Six SHSAT Questions

3 English and 3 math

Here are 6 random questions to try. Takers earning below 75% are unlikely to receive an offer. You have 1 minute 48 seconds per question on the real exam.

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.

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

2024 Test A English, question 28
Passage Champion of the Channel

Champion of the Channel

In 1926 an editor at the London Daily News predicted that Gertrude Ederle, an American swimmer with eighteen world records and three Olympic medals, would fail in her attempt to swim across the English Channel. He claimed that “even the most uncompromising champion of the rights and capacities of women must admit that in contests of physical skill, speed and endurance they must remain forever the weaker sex.” Yet, at only nineteen years old, Ederle not only became the first woman to accomplish this feat, she also broke the men’s record by two hours. Gertrude Ederle’s triumphant swim across the English Channel was a testimony to her determination, innovative spirit, and passion for swimming.

Crossing the English Channel is a daunting task for any swimmer. At its narrowest point, the channel measures twenty-one miles across. Its icy waters hover around sixty degrees Fahrenheit, and its unruly tides and currents toss swimmers about like bobbing corks. Stinging jellyfish, seaweed, and floating debris from shipwrecks and lost cargoes present added hazards.

For decades the channel’s perils have defeated countless swimmers. Ederle, too, failed in her first attempt to cross the channel in 1925. Just six miles short of finishing, she became ill, and her coach had to haul her out of the water. Undeterred, Ederle decided to try again. Ederle knew that if she did not complete the challenge this time, she might never get the opportunity to set this record, because a rival female swimmer was preparing to make her second attempt at the crossing as well.

To prepare for the marathon swim, Ederle found ways to improve her equipment. She and her sister Meg discovered that melted candle wax perfectly sealed goggle edges, effectively waterproofing Ederle’s goggles against hammering waves. The sisters also designed a two-piece silk swimsuit for Ederle. During her first channel-crossing attempt she had worn a standard one-piece swimsuit that, after the lengthy hours of swimming across the channel, had stretched out, filling with water and creating drag, making an already challenging task almost insurmountable. Unlike the cumbersome typical bathing suit, this silk invention weighed little and allowed for easy movement.

On August 6, 1926, Ederle waded into the channel near Cape Gris-Nez, France. At first she shivered in the bone-chilling water even though she had covered her body in eight layers of grease for insulation. Her limbs felt stiff. Her strokes were irregular. Driving forward, she fought to clear her mind and find what she called her “sphere,” a place where the sea became her only companion and the shrieks of gulls and the humming of boat engines faded away. Using a new overhand stroke called the American crawl, Ederle eventually settled into a steady pace, briskly breaking through waves.

Throughout Ederle’s swim, two tugboats accompanied her. One carried newspaper reporters who wired dispatches of her progress to shore. The other, displaying a sign that read “This way, ole kid!” with an arrow pointing forward, transported her coach, family, and friends. Her coach played songs, such as “Yes, We Have No Bananas,” on a phonograph so that Ederle could time her strokes to the rhythm. Using a net, her coach also passed her baby bottles of broth for nourishment.

For hours Ederle swam, dodging debris with an amused smile. However, as she neared the English shore, a sudden fierce storm erupted. The tides and waves forced Ederle backward, and she fought the stubborn swells for several hours. The salty water caused her tongue to swell and inflamed her ears. Yet Ederle felt indescribably happy as she churned through the sea. Finally, as she neared the English shore, the storm abated, and the tide turned. No longer fighting against her, the sea pushed her toward the shore and victory.

After fourteen hours and thirty-one minutes, Ederle, on wobbly legs, stepped onto the English shore. The waiting crowd roared, honked their automobile horns, blasted their tugboat whistles, and set off flares that flashed in the sky. Ederle had swum into history.

When Ederle returned to New York, she received a parade, where thousands of people shouted “Trudy!” Not only were everyday American citizens proud of Ederle, but she also inspired them to be more active. Over the next few years, more than 60,000 people credited her with motivating them to earn their American Red Cross swimming certificates. Gertrude Ederle’s accomplishment proved to the world that with determination and passion, it was possible for a person to achieve his or her goals.

SOLO SWIMS ACROSS THE ENGLISH CHANNEL

Earliest Speed Records

Year Swimmer Time
1875 Matthew Webb (M) 21 hours, 45 minutes
1923 Enrico Tiraboschi (M) 16 hours, 33 minutes
1926 Gertrude Ederle (F) 14 hours, 31 minutes
1926 Arnst Vierkotter (M) 12 hours, 38 minutes
Current Speed Records
Year Swimmer Time
2012 Trent Grimsey (M) 6 hours, 55 minutes
2006 Yvetta Hlavacova (F) 7 hours, 25 minutes

Question

Which statement describes how the author’s use of a problem-and-solution structure in paragraph 5 contributes to the development of ideas in the passage?

