary tests than did the students who sat still.

They also became more proficient at recognizing proper sentences than the sedentary students, although that difference did not emerge until after several weeks of instruction.

Perhaps most interesting, the gains in vocabulary and comprehension lingered longest for the cyclists. When the researchers asked the students to return to the lab for a final round of testing a month after the lessons—without practicing in the meantime—the cyclists remembered words and understood them in sentences more accurately than did the students who had not moved.

“The results suggest that physical activity during learning improves that learning,” says Simone Sulpizio, a professor of psychology and linguistics at the University Vita-Salute San Raffaele in Milan, Italy, and a study co-author.

These improvements extend beyond simply aiding in memorization, she added. The exercise also deepened language learners’ grasp of how to use their newly acquired words.

This study involved college students performing relatively light exercise, though, and cannot tell us whether other people completing other types of exercise would achieve the same results.

It also offers no clues about what is occurring inside the brain that might be contributing to the benefits of the exercise. But many past studies have shown that exercise prompts the release of multiple neurochemicals in the brain that increase the number of new brain cells and the connections between neurons, Dr. Sulpizio says. These effects improve the brain’s plasticity and augment the ability to learn.

From a real-world standpoint, the study’s implications might seem at first to be impractical. Few classrooms are equipped with stationary bicycles. But specialized equipment is probably unnecessary, Dr. Sulpizio says.

“We are not suggesting that schools or teachers buy lots of bicycles,” she says. “A simpler take-home message may be that instruction should be flanked by physical activity.”

From “How Exercise Could Help You Learn a New Language” by Gretchen Reynolds from THE NEW YORK TIMES, August 16, 2017. Copyright © 2017 The New York Times Company.

1linguists: scientists who study language

Question

Read these sentences from paragraph 17.

These improvements extend beyond simply aiding in memorization, she added. The exercise also deepened language learners’ grasp of how to use their newly acquired words.

Which sentence from the excerpt best explains why Sulpizio feels confident in the conclusion stated in these sentences?

  • A“They were shown 40 words per session, with the sequence repeated several times.” (paragraph 10)
  • B“They also responded to sentences using the new words, marking whether the sentences were accurate or, in the case of ‘The apple is a dentist,’ nonsensical.” (paragraph 11)
  • C“And at the end of each lesson, the students who had ridden bikes performed better on the subsequent vocabulary tests than did the students who sat still.” (paragraph 13)
  • D“They also became more proficient at recognizing proper sentences than the sedentary students, although that difference did not emerge until after several weeks of instruction.” (paragraph 14)
Show the answer

Correct answer: D

The question asks which sentence from the excerpt best supports Sulpizio’s assertion in paragraph 17 that exercise went beyond helping with memorization to deepen the language learners’ ability to use new vocabulary.

A. Incorrect. This sentence merely describes what the language-learning sessions were like, without making any claims about how the exercise affected the subjects’ understanding of how to use new words.

B. Incorrect. While this sentence does address the fact that learners were required to think about how the new words should be used rather than just memorizing the words, it does not discuss results such as how the exercise affected their ability to do this.

C. Incorrect. This sentence establishes only that exercise helped with the memorization of new words, not that exercise deepened learners’ grasp of how to use the new words.

D. CORRECT. The fact that learners who exercised were better at identifying when the new words were used correctly in sentences directly supports Sulpizio’s assertion that the exercise deepened their grasp of how to use the new words.

Question analysis

This textual evidence question quotes Simone Sulpizio’s conclusion that exercise did more than help learners memorize new English words. Students choose the sentence from the article that best explains why she can be confident of it. All four choices come from the article’s account of the study, so students must match evidence to the exact claim rather than to its general topic.

NYS standards
  • 7R1 textual evidence and inferences
  • 7R8 evaluating arguments and claims
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 evidence questions usually match a quotation to a stated claim. This claim has two parts, gains beyond memorizing and a better grasp of usage, and two quotations touch it closely, a sharper test than typical grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from several paragraphs or stanzas
Reading level
Passage: about grade 11, 764 words; question and choices: about grade 11, 142 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Sulpizio’s claim has two parts, gains beyond memorizing and a better grasp of using words, and two of the quotations each touch one part. The vocabulary result is real evidence that exercise helped, but of the very memorizing she says the gains went beyond, and the sentence-task description mentions using words but reports no result. Only a result about sentences proves the claim, so the question rewards asking of each line what it shows, not what it is about.

  1. A very close wrong answer major Choosing the answer

    The vocabulary-test result in paragraph 13 and the sentence result in paragraph 14 are worded alike, cyclists outperforming students who sat still; only the skill measured, memorizing words or using them, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  2. Reading between the lines moderate Working it out

    Students must map the claim’s two halves onto the study’s two measures: vocabulary tests show memorization, and recognizing proper sentences shows the “grasp of how to use” new words. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  3. Evidence in several places minor Working it out

    The four quotations come from paragraphs 10, 11, 13 and 14, and each must be weighed against a claim made later, in paragraph 17. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: Pin down what the quoted claim says the exercise achieved, then test each sentence by asking whether it reports a result that proves that specific achievement.

Traps

  • Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
  • True but not the answer: A choice says something accurate about the text that does not answer this question.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    Sulpizio says the exercise did more than help students memorize words. It “deepened language learners’ grasp of how to use their newly acquired words.” A grasp is an understanding. You need the sentence that best proves this claim. Proof should be a result, not just a description.

  2. Break the claim into two parts

    • Part 1: the gains went “beyond simply aiding in memorization.” Memorization is learning words by heart.
    • Part 2: the cyclists got better at using the words.