  • ADetailing the challenges presented by the cold channel waters highlights the effectiveness of Ederle’s training.
  • BDescribing Ederle’s physical difficulties during her swim provides evidence of the team effort required to ensure her safety.
  • CExplaining the difficulties that arose early in the effort helps predict the additional obstacles that occurred during Ederle’s attempt.
  • DIllustrating Ederle’s process of blocking out her discomfort shows that swimming the channel was both a mental and a physical challenge.
Show the answer

Correct answer: D

The question asks how a problem-and-solution structure in paragraph 5 contributes to the ideas presented in the passage.

A. Incorrect. The details in paragraph 5 do not provide a connection between the cold temperature of the water and the effectiveness of Ederle’s training.

B. Incorrect. The difficulties Ederle encountered were only partially relieved by her team, and her team’s efforts to ensure Ederle’s safety are not explained in the passage.

C. Incorrect. The paragraph does not focus on the relationship between the problems Ederle encountered at the start of her swim and the problems she encountered during or near the end of her swim.

D. CORRECT. The paragraph describes how the water’s temperature made Ederle uncomfortable and made it difficult for her to regulate her stroke. The paragraph continues with the explanation of how she overcame these issues by focusing her mind on the sea and tuning out the distractions in her surroundings (“the sea became her only companion and the shrieks of gulls and the humming of boat engines faded away” [paragraph 5]).

Question analysis

Gertrude Ederle's cold, stiff first hours in the English Channel are told as problem and solution, and this text-structure question asks what that pattern adds to the passage's ideas. Students must spot the troubles she met in the cold water and how she handled them, then pick the abstract statement that accounts for both halves of the pattern.

NYS standards
  • 7R5 structure and genre features
  • 7R3 plot elements and ideas
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 A problem-and-solution question about one paragraph is familiar grade 7 fare, yet these four answers are general claims about the swim, each tied to a real hardship, so students need a clear map of the paragraph before judging them.
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 9, 790 words; question and choices: about grade 14, 95 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 opening halves of the choices are all accurate, which moves the whole decision onto their second halves. Readers who notice only the physical side of the paragraph, the cold and the stiffness, reach for training, teamwork or foreshadowing to explain it. The paragraph's turning point is a mental one, clearing her mind until the noise faded, and only the statement that names both a mental and a physical challenge accounts for the problem and the solution together.

  1. How, not what major Working it out

    The question asks what paragraph 5's pairing of problems (bone-chilling water, stiff limbs, irregular strokes) with solutions (finding her “sphere”, the American crawl) does for the passage, so retelling the hardships earns nothing. (Anderson & Krathwohl, 2001)

  2. Every choice must be checked moderate Choosing the answer

    Each choice opens with a fair description of paragraph 5, the cold water, her physical difficulties, the early struggle, so only what each claims that description shows can be tested. (Embretson & Wetzel, 1987)

  3. Figurative or literary language minor Understanding the question

    The mental half of the solution is told in images, a place where “the sea became her only companion” and gulls and engines “faded away”, which must be read as blocking out discomfort. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

Strategy: Sort paragraph 5 into two lists, what went wrong for Ederle early in the swim and what she did about it, then ask what that pairing shows about the swim as a whole.

Traps

  • 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.
  • Outside knowledge: A choice is plausible in the real world but not supported by this text.
  • Wrong part of the text: A choice is true of another paragraph, stanza or speaker than the one asked about.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Learn what the question asks

    A problem-and-solution structure tells about a difficulty and then how someone deals with it. The question asks what this pattern in paragraph 5 adds to the ideas of the passage. So first sort the paragraph into problems and solutions.

  2. List the problems in paragraph 5

    When Ederle waded in, “she shivered in the bone-chilling water.” Next, “Her limbs felt stiff. Her strokes were irregular.” Limbs are arms and legs. Irregular means uneven, not steady. All of these are troubles with her body.

  3. List her solutions

    Ederle “fought to clear her mind.” She looked for what she called her “sphere.” There, “the sea became her only companion and the shrieks of gulls and the humming of boat engines faded away.” In other words, she shut out the noise and her discomfort. Then, using the American crawl, she “settled into a steady pace.”

  4. Connect problems and solutions

    The problems were physical, which means of the body. A big part of the fix was mental, which means of the mind. She calmed her thoughts so her body could keep working. So the paragraph shows that the swim tested her mind as well as her body.