    So the proof must show the bike riders did better with words in sentences. A test that only checks memory won’t prove it.

  3. Check each choice

    • A (paragraph 10) tells how many words were shown. It gives no result.
    • B (paragraph 11) describes the sentence task. But it doesn’t say who did better.
    • C (paragraph 13) is a result. But it is about “vocabulary tests,” which check memory. That is the part she says the gains went beyond.
    • D (paragraph 14) says the cyclists “became more proficient at recognizing proper sentences than the sedentary students.” Proficient means skilled. Sedentary means sitting still. That is a result about using words.

  4. Pick the answer

    Watch out: C is very tempting. It shows that exercise helped. But it proves the wrong kind of help. Only one choice shows the cyclists did better at using words in sentences. So the answer is D.

Why this answer and not the closest wrong one

C is the closest wrong answer. Both C and D say the bike riders beat the students who sat still. The difference is the skill that was tested. C’s vocabulary tests show memory. D’s sentence test shows the learners knew how to use the words, which is exactly Sulpizio’s claim.

More questions like this

The original DOE question
Question 20 as printed on page 174 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 174, question 20. Open page 174 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).
The passage “Excerpt from “How Exercise Could Help You Learn a New Language”” as printed (pages 171–172)The passage “Excerpt from “How Exercise Could Help You Learn a New Language”” as printed on page 171 of the DOE handbook.The passage “Excerpt from “How Exercise Could Help You Learn a New Language”” as printed on page 172 of the DOE handbook.

Question 2 of 6

2026 Practice Test D English, question 8
Passage Excerpt from “How We Made the First Flight”

Excerpt from “How We Made the First Flight”

by Orville Wright

In 1903 brothers Wilbur and Orville Wright conducted experiments related to flying machines. These experiments would eventually lead to air travel becoming a reliable form of transportation.

During the night of December 16, 1903, a strong cold wind blew from the north. When we arose on the morning of the 17th, the puddles of water, which had been standing about camp since the recent rains, were covered with ice. The wind had a velocity of 10 to 12 meters per second (22 to 27 miles an hour). We thought it would die down before long, and so remained indoors the early part of the morning. But when ten o’clock arrived, and the wind was as brisk as ever, we decided that we had better get the machine out and attempt a flight. We hung out the signal for the men of the Life Saving Station.1 We thought that by facing the flyer into a strong wind, there ought to be no trouble in launching it from the level ground about camp. We realized the difficulties of flying in so high a wind, but estimated that the added dangers in flight would be partly compensated for by the slower speed in landing.

Final Preparations

We laid the track on a smooth stretch of ground about one hundred feet north of the new building. The biting cold wind made work difficult, and we had to warm up frequently in our living room, where we had a good fire in an improvised stove made of a large carbide2 can. By the time all was ready, J. T. Daniels, W. S. Dough and A. D. Etheridge, members of the Kill Devil3 Life Saving Station; W. C. Brinkley of Manteo, and Johnny Moore, a boy from Nags Head,4 had arrived.

We had a “Richard” hand anemometer with which we measured the velocity of the wind. Measurements made just before starting the first flight showed velocities of 11 to 12 meters per second, or 24 to 27 miles per hour. . . .

Audacity—and Calculation

Wilbur having used his turn in the unsuccessful attempt on the 14th, the right to the first trial now belonged to me. After running the motor a few minutes to heat it up, I released the wire that held the machine to the track, and the machine started forward in the wind. Wilbur ran at the side of the machine, holding the wing to balance it on the track. Unlike the start on the 14th, made in a calm, the machine, facing a 27-mile wind, started very slowly. Wilbur was able to stay with it till it lifted from the track after a forty-foot run. One of the Life Saving men snapped the camera for us, taking a picture just as the machine had reached the end of the track and had risen to a height of about two feet. The slow forward speed of the machine over the ground is clearly shown in the picture by Wilbur’s attitude. He stayed along beside the machine without any effort.

Flight

The course of the flight up and down was exceedingly erratic, partly due to the irregularity of the air, and partly to lack of experience in handling this machine. The control of the front rudder was difficult on account of its being balanced too near the center. This gave it a tendency to turn itself when started; so that it turned too far on one side and then too far on the other. As a result the machine would rise suddenly to about ten feet, and then as suddenly dart for the ground. A sudden dart when a little over a hundred feet from the end of the track, or a little over 120 feet from the point at which it rose into the air, ended the flight. As the velocity of the wind was over 35 feet per second and the speed of the machine over the ground against this wind ten feet per second, the speed of the machine relative to the air was over 45 feet per second, and the length of the flight was equivalent to a flight of 540 feet made in calm air. This flight lasted only 12 seconds, but it was nevertheless the first in the history of the world in which a machine carrying a man had raised itself by its own power into the air in full flight, had sailed forward without reduction of speed and had finally landed at a point as high as that from which it started.

From “How We Made the First Flight” by Orville Wright—Public Domain/Federal Aviation Administration

1Life Saving Station: one of the rescue stations along the Atlantic coastline that provided assistance to mariners in distress

2carbide: a very hard material composed of carbon and other heavy metals

3Kill Devil: the town of Kill Devil Hills in eastern North Carolina

4Nags Head: a town in eastern North Carolina

Question

How does paragraph 1 introduce the idea that the Wright brothers knew that their flight attempt was risky?

  • Athrough the mention of a signal to notify lifesaving experts that the flight attempt was about to begin
  • Bby providing specific details about the speed of the wind and the Wright brothers’ response to the windy conditions
  • Cby suggesting that a slower landing would be necessary at the end of the flight in order to maintain safety
  • Dthrough the indication that the Wright brothers waited indoors for most of the morning because of the poor weather
Show the answer

Correct answer: A

The question asks how paragraph 1 introduces the idea that the Wright brothers knew that their flight attempt was risky.

A. CORRECT. Paragraph 1 describes the Wright brothers hanging out “the signal” to notify the lifesaving crew to stand by as they attempted flight; the need for lifesaving experts to be available in case of an accident introduces the idea that the attempted flight might crash.

B. Incorrect. The specifics on the speed of the wind by themselves do not emphasize the danger of the flight. While the brothers admitted that the strong wind posed certain risks, they also noted that the windy conditions might make landing safer (“estimated that the added dangers in flight would be partly compensated for by the slower speed in landing” [paragraph 1]).

C. Incorrect. A slower landing was expected as a result of the windy conditions, but it was not part of a plan to increase the safety of the flight.

D. Incorrect. While the Wright brothers’ initial decision to wait to see whether the wind would die down does suggest they were concerned about the safety of the flight, the explanation of their decision to proceed with the flight shows that they expected one benefit from the poor weather: “the slower speed in landing” (paragraph 1).

Question analysis

This question on Orville Wright’s account “How We Made the First Flight” asks how the opening paragraph, which describes a cold, windy December morning at the brothers’ camp, introduces the idea that the Wright brothers knew their flight attempt was risky. Students must judge which of four details from the paragraph does that work, and the paragraph mentions both dangers and reasons for confidence.

NYS standards
  • 7R1 textual evidence and inferences
  • 7R3 plot elements and ideas
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Finding how a paragraph introduces an idea is grade 7 work, but this paragraph is long and old-fashioned, every choice points to something it mentions, and students must decide which detail most clearly signals that the brothers saw a risk.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from one paragraph or stanza
Reading level
Passage: about grade 7, 816 words; question and choices: about grade 10, 93 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Paragraph 1 states the danger outright only in its last sentence, and that sentence then weighs it against a gentler landing, so the choice built on the brothers’ response to the wind is the strongest pull. The key rests on a quieter detail whose meaning comes from a footnote: men from a rescue station were signaled before the attempt. Students must decide which detail shows the brothers preparing for trouble, not just noticing the weather, and that test is narrower than most expect.

  1. Reading between the lines moderate Working it out

    The key never says danger: students must connect “the signal for the men of the Life Saving Station” to footnote 1, rescue stations for “mariners in distress,” and see that summoning rescuers means expecting trouble. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  2. Every choice must be checked moderate Choosing the answer

    All four details come from paragraph 1, and its plainest admission of danger, “We realized the difficulties of flying in so high a wind,” sits inside a wrong choice, so each detail must be weighed for what it shows. (Embretson & Wetzel, 1987)

  3. Complex sentences minor Understanding the question

    The paragraph’s last sentence sets danger against benefit, “the added dangers in flight would be partly compensated for by the slower speed in landing,” and students must untangle it to see the brothers playing the risk down. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)

Strategy: Locate each of the four details in paragraph 1, reread the sentence it sits in, and ask what that detail on its own reveals about what the brothers feared could go wrong.

Traps

  • Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
  • Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    This asks how paragraph 1 first shows that the Wright brothers knew their flight was risky. Risky means it could end badly. All four choices name details from paragraph 1. Your job is to find the detail that shows them getting ready for trouble.

  2. Find the signal in paragraph 1

    Paragraph 1 says “We hung out the signal for the men of the Life Saving Station.” The small number 1 after “Station” points to footnote 1 at the end of the excerpt. Read it. A Life Saving Station was “one of the rescue stations along the Atlantic coastline that provided assistance to mariners in distress.” Mariners are sailors. Distress means danger or trouble.

  3. Work out what the signal means

    The brothers called rescue workers before they tried to fly. People call rescuers only when someone might get hurt. So the signal shows the brothers knew the flight could go wrong. They wanted help close by in case of a crash.

  4. Check each choice

    • A fits. Signaling rescuers shows the brothers planned for trouble.
    • B does not fit. The wind speeds are only numbers. The brothers’ response was to fly anyway, thinking “there ought to be no trouble in launching.”
    • C does not fit. The slower landing was a side effect of the wind. They counted it as a plus, not as a safety step they needed.
    • D does not fit. They stayed inside only “the early part of the morning,” hoping the wind would die down. Then they went out in the same wind.

    Watch out: B is tempting because the paragraph says “We realized the difficulties of flying in so high a wind.” But that same sentence weighs those dangers against a slower landing. It plays the risk down.

  5. Choose the answer

    The call to the rescue station is the detail that shows the brothers preparing for danger. So the answer is A, “through the mention of a signal to notify lifesaving experts that the flight attempt was about to begin.”

Why this answer and not the closest wrong one

B is the closest wrong choice. The paragraph does admit the wind made flying harder. But the brothers then argue the danger down: a slower landing would partly make up for it. A shows them acting on the risk. They called in rescuers before they flew. You only do that if you think something could go wrong.

More questions like this

The original DOE question
Question 8 as shown on the DOE’s digital test, page 15 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test D English, page 15, question 8.
The passage “Excerpt from “How We Made the First Flight”” as printed (pages 13–14)The passage “Excerpt from “How We Made the First Flight”” as printed on page 13 of the DOE handbook.The passage “Excerpt from “How We Made the First Flight”” as printed on page 14 of the DOE handbook.