  5. Check each choice

    • D fits: blocking out her discomfort shows the swim was “both a mental and a physical challenge.”
    • A is wrong because paragraph 5 never mentions her training.
    • B is wrong because her team on the tugboats appears in paragraph 6, and her safety is never discussed.
    • C is wrong because the early troubles are solved inside this paragraph instead of setting up later ones.

    Watch out: A storm does hit in paragraph 7, so C may look right. But paragraph 5 does not point ahead to it.

  6. Choose the answer

    Only D explains both the problem and the way Ederle solved it. So the answer is D.

Why this answer and not the closest wrong one

C is tempting, since a storm really does strike in paragraph 7. But paragraph 5 never hints at it. The paragraph ends with its problem solved, as Ederle is “briskly breaking through waves.” D explains both halves of the pattern: troubles of the body, eased by the mind.

The original DOE question
Question 28 as printed on page 54 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 54, question 28. Open page 54 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 “Champion of the Channel” as printed (pages 56–57)The passage “Champion of the Channel” as printed on page 56 of the DOE handbook.The passage “Champion of the Channel” as printed on page 57 of the DOE handbook.

Question 3 of 6

2026 Practice Test B English, question 17
Passage Excerpt from In Search of the Unknown

Excerpt from In Search of the Unknown

by Robert W. Chambers

It was at that time the policy of the trustees and officers of the Zoological Gardens neither to employ collectors nor to send out expeditions in search of specimens. The society decided to depend upon voluntary contributions, and I was always busy, part of the day, in dictating answers to correspondents who wrote offering their services as hunters of big game, collectors of all sorts of fauna, trappers, snarers, and also to those who offered specimens for sale, usually at exorbitant rates.

To the proprietors of . . . mangy lynxes, moth-eaten coyotes, and dancing bears I returned courteous but uncompromising refusals—of course, first submitting all such letters, together with my replies, to Professor Farrago.

One day towards the end of May, however, just as I was leaving Bronx Park to return to town, Professor Lesard, of the reptilian department, called out to me that Professor Farrago wanted to see me a moment; so I . . . retraced my steps to the temporary, wooden building occupied by Professor Farrago, general superintendent of the Zoological Gardens. The professor, who was sitting at his desk before a pile of letters and replies submitted for approval by me, pushed his glasses down and looked over them at me with a whimsical smile that suggested amusement, impatience, annoyance, and perhaps a faint trace of apology.

“Now, here’s a letter,” he said, with a deliberate gesture towards a sheet of paper impaled on a file—“a letter that I suppose you remember.” He disengaged the sheet of paper and handed it to me.

“Oh yes,” I replied, with a shrug; “of course the man is mistaken—or—”

“Or what?” demanded Professor Farrago, tranquilly, wiping his glasses.

“—Or a liar,” I replied.

After a silence he leaned back in his chair and bade me read the letter to him again, and I did so with a contemptuous tolerance for the writer, who must have been either a very innocent victim or a very stupid swindler. I said as much to Professor Farrago, but, to my surprise, he appeared to waver.

“I suppose,” he said, with his near-sighted, embarrassed smile, “that nine hundred and ninety-nine men in a thousand would throw that letter aside and condemn the writer as a liar or a fool?”

“In my opinion,” said I, “he’s one or the other.”

“He isn’t—in mine,” said the professor, placidly.

“What!” I exclaimed. “Here is a man living all alone on a strip of rock and sand between the wilderness and the sea, who wants you to send somebody to take charge of a bird that doesn’t exist!”

“How do you know,” asked Professor Farrago, “that the bird in question does not exist?”

“It is generally accepted,” I replied, sarcastically, “that the great auk has been extinct for years. Therefore I may be pardoned for doubting that our correspondent possesses a pair of them alive.”

“Oh, you young fellows,” said the professor, smiling wearily, “you embark on a theory for destinations that don’t exist.”

He leaned back in his chair, his amused eyes searching space for the imagery that made him smile.

“Like swimming squirrels, you navigate with the help of Heaven and a stiff breeze, but you never land where you hope to—do you?”

Rather red in the face, I said: “Don’t you believe the great auk to be extinct?”

“Audubon saw the great auk.”

“Who has seen a single specimen since?”

“Nobody—except our correspondent here,” he replied, laughing.

I laughed, too, considering the interview at an end, but the professor went on, coolly:

“Whatever it is that our correspondent has—and I am daring to believe that it is the great auk itself—I want you to secure it for the society.”

When my astonishment subsided my first conscious sentiment was one of pity. Clearly, Professor Farrago was on the verge of dotage—ah, what a loss to the world!

I believe now that Professor Farrago perfectly interpreted my thoughts, but he betrayed neither resentment nor impatience. I drew a chair up beside his desk—there was nothing to do but to obey, and this fool’s errand was none of my conceiving.

Together we made out a list of articles necessary for me and itemized the expenses I might incur, and I set a date for my return, allowing no margin for a successful termination to the expedition.

“Never mind that,” said the professor. “What I want you to do is to get those birds here safely. Now, how many men will you take?”

“None,” I replied, bluntly; “it’s a useless expense, unless there is something to bring back. If there is I’ll wire you, you may be sure.”

“Very well,” said Professor Farrago, good-humoredly, “you shall have all the assistance you may require. Can you leave to-night?”

The old gentleman was certainly prompt. I nodded, half-sulkily, aware of his amusement.

“So,” I said, picking up my hat, “I am to start north to find a place called Black Harbor, where there is a man named Halyard who possesses, among other household utensils, two extinct great auks—”

We were both laughing by this time. I asked him why on earth he credited the assertion of a man he had never before heard of.

“I suppose,” he replied, with the same half-apologetic, half-humorous smile, “it is instinct. I feel, somehow, that this man Halyard has got an auk—perhaps two. I can’t get away from the idea that we are on the eve of acquiring the rarest of living creatures. It’s odd for a scientist to talk as I do; doubtless you’re shocked—admit it, now!”

But I was not shocked; on the contrary, I was conscious that the same strange hope that Professor Farrago cherished was beginning, in spite of me, to stir my pulses, too.

“If he has—” I began, then stopped.

The professor and I looked hard at each other in silence.

“Go on,” he said, encouragingly.

But I had nothing more to say, for the prospect of beholding with my own eyes a living specimen of the great auk produced a series of conflicting emotions within me which rendered speech profanely superfluous.

From IN SEARCH OF THE UNKNOWN by Robert W. Chambers—Public Domain

Audubon: John James Audubon, an ornithologist and artist who created scientific illustrations of birds
dotage: a loss of reasoning brought about by old age

Question

The professor’s observations in paragraphs 15–17 create tension in the excerpt by causing the narrator to feel

  • Aflustered by the professor’s criticism of his logic.
  • Bannoyed by the professor’s sarcasm about his inexperience.
  • Cconfused by the professor’s lack of respect for his opinion.
  • Dfrustrated by the professor’s lack of interest in his theory.
Show the answer

Correct answer: A

The question asks how the professor’s observations in paragraphs 15–17 create tension in the excerpt.

A. CORRECT. The professor criticizes “ ‘you young fellows’ ” (paragraph 15), suggesting that the ideas of young scientists like the narrator are unsupported (“ ‘like swimming squirrels’ ” [paragraph 17]) and inaccurate (“ ‘but you never land where you hope to—do you?’ ” [paragraph 17] and “ ‘you embark on a theory for destinations that don’t exist’ ” [paragraph 15]). The narrator then becomes “red in the face” (paragraph 18), indicating that the narrator is upset by the professor’s criticism, and asks the professor about the great auk in an attempt to defend himself.

B. Incorrect. While the narrator does experience a negative reaction to the professor’s words, the professor is being genuine, not sarcastic. In fact, the sarcasm comes from the narrator in paragraph 14 (“ ‘It is generally accepted,’ I replied, sarcastically, ‘that the great auk has been extinct for years. Therefore I may be pardoned for doubting that our correspondent possesses a pair of them alive’ ”), not from the professor.

C. Incorrect. The professor’s observations cause the narrator to blush with embarrassment (“rather red in the face” [paragraph 18]), but the narrator understands the point that the professor is making about the narrator’s acceptance of the idea that great auks do not exist. The narrator recognizes that the professor is criticizing his youthful ideas, not his opinion.

D. Incorrect. The professor shows amusement with the narrator’s perspective. The narrator is embarrassed and upset by the professor’s words, but the narrator does not display frustration with the professor’s lack of interest in a commonly held view of the existence of a certain species of bird.

Question analysis

In this question on In Search of the Unknown, Professor Farrago makes remarks about “you young fellows,” comparing them to swimming squirrels that never land where they hope. Students must decide how these remarks in paragraphs 15–17 make the narrator feel and so create tension. The comparison is odd and old-fashioned, and the four choices name similar negative feelings with different causes.