Question 3 of 6

2024 Test A English, question 38
Passage 5 Reasons Physical Books Might Be Better Than E-Books

5 Reasons Physical Books Might Be Better Than E-Books

by Shaunacy Ferro

Though e-book1 readers have become a more common sight around town, traditional books still have their evangelists.2 According to The New York Times, e-book sales have been falling in 2015. Print definitely isn’t dead. In fact, according to some research, it may actually be a better choice for some readers. While scientists are still trying to tease out exactly how digital reading affects us differently, here are five ways e-books might be inferior to their dead-tree cousins.

E-books can reduce reading comprehension.

In a study of middle schoolers, West Chester University researchers found that students who read on iPads3 had lower reading comprehension than when they read traditional printed books. They discovered that the kids sometimes skipped text in favor of interactive features in the e-books, suggesting that certain multimedia in children’s e-books can be detrimental to the practice of reading itself. However, the researchers noted that some interactive features in e-books are designed to enhance comprehension, and that those might be more helpful than game-type interactive graphics.

Young kids can get distracted by e-books.

Similar results were found by a small study by the Joan Ganz Cooney Center that consisted of 32 kids reading e-books and print books with their parents. It found that “enhanced” e-books might be distracting. Kids who read enhanced e-books—ones with interactive, multimedia experiences—were more engaged with them physically, but in the end they remembered fewer narrative details than those who read print books or basic e-books.

You remember less about a book’s timeline.

Another study of adults also found that e-books can be hard to absorb. The researchers asked 25 people to read a 28-page story on a Kindle4 and 25 to read the story in paperback, then asked the readers to put 14 events from the story in chronological order. Those who read the story on a Kindle performed worse on the chronology test than the book readers, though they performed about the same as print readers in other tests. Earlier research by the same scholars, from Stavanger University in Norway, found that Norwegian 10th graders also remembered more about texts if they read them in print rather than on a computer screen.

They’re not great as textbooks.

While e-book textbooks are often cheaper (and easier to carry) than traditional door-stop5 textbooks, college students often don’t prefer them. In some surveys of college kids, the majority of students have reported preferring print books. However, a 2012 study from the UK’s National Literacy Trust of kids ages 8 to 16 found that more than 50 percent of children reported preferring screen reading.

They’re tiring.

Staring at a lit screen can be tiring for the eyes and the brain. A 2005 study from Sweden found that reading digitally required a higher cognitive workload than reading on paper. Furthermore, staring at LED6 screens at night can disrupt sleep patterns. A 2014 Harvard study found that people who used e-readers with LED screens at night slept worse and were more tired the next day. So, if you’re going to go for an e-book, go for one without the backlight.

The take-away message? If you’re really trying to absorb material, you might want to go for a physical book. And if you’re going to be up all night studying, turn off the backlight.

However, all this may not mean that reading on a Kindle is really going to melt your brain. For instance, reading an e-book on a computer is a much different experience than reading on a Kindle, which is specifically designed for consuming books. So, too, is playing with an interactive e-book on an iPad, compared to using a simpler e-book device that only presents the text, with no opportunities to click away into digital distractions.

And some studies have found that part of the difference between the way people absorb information from e-books versus paper might be due to approaching e-books differently—in one test, participants didn’t regulate their study time with digital books like they did with paper texts, leading to worse performances. It’s possible that our expectations of e-book reading—as well as the different designs of the digital reading experience on a computer or iPad or Kindle—might affect how we approach the text and how much effort we put into studying them. As generations of e-book readers evolve, and people become more accustomed to the idea of sitting down with a digital textbook, these factors could change—for better or for worse.

“5 Reasons Physical Books Might Be Better Than E-Books” by Shaunacy Ferro from MENTAL FLOSS, October 2, 2015. Copyright © 2015 Mental Floss, Inc.

1e-book: an electronic book, a publication made available digitally for reading on a computer or other device

2evangelists: advocates or supporters

3iPads: tablet computers

4Kindle: device for reading e-books

5door-stop: a reference to the idea that some textbooks are large and heavy enough to hold a door open

6LED: Light-emitting diode; LEDs are often used as a backlight for electronic devices such as smart phones and tablets.

Question

How does paragraph 7 fit into the overall structure of the passage?

  • AIt indicates where the author changes the purpose of the writing.
  • BIt introduces the author’s opinion on the issue.
  • CIt signals a shift in the position of the author.
  • DIt begins the author’s commentary on the preceding information.
Show the answer

Correct answer: D

The question asks for an explanation of the role of paragraph 7 in the overall structure of the passage.

A. Incorrect. The purpose of paragraphs 2–6 is to present reasons physical books might be better than e-books, and paragraph 7 offers summarizing “take-away” advice based on those reasons. As a result, it may seem as though the author’s purpose for writing the entire passage has shifted. However, the author’s advice in paragraph 7, that readers who want to learn from reading “might want to go for a physical book,” makes it clear that paragraph 7, like paragraphs 2–6, continues to serve the same purpose for the passage that the writer expresses in paragraph 1: to inform readers that printed books “may actually be a better choice for some readers” than e-books.

B. Incorrect. In paragraph 7, the author does offer the advice that readers who want to absorb material “might want to go for a physical book” rather than an e-book. Even though the author makes the statement favoring physical books for those who want to learn from their reading, the author is not sharing a personal opinion. Instead, the author offers the advice as a summary of the information presented in paragraphs 2–6, which explore various studies about the advantages of physical books over e-books. Furthermore, the idea that physical books are sometimes a better option is not introduced for the first time in paragraph 7. Instead, it is introduced early in the passage, when the author states in paragraph 1 that physical books “may actually be a better choice for some readers.”