NYS standards
  • 7R3 plot elements and ideas
  • 7R4 word meaning and choice
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 students infer feelings from a character’s reactions, usually from plainly stated emotions. Here the cause is a puzzling figurative jab about “swimming squirrels,” the reaction is shown only through a physical sign, and the choices offer four close negative feelings.
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 9, 1066 words; question and choices: about grade 9, 52 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 professor’s two images are odd, and students must decode them as a comment on how the narrator reasons before they can say why he blushes. Every choice names an unpleasant feeling, so the decision rests on its cause. “You young fellows” makes sarcasm about inexperience the natural guess, but the sarcasm in this scene is the narrator’s own, and the professor smiles “wearily” and speaks in earnest. The narrator’s pointed reply shows he followed the criticism, not that it confused him.

  1. Figurative or literary language major Understanding the question

    The criticism comes in images: young men who “embark on a theory for destinations that don’t exist” and who, like swimming squirrels, “never land where you hope to,” a picture of reasoning that goes astray. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  2. A very close wrong answer moderate Choosing the answer

    The choice about annoyance at sarcasm and the right one both name a bad reaction to the professor’s remarks; they part on the cause, sincere criticism of his logic or mockery of his youth. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  3. Reading between the lines moderate Working it out

    The narrator never names his feeling; it shows only in “Rather red in the face” and in the defensive question that follows about whether the great auk is extinct. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

Strategy: Paraphrase what the professor says about “you young fellows” in paragraphs 15–17, find how the narrator reacts in paragraph 18, and choose the feeling and the cause that both fit.

Traps

  • Wrong tone or attitude: Misjudges the tone, attitude or point of view, such as reading admiration as criticism, or taking a character's or subject's feelings for the author's.
  • 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.
  • Word match: Repeats striking words or phrases from the text, so it looks supported, but its meaning does not fit the 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

    This asks how the professor’s words in paragraphs 15–17 make the narrator feel. Tension is a feeling of strain between characters. Each choice names a feeling and a cause. Both parts must be right.

  2. Read what the professor says

    In paragraph 15 he says, “Oh, you young fellows,” and “you embark on a theory for destinations that don’t exist.” To embark means to set out on a trip. He means young men set out with an idea toward places that are not there. Their reasoning leads them to wrong answers. In paragraph 17 he adds, “Like swimming squirrels, you navigate with the help of Heaven and a stiff breeze, but you never land where you hope to—do you?”

  3. Understand the picture

    A swimming squirrel can’t really steer. It drifts with luck and the wind. The professor is saying the narrator’s thinking drifts the same way and misses the truth. That is a criticism of his logic, or reasoning. In paragraph 18, the narrator is “Rather red in the face.” He is flustered, which means embarrassed and upset.

  4. Check each choice

    • A fits. He turns red after the professor criticizes his reasoning.
    • B does not fit. Sarcasm is saying the opposite of what you mean in order to mock. The professor means what he says. The sarcastic one is the narrator, in paragraph 14.
    • C does not fit. He is not confused. He fires back a sharp question right away.
    • D does not fit. The professor answers the narrator’s idea closely, so he is interested in it.

    Watch out: B is tempting because “you young fellows” points to the narrator’s youth. But the professor is sincere, not sarcastic.

  5. Choose the answer

    The professor says the narrator’s reasoning goes astray, and the narrator turns red. So the answer is A, “flustered by the professor’s criticism of his logic.”

Why this answer and not the closest wrong one

B is the closest wrong choice. Both A and B say the narrator feels bad. But B blames sarcasm. Paragraph 14 says the narrator “replied, sarcastically,” so the sarcasm is his own. The professor means his words seriously. A names the real cause: criticism of the narrator’s thinking.

The original DOE question
Question 17 as shown on the DOE’s digital test, page 25 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test B English, page 25, question 17.
The passage “Excerpt from In Search of the Unknown” as printed (page 21)The passage “Excerpt from In Search of the Unknown” as printed on page 21 of the DOE handbook.

Question 4 of 6

2018 Test A Math, question 40

Question

In the set of consecutive integers from 12 to 30, inclusive, there are four integers that are multiples of both 2 and 3. How many integers in this set are multiples of neither 2 nor 3?

  • A5
  • B6
  • C13
  • D15
Show the answer

Correct answer: B

The question asks for integers from 12 to 30 that are not divisible by 2 or 3. The set of consecutive integers is

{12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}

Since all even numbers are divisible by 2, eliminate all even numbers, leaving the odd numbers in the set:

{13, 15, 17, 19, 21, 23, 25, 27, 29}

Eliminate those integers that are multiples of 3 (15, 21, and 27). The remaining integers are:

{13, 17, 19, 23, 25, 29}

Therefore, there are 6 numbers in the set that are multiples of neither 2 nor 3.