C. Incorrect. Paragraph 7 presents a clear shift in style and content from paragraphs 2–6. Paragraphs 2–6 are each preceded by a heading stating a reason physical books might be a better choice than e-books, and each paragraph provides research evidence. Paragraph 7 shifts to stating a “take-away message”—the author’s advice—which is based on the reasons in paragraphs 2–6. Paragraph 7’s different style and content do not, however, signal a change in the author’s position. Instead, the author’s advice in paragraph 7 (“if you’re really trying to absorb material, you might want to go for a physical book”) actually reinforces the position first introduced in paragraph 1 that physical books “may actually be a better choice for some readers.”

D. CORRECT. The author uses paragraphs 2–6 to present “five ways e-books might be inferior” (paragraph 1) to physical books. Each of paragraphs 2–6 presents one reason for the inferiority of e-books, based on a scientific study. Paragraph 7 indicates a shift because it describes neither a reason e-books might be inferior nor a scientific study. Instead, it presents personal commentary: the “take-away,” or conclusion, the author draws from the studies and evidence presented in paragraphs 2–6. That commentary consists of the author’s own practical advice to readers who want to retain information that they read (“you might want to go for a physical book”) and to those who are “going to be up all night studying” (“turn off the backlight”).

Question analysis

This text-structure question asks how paragraph 7, a two-sentence paragraph that follows the five research sections, fits into the overall structure of an article arguing that printed books might be better than e-books. Students must compare it with the opening claim and the paragraphs around it, and the four choices use similar abstract wording about the author's purpose, opinion and position.

NYS standards
  • 7R5 structure and genre features
  • 7R6 point of view and author position
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 students analyze how sections contribute to a text, but here all four choices are abstract statements about the author's purpose and position, and telling them apart means tracking the argument from the first paragraph to the last.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from the whole text
Reading level
Passage: about grade 10, 829 words; question and choices: about grade 8, 49 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

All four choices are abstract claims about the author's purpose and position, so none can be checked against a single sentence. Paragraph 7 does feel like a turn, from studies to advice, which makes the choices about a changed purpose or position tempting, but the advice repeats the view the first paragraph set out. The real hedge comes one paragraph later, and the closest call is whether paragraph 7 introduces a view or comments on evidence already given.

  1. A very close wrong answer major Choosing the answer

    The right choice and the one saying paragraph 7 introduces the author's opinion both find the author's own voice there; they part on whether that view is new, and paragraph 1 already said print “may actually be a better choice”. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  2. How, not what moderate Working it out

    The question asks what paragraph 7 does in the article, a short take-away after five research sections, so its advice about physical books and backlights matters only for its role. (Anderson & Krathwohl, 2001)

  3. Evidence in several places minor Working it out

    Judging the claims of a shift or a change needs both ends of the article, the stance of paragraph 1 and the “However” that opens paragraph 8. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: Compare what paragraph 7 does with what paragraphs 1–6 do: where was the author's view first stated, and what is new in paragraph 7? Then match that role to a choice.

Traps

  • Wrong part of the text: A choice is true of another paragraph, stanza or speaker than the one asked about.
  • Wrong purpose or structure: Names a purpose, structure or effect that the part does not serve, or describes what a part says when the question asks what it does.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Know what the question asks

    This asks about the structure of the passage, which means how its parts fit together. You need to name the job paragraph 7 does compared with the paragraphs around it.

  2. Map the passage first

    Paragraph 1 states the author’s view: print “may actually be a better choice for some readers.” Paragraphs 2 through 6 each sit under a bold heading. Each one reports research on one way e-books might be worse than print.

  3. Read paragraph 7

    It begins, “The take-away message?” A take-away is the lesson you carry away. Then the author advises, “If you’re really trying to absorb material, you might want to go for a physical book.” The author also says to “turn off the backlight” when studying late. Both tips come from the studies just before. So paragraph 7 is the author commenting on that evidence.

  4. Check each choice

    • D fits: it “begins the author’s commentary on the preceding information,” and preceding means coming before.
    • A is wrong because the purpose doesn’t change, since the advice still shows print may be better.
    • B is wrong because the author’s opinion first appears in paragraph 1, not paragraph 7.
    • C is wrong because the author softens the view only later, in paragraph 8, with “all this may not mean.”

    Watch out: B is tempting because paragraph 7 really is the author’s own voice. But it is not the first time you hear it.

  5. Choose the answer

    Paragraph 7 turns the research in the five sections into advice, which is commentary on what came before. So the answer is D.

Why this answer and not the closest wrong one

B comes closest, since paragraph 7 really is the author speaking. But the author’s view already appeared in paragraph 1. Paragraph 7 doesn’t introduce it. It sums up the research before it and turns that research into advice. That is commentary on the preceding information, as D says.

More questions like this

The original DOE question
Question 38 as printed on page 61 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 61, question 38. Open page 61 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).
The passage “5 Reasons Physical Books Might Be Better Than E-Books” as printed (pages 58–59)The passage “5 Reasons Physical Books Might Be Better Than E-Books” as printed on page 58 of the DOE handbook.The passage “5 Reasons Physical Books Might Be Better Than E-Books” as printed on page 59 of the DOE handbook.

Question 4 of 6

2018 Test B Math, question 8

Question

M=3N=P4=Q+5=R7>0M=3N=\frac{P}{4}=Q+5=\frac{R}{7}> 0

Based on the statement above, which variable has the greatest value?

  • AMM
  • BNN
  • CPP
  • DRR
Show the answer

Correct answer: D

Break the equations apart to each equal MM:

M=3NM=3N

M=P4M=\frac{P}{4}

M=Q+5M=Q+5

M=R7M=\frac{R}{7}

Pick a number to substitute into the equations, and solve the equations to find the values of MM, NN, PP, QQ, and RR.

Let M=2M=2. Since all the equations are equal to 2, substitute 2 to find each variable.

M=3NM=3N

2=3N2=3N

23=N\frac{2}{3}=N

M=P4M=\frac{P}{4}

2=P42=\frac{P}{4}

8=P8=P

M=Q+5M=Q+5

2=Q+52=Q+5

−3=Q-3=Q

M=R7M=\frac{R}{7}

2=R72=\frac{R}{7}

14=R14=R

Variable RR has the greatest value.

Question analysis

This algebra question sets five expressions equal to one another and to a positive number, then asks which variable has the greatest value. It tests whether students can rewrite each variable in terms of one shared value and compare them. What makes it tricky is that there are no numbers to compute, so each variable's size has to be reasoned out.

NYS standards
  • 7.EE.2 rewriting expressions to show relationships
  • 6.EE.7 one-step equations
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students rewrite expressions to see how quantities relate, usually one equation at a time. This chain of five linked expressions, with no numbers to compute and a positivity condition to use, is a reasoning task beyond routine grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
3 steps
Reading level
Question and choices: about grade 10, 16 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The question rewards a strategy, not a calculation: once the shared value is named, each variable follows in one line and R is clearly largest. Without that step, students judge by how the expressions look, and the look is backwards, since the 3 in 3N makes N small and the 7 under R makes R large. The positivity condition at the end is easy to skip but is what fixes the order.

  1. Variables instead of numbers major Understanding the question

    There are no numbers to compute: five variables are tied together in the one chain M = 3N = P/4 = Q + 5 = R/7, and each must be compared through the shared value. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)

  2. No obvious method moderate Working it out

    Nothing says how to compare; the efficient move is to name the common value, or pick one such as 12, and rewrite each variable, which students must think of themselves. (Schoenfeld, 1985)

  3. Much to keep track of minor Working it out

    Five relations and the condition > 0 must be held at once; the condition matters, since with a negative common value the order of M, N, P and R would reverse. (Sweller, 1988; Carpenter, Just & Shell, 1990)

Strategy: Call the shared value k, a positive number, and rewrite each variable as an expression in k; or substitute a convenient positive value such as 12 and compare the results.

Traps

  • Equation written backwards: Writes a comparison the wrong way round, word for word: "six times as many students as professors" as 6S = P. The bigger quantity gets the bigger number.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Undoing division
ab=c means a=b×c\frac{a}{b} = c \text{ means } a = b \times c
a is the top of the fraction, b is the bottom, and c is the result. Multiplying undoes dividing. So if a divided by b is c, then a is b times c.
Undoing multiplication
b×a=c means a=c÷bb \times a = c \text{ means } a = c \div b
b is the number multiplied by a, and c is the result. Dividing undoes multiplying. So to get a alone, divide c by b.

  1. Understand the chain

    The statement is a chain of equal signs. It says five expressions all have the same value. The last part says that value is greater than 0, so it is positive.

    You need to find which letter has the largest value.

  2. Pick a value to test

    All five expressions are equal, so give them one shared value. Pick a positive number that 3 divides evenly. That way N will be a whole number.

    Let the shared value be 12. Then M=12M = 12, and each of the other four expressions also equals 12.

  3. Solve for each letter

    Undo each operation to find each letter. Divide to undo times. Multiply to undo divide. Subtract to undo plus.

    3N=12, so N=12÷3=43N = 12 \text{, so } N = 12 \div 3 = 4

    P4=12, so P=12×4=48\frac{P}{4} = 12 \text{, so } P = 12 \times 4 = 48

    Q+5=12, so Q=12−5=7Q + 5 = 12 \text{, so } Q = 12 - 5 = 7

    R7=12, so R=12×7=84\frac{R}{7} = 12 \text{, so } R = 12 \times 7 = 84

  4. Compare the values

    The values are M = 12, N = 4, P = 48, Q = 7 and R = 84. R is the largest.

    Watch out: 3N does not make N big. It means 3 times N equals M, so N is only one third of M. That trap points to choice B. Also, P is big, but R is bigger. Check every letter before you pick choice C.

    So the answer is D, R.

Check your answer

Think without numbers. R divided by 7 is M, so R is 7 times M. P is only 4 times M. N is a third of M, and Q is 5 less than M. Since M is positive, 7 times M is the biggest.

More questions like this

The original DOE question
Question 65 as printed on page 154 of the DOE handbook.
As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 154, question 65. Open page 154 of the handbook (PDF)

Question 5 of 6

2026 Practice Test D Math, question 48

Question

The perimeter of square W is twice the perimeter of equilateral triangle X. What is the ratio of the length of one side of square W to the length of one side of equilateral triangle X?

  • A3:8
  • B2:3
  • C3:2
  • D2:1
Show the answer

Correct answer: C

First, set up the ratio of the perimeter of the square to the triangle as 2:1 because the question states that the perimeter of the square is twice the perimeter of the triangle.

Recognizing that the square has 4 equal sides and that an equilateral triangle has 3 sides, use division to find the ratio of the sides.