Question analysis

This number properties question takes the integers from 12 to 30, inclusive, and asks how many are multiples of neither 2 nor 3. Students must count the whole set, remove multiples of 2 and of 3 without removing any number twice, and count what remains. Inclusive endpoints and the overlap make it easy to miscount.

NYS standards
  • 6.NS.4 common factors and multiples
Grade level
Grade 6 content, by NYS standard
Compared with grade 7
Above grade 7 Multiples are sixth-grade content, but grade 7 problems rarely ask students to count a set under two overlapping conditions. The inclusive range and the numbers that are multiples of both make this longer and trickier than usual.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Solution
3 steps
Reading level
Question and choices: about grade 9, 30 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 gives the overlap, four multiples of both 2 and 3, which invites a subtraction method with three places to go wrong: the count of the set, the overlap, and the final complement. Each of those errors has its own choice. Listing the 19 numbers and crossing out evens and then odd multiples of 3 is slower to describe but faster and safer to do.

  1. Much to keep track of moderate Working it out

    Each of the 19 integers must be checked against two conditions, and the four multiples of 6 meet both, so they must be removed once, not twice. (Sweller, 1988; Carpenter, Just & Shell, 1990)

  2. A very close wrong answer moderate Choosing the answer

    The choices 5 and 6 differ by one, the result of counting 30 − 12 = 18 integers instead of 19, so only counting the inclusive set exactly separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

Strategy: Cross out every even number first, then cross out the odd multiples of 3 that remain, and count the survivors; listing all nineteen numbers is quick enough.

Traps

  • Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
  • Counting the ends: Inclusive or exclusive ends, fence posts, consecutive numbers: an answer that is one too many or too few, or an endpoint drawn open where it belongs closed (or the reverse).

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Counting whole numbers in a list
n=b−a+1n = b - a + 1
a is the first number and b is the last. n is how many whole numbers there are, counting both ends. You add 1 because subtracting counts the gaps, and there is one more number than gaps.
  1. Sort out the question

    The set is every integer (whole number) from 12 to 30. “Inclusive” means 12 and 30 are both in.

    A multiple of 2 is an even number. A multiple of 3 is a number in the 3 times table. You need the numbers that are neither: not even, and not in the 3 times table.

  2. Count the numbers in the set

    n=30−12+1=19n = 30 - 12 + 1 = 19

    There are 19 integers. Watch out: 30 − 12 = 18 forgets one end. That slip leads to choice A, 5.

  3. Cross out the even numbers

    Every even number is a multiple of 2, so remove them all. The odd numbers are left:

    13, 15, 17, 19, 21, 23, 25, 27, 29

    That is 9 numbers.

  4. Cross out the multiples of 3

    Check each odd number for 3. A quick test: add its digits. If the sum is in the 3 times table, so is the number. That removes 15, 21 and 27. These are left:

    13, 17, 19, 23, 25, 29

    Watch out: only 12, 18, 24 and 30 are multiples of both. Removing just those gives 19 − 4 = 15, choice D. “Neither” means you remove every multiple of 2 and every multiple of 3.

  5. Count what is left

    Six numbers are left. Watch out: 13 is how many you crossed out, choice C. The question asks for the ones left. So the answer is B, 6.

Check your answer

Count another way. Of the 19 numbers, 10 are even. Of the 9 odd ones, 3 are multiples of 3. So 10 + 3 = 13 are crossed out, and 19 − 13 = 6 are left. Same answer.

The original DOE question
Question 97 as printed on page 88 of the DOE handbook.
As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 88, question 97. Open page 88 of the handbook (PDF)

Question 5 of 6

2024 Test B Math, question 56

Question

A rectangular field had a length of 80 meters and a width of 50 meters. The field was recently enlarged, with the length increased by 15% and the width increased by 10 meters. By what percentage was the area of the field increased?

  • A26.5%
  • B35%
  • C38%
  • D42.5%
Show the answer

Correct answer: C

The original area of the field was 4,000 square meters.

80×50=4,00080\times 50=4{,}000

When the field was enlarged, the length increased by 15%, so the new length is 92 meters.

80×15%80\times 15\%

80×0.15=1280\times 0.15=12

80+12=9280+12=92

The width increased by 10 meters, so the new width is 60 meters.

50+10=6050+10=60

The new area of the field is 5,520 square meters.

92×60=5,52092\times 60=5{,}520

The percent increase is found by finding the difference between the two areas and dividing the increase by the original area.