Perimeter: 2:1=212 : 1 = \frac{2}{1}

Sides:

2413=24÷13=\frac{\frac{2}{4}}{\frac{1}{3}} = \frac{2}{4} \div \frac{1}{3} =

24×31=64=\frac{2}{4} \times \frac{3}{1} = \frac{6}{4} =

32=3:2\frac{3}{2} = 3 : 2

Question analysis

The perimeter of square W is twice the perimeter of equilateral triangle X, and students find the ratio of a side of the square to a side of the triangle. This ratio question uses perimeters of regular shapes with no lengths given. Turning a comparison of perimeters into one of sides, and keeping the ratio in the order asked, are the tricky parts.

NYS standards
  • 7.RP.3 multistep ratio and percent problems
  • 7.EE.4 equations and inequalities from problems
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 ratio problems usually supply numbers to work with. This one gives only a relationship between two perimeters, so students must bring in the number of sides of each shape themselves and keep the ratio in the order asked.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
3 steps
Reading level
Question and choices: about grade 9, 36 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The question turns a statement about perimeters into a ratio of sides, and the natural guess, that the sides keep the perimeters’ 2 to 1, ignores that the square shares its perimeter among 4 sides and the triangle among 3. Choosing a triangle perimeter such as 12 makes the comparison concrete. The order of the ratio still has to be checked at the end, because its reverse is listed too.

  1. Turning words into math moderate Understanding the question

    “The perimeter of square W is twice the perimeter of equilateral triangle X” must become 4s = 2 × 3t, with the 2 on the triangle’s side; written backward, it gives the triangle the larger perimeter. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

  2. Variables instead of numbers moderate Understanding the question

    No side length is given, so students must either work with letters for the two sides or choose a convenient perimeter themselves, such as 12 for the triangle. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)

  3. A very close wrong answer minor Choosing the answer

    The ratios 3:2 and 2:3 use the same two numbers, so only keeping the square’s side first, as the question orders it, separates the answer from its reverse. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

Strategy: Pick an easy side length for the triangle, find its perimeter, double that for the square, divide by the square's number of sides, and write square to triangle.

Traps

  • Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
  • Wrong operation: Adds instead of multiplying, divides the wrong way round, turns a ratio or rate upside down, or undoes a step in the wrong direction (subtracts what should be added back).
  • Equation written backwards: Writes a comparison the wrong way round, word for word: "six times as many students as professors" as 6S = P. The bigger quantity gets the bigger number.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Perimeter of a square
P=4sP = 4s
P is the perimeter, the distance around the shape. s is the length of one side. A square has 4 equal sides, so its perimeter is 4 times one side.
Perimeter of an equilateral triangle
P=3tP = 3t
An equilateral triangle has 3 equal sides. t is the length of one side. So its perimeter is 3 times one side.
Ratio
a:ba : b
A ratio compares two amounts in order. a : b means a compared with b. The order matters, so write the amounts in the order the question names them.

  1. Sort out the question

    Square W has a perimeter twice as long as the perimeter of triangle X. Equilateral means all 3 sides of X are equal.

    You need the ratio of one side of the square to one side of the triangle, in that order. No lengths are given, so you can pick a size to try.

  2. Pick a size for the triangle

    Choose an easy side length for the triangle, such as 2 units. All 3 sides are 2, so its perimeter is:

    P=3×2=6P = 3 \times 2 = 6

  3. Find the square’s side

    The square’s perimeter is twice the triangle’s:

    2×6=122 \times 6 = 12

    The square has 4 equal sides, so divide by 4:

    s=12÷4=3s = 12 \div 4 = 3

    Each side of the square is 3 units.

  4. Write the ratio in order

    The square comes first, then the triangle. Their sides are 3 and 2, so the ratio is 3 : 2.

    Watch out: 2 : 1, choice D, compares the perimeters, not the sides. The square splits its perimeter into 4 sides, the triangle into only 3. Choice B, 2 : 3, puts the triangle first. Choice A, 3 : 8, comes from giving the triangle the bigger perimeter.

    So the answer is C, 3:2.

Check your answer

Try a different size. Give the triangle sides of 4. Its perimeter is 12, so the square’s is 24. Each side of the square is 24÷4=624 \div 4 = 6. The ratio 6 : 4 simplifies to 3 : 2. The size does not change the ratio.

More questions like this

The original DOE question
Question 48 as shown on the DOE’s digital test, page 121 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test D Math, page 121, question 48.

Question 6 of 6

2026 Practice Test C Math, question 18

Question

I. s−ts - t
II. st2st^{2}
III. sts^{t}

If s is a positive integer and t is a negative integer, which of the above expressions must be a positive number?

  • AII only
  • BI and II only
  • CII and III only
  • DI, II, and III
Show the answer

Correct answer: D

Each of the three expressions must be considered:

Expression I: s−ts - t, where s is a positive integer and t is a negative integer:

Subtracting a negative integer is the equivalent of adding a positive integer, so s−ts - t is equivalent to finding the value of s+(−t)s + (-t), which must result in a positive number.

Expression II: st2st^{2}, where s is a positive integer and t is a negative integer:

Squaring a negative integer results in a positive integer, so s(−t)2s(-t)^{2} is equivalent to finding the value of st2st^{2}, which must result in a positive number.

Expression III: sts^{t}, where s is a positive integer and t is a negative integer:

A negative exponent results in the reciprocal of the same exponential expression, so sts^{t} is equivalent to finding the value of 1s(−t)\frac{1}{s^{(-t)}}, which must result in a positive number.

Therefore, Expressions I, II, and III must all result in a positive number.

Question analysis

Three expressions, s − t, s times t squared, and s to the power t, are listed, and students decide which must be positive when s is a positive integer and t is a negative integer. It tests sign rules for subtraction and multiplication and the meaning of a negative exponent. Each expression has to be judged for every possible pair, not just one example.

NYS standards
  • 8.EE.1 integer exponent properties
  • 7.NS.1c rational number subtraction
  • 7.NS.2a rational number multiplication
Grade level
Grade 8 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students learn sign rules for subtracting and multiplying signed numbers. Here they reason about letters rather than numbers, decide what must always hold, and handle a negative exponent, a grade 8 idea.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
3 steps
Reading level
Question and choices: about grade 5, 42 words.
Corrected from the DOE handbook
  • Two steps of the explanation that treated t as a positive number were corrected.
  • A punctuation error in the explanation was corrected.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The three expressions test three different sign facts: subtracting a negative, squaring a negative, and raising to a negative power. The last is the trap, since a negative exponent seems to promise a negative result when it really gives a fraction, and that belief alone leads to a listed choice. Trying s = 2 and t = −3 gives 5, 18 and 1/8, all positive, and the rules show why no other pair can change that.

  1. Variables instead of numbers moderate Understanding the question

    No values are given for s and t, only their signs, and must means each expression has to be positive for every such pair, not just for one example. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)

  2. Something you must already know moderate Working it out

    Expression III needs the meaning of a negative exponent, s to the power t equals 1 over s to the power −t, a grade 8 rule the question does not state. (Anderson & Krathwohl, 2001)

  3. Every choice must be checked minor Choosing the answer

    Each of the three expressions is judged on its own and the choices combine the verdicts, so one wrong judgment anywhere points to a wrong combination. (Embretson & Wetzel, 1987)

Strategy: Try a pair such as s = 2 and t = −3 in each expression, then explain why its sign could or could not change for any other positive s and negative t.

Traps

  • Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
  • Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: The question makes t the negative integer, but two steps of the DOE’s explanation write the negative integer as −t, as if t were positive. For Expression I it says “s − (−t) is equivalent to finding the value of s + t, which must result in a positive number”: s − (−t) is not Expression I, and with the question’s t, s + t need not be positive (s = 1 and t = −2 give −1). For Expression III it says “s^(−t) is equivalent to finding the value of 1/s^t”, about s^(−t) rather than Expression III. The site now says that s − t is equivalent to s + (−t), and that s^t is equivalent to 1/s^(−t). Since t is negative, −t is a positive integer, so s + (−t) is the sum of two positive integers and 1/s^(−t) is the reciprocal of a positive integer: both positive, and the answer, I, II and III, is unchanged. The step for Expression II, s(−t)² = st², is true for any t and is unchanged.
  • Explanation: The DOE’s explanation introduces Expression III as “s^t. where s is a positive integer and t is a negative integer”, with a period where Expressions I and II (and the 2022–23 guide, which first printed this explanation) have a comma. The site has the comma.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Subtracting a number
s−t=s+(−t)s - t = s + (-t)
s and t are integers, and −t is the opposite of t. Subtracting a number is the same as adding its opposite. When t is negative, −t is positive. So subtracting t adds a positive amount.
A negative exponent
st=1s−ts^{t} = \frac{1}{s^{-t}}
s is the base and t is the exponent. When t is negative, −t is positive. So a negative exponent means 1 over the base to a positive exponent. For example, 2 to the power −3 is 1 over 2³, which is 1/8.

  1. Sort out the question

    An integer is a whole number or its opposite, such as −2, 0 or 5. Here s is a positive integer, like 1, 2 or 3. And t is a negative integer, like −1, −2 or −3. Must means always. An expression counts only if it is positive for every such pair.

  2. Try one pair of numbers

    Try s = 2 and t = −3 in each expression:

    • I: 2−(−3)=2+3=52 - (-3) = 2 + 3 = 5
    • II: 2×(−3)2=2×9=182 \times (-3)^{2} = 2 \times 9 = 18
    • III: 2−3=123=182^{-3} = \frac{1}{2^{3}} = \frac{1}{8}

    All three are positive this time. Now see why that always happens.

  3. Explain expression I

    Use the rule for subtracting:

    s−t=s+(−t)s - t = s + (-t)

    t is negative, so its opposite, −t, is positive. So s − t is a positive plus a positive. That is always positive.

    Watch out: subtracting does not always make a number smaller. Subtracting a negative makes it bigger. Missing this leads to choice C.

  4. Explain expression II

    t2t^{2} means t × t. A negative times a negative is positive, so t2t^{2} is always positive. Then s×t2s \times t^{2} is a positive times a positive. That is always positive too.

  5. Explain expression III

    Use the rule for a negative exponent:

    st=1s−ts^{t} = \frac{1}{s^{-t}}

    −t is a positive integer, so s−ts^{-t} is a positive integer. So sts^{t} is 1 over a positive number. That is a positive fraction.

    Watch out: a negative exponent does not make the answer negative. It makes a fraction. Thinking it does leads to choice B, I and II only.

  6. Choose the answer

    Each of the three expressions is positive for every positive s and negative t. None of them can ever be zero or negative.

    So the answer is D, I, II, and III.

Check your answer

Try the values closest to 0: s = 1 and t = −1. I gives 1−(−1)=21 - (-1) = 2. II gives 1×(−1)2=11 \times (-1)^{2} = 1. III gives 1−1=11=11^{-1} = \frac{1}{1} = 1. All three are still positive.

More questions like this

The original DOE question
Question 18 as shown on the DOE’s digital test, page 91 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test C Math, page 91, question 18. This is the DOE’s version, before the corrections listed in the analysis.

Sample #572945