5,520−4,000=1,5205{,}520-4{,}000=1{,}520

1,520÷4,000=0.38=38%1{,}520\div 4{,}000=0.38=38\%

Question analysis

A rectangular field 80 meters long and 50 meters wide has its length increased by 15 percent and its width by 10 meters. Students find the percent by which the field's area grew. It tests percent increase with rectangle area, and the tricky part is that one side changes by a percent and the other by a fixed length.

NYS standards
  • 7.RP.3 multistep ratio and percent problems
  • 6.G.1 area of polygons
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 percent problems usually apply one percent change to one quantity. This changes a length by a percent and a width by a fixed amount, then asks for the percent change in area, a five-step chain with two kinds of change.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Solution
5 steps
Reading level
Question and choices: about grade 6, 39 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

Each step is ordinary, but the two changes are stated in different units, one a percent and one in meters, which tempts students to force them into the same form. Adding the two percents is the most natural shortcut and lands close to the right value, because it misses only the small extra area where both changes overlap. Computing the old and new areas directly is slower but leaves nothing to chance.

  1. Combines ideas moderate Working it out

    Percent change has to be combined with area: the length grows by a percent and the width by meters, and the question asks for the percent change of their product. (Embretson, 1998; Daniel & Embretson, 2010)

  2. Many steps moderate Working it out

    Five computations are chained: the new length 92, the new width 60, the areas 4,000 and 5,520, and the increase 1,520 as a share of 4,000. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)

  3. A very close wrong answer minor Choosing the answer

    The 35% from adding 15% and 20% sits only 3 points below 38%, so a rough estimate of the new area cannot rule it out. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

Strategy: Compute the new length and the new width, find the old and new areas, and divide the increase in area by the original area.

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.
  • Units or scale: The answer is wanted in other units, or a rate or scale must be converted first.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Area of a rectangle
A=l×wA = l \times w
A is the area, the flat space inside. l is the length and w is the width. Multiplying counts how many unit squares fit, row by row.
Percent increase
percent increase=new−oldold×100\text{percent increase} = \frac{\text{new} - \text{old}}{\text{old}} \times 100
old is the starting amount, and new is the amount after. new − old is how much it grew. Dividing by old compares the growth with the start. Multiplying by 100 turns that into a percent.
  1. Sort out the question

    The field was 80 meters long and 50 meters wide. The length grew by 15%, a percent. The width grew by 10 meters, a number of meters. These are two different kinds of increase.

    You need the percent by which the area grew.

  2. Find the old area

    You need the old area to compare with the new one.

    A=80×50=4,000A = 80 \times 50 = 4{,}000

    The old field covered 4,000 square meters.

  3. Find the new length and width

    15% of 80 is 0.15×80=120.15 \times 80 = 12. So the new length is 80+12=9280 + 12 = 92 meters.

    The new width is 50+10=6050 + 10 = 60 meters.

    Watch out: 10 meters is not 10%. Treating it as 10% leads to 26.5%, choice A. Treating 15% as 15 meters leads to 42.5%, choice D.

  4. Find the new area

    Multiply the new length by the new width.

    A=92×60=5,520A = 92 \times 60 = 5{,}520

    The new field covers 5,520 square meters. That is 5,520−4,000=1,5205{,}520 - 4{,}000 = 1{,}520 square meters more.

  5. Find the percent increase

    percent increase=5,520−4,0004,000×100=1,5204,000×100=38\text{percent increase} = \frac{5{,}520 - 4{,}000}{4{,}000} \times 100 = \frac{1{,}520}{4{,}000} \times 100 = 38

    The area grew by 38%. Watch out: The width grew by 20%, since 10 is 20% of 50. Adding 15% + 20% = 35% gives choice B. That misses the extra corner piece where both new strips meet.

    So the answer is C, 38%.

Check your answer

Use growth factors. The length is multiplied by 1.15. The width goes from 50 to 60, so it is multiplied by 1.2. The area is multiplied by 1.15×1.2=1.381.15 \times 1.2 = 1.38, which is 38% more.

The original DOE question
Question 113 as printed on page 215 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 215, question 113. Open page 215 of the handbook (PDF)

Question 6 of 6

2018 Test A Math, question 30

Question

Today, Tien’s age is 14\frac{1}{4} of Jordan’s age. In 2 years, Tien’s age will be 13\frac{1}{3} of Jordan’s age. How old is Jordan today? 

  • A4 years old
  • B6 years old
  • C12 years old
  • D16 years old
Show the answer

Correct answer: D

First, set up an equation to express Tien’s age (TT) and Jordan’s age (JJ) today:

T=14JT=\frac{1}{4}J

Two years from now, Tien’s age will be T+2T+2, and Jordan’s age will be J+2J+2.

Set up an equation about the relationship between Tien’s age and Jordan’s age in two years:

T+2=13(J+2)T+2=\frac{1}{3}(J+2)

Solve the above equation for TT:

T=13(J+2)−2T=\frac{1}{3}(J+2)-2

Now set the two equations equal to each other and solve for JJ:

14J=13(J+2)−2\frac{1}{4}J=\frac{1}{3}(J+2)-2

14J=13J−43\frac{1}{4}J=\frac{1}{3}J-\frac{4}{3}

−112J=−43-\frac{1}{12}J=-\frac{4}{3}

J=−43(−121)J=-\frac{4}{3}\left(-\frac{12}{1}\right)

J=16J=16

Question analysis

This age word problem says Tien is one fourth of Jordan's age today and will be one third of Jordan's age in two years, then asks for Jordan's current age. Students must turn two fractional relationships into equations and solve them together. Both people age by the same two years, and it is easy to solve for the wrong person.

NYS standards
  • 8.EE.8c systems in real-world problems
  • 8.EE.7b linear equations with rational coefficients
Grade level
Grade 8 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 equations have one unknown on one side, like 3x + 5 = 20. This one links two unknown ages with fractional coefficients and leads to a variable on both sides, which is grade 8 algebra.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Solution
4 steps
Reading level
Question and choices: about grade 1, 31 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 difficulty is in the setup: two fractional relationships at two different times, with both people aging. Once the equations are right, the algebra is short, but it ends with two ages and only one is asked for. Testing the choices against both conditions is a reliable alternative that avoids the algebra entirely.

  1. Turning words into math major Understanding the question

    The second sentence must become T + 2 = (J + 2)/3; writing J/3, or forgetting that Jordan also ages two years, breaks the equation. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

  2. Error-prone arithmetic moderate Working it out

    Substituting J/4 for T leaves J/4 + 2 = (J + 2)/3, an equation with fractions on both sides that must be cleared, usually by multiplying by 12. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

Strategy: Let Jordan's age be J, write Tien's age as J/4, and set J/4 + 2 equal to one third of (J + 2); or test each choice against both conditions.

Traps

  • Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Distributive property
a×(b+c)=a×b+a×ca \times (b + c) = a \times b + a \times c
a, b and c are any numbers. To multiply a sum by a number, multiply each part of the sum, then add. It works because a groups of (b + c) is the same as a groups of b plus a groups of c.
  1. Sort out what you know

    Today, Tien’s age is 14\frac{1}{4} of Jordan’s age. That means Jordan is 4 times as old as Tien.

    In 2 years, both of them will be 2 years older. Then Tien’s age will be 13\frac{1}{3} of Jordan’s. So Jordan will be 3 times as old as Tien. You need Jordan’s age today.

  2. Name the ages with a letter

    Let t stand for Tien’s age today. Jordan is 4 times as old, so his age is 4t, which means 4 times t. Add 2 years to each age:

    PersonTodayIn 2 years
    Tienttt+2t + 2
    Jordan4t4t4t+24t + 2

    Watch out: Jordan gets 2 years older too. Do not forget to add 2 to his age.

  3. Write an equation for later

    In 2 years, Jordan’s age will be 3 times Tien’s age. Write that as an equation:

    4t+2=3×(t+2)4t + 2 = 3 \times (t + 2)

    Use the distributive property on the right side. Multiply both t and 2 by 3:

    4t+2=3t+64t + 2 = 3t + 6

  4. Solve for Tien’s age

    Take 3t away from both sides. Doing the same thing to both sides keeps them equal:

    t+2=6t + 2 = 6

    Now take 2 away from both sides:

    t=4t = 4

    So Tien is 4 years old today. Watch out: 4 is Tien’s age, not Jordan’s. Choice A, 4 years old, is a trap.

  5. Find Jordan’s age

    Jordan is 4 times as old as Tien:

    4×4=164 \times 4 = 16

    So the answer is D, 16 years old.

Check your answer

Put 16 back into the story. Today, Tien is 16 ÷ 4 = 4. In 2 years, Tien is 6 and Jordan is 18. Is 6 one third of 18? Yes, because 18 ÷ 3 = 6. Choice C fails: Tien would be 3, then 5, and 5 is not a third of 14.

The original DOE question
Question 87 as printed on page 87 of the DOE handbook.
As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 87, question 87. Open page 87 of the handbook (PDF)

Sample #10