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 A English, question 49
Passage Excerpt from The Highest Tide

Excerpt from The Highest Tide

by Jim Lynch

The narrator’s summer job is collecting marine specimens in Puget Sound, Washington. In this excerpt, he is looking for specimens in the mudflats before daybreak. Mudflats, or flats, are coastal landforms created when sediment and silt from tides are deposited as the tides recede.

I rounded the oyster beds, to the far side. . . . It was low tide by then, and I saw the water hesitating at its apex, neither leaving nor returning, patiently waiting for the gravitational gears to shift. Dozens of anxious clams started squirting in unison like they did whenever vibrating grains of sand warned them predators were approaching. I stopped and waited with them, to actually see the moment when the tide started returning with its invisible buffet of plankton for the clams, oysters, mussels and other filter feeders. It was right then, ankle deep in the Sound, feet numbing, eyes relaxed, that I saw the nudibranch.1

In all my time on the flats I’d never seen one before. I’d read about them, sure. I’d handled them at aquariums but never in the wild, and I’d never even seen a photo of one this stunning. It was just three inches long but with dozens of fluorescent, orange-tipped hornlike plumes jutting from the back of its see-through body that appeared to be lit from within.

Nudibranchs are often called the butterflies of the sea, but even that understates their dazzle. Almost everything else in the northern Pacific is dressed to blend with pale surroundings. Nudibranchs don’t bother, in part because they taste so lousy they don’t need camouflage to survive. But also, I decided right then, because their beauty is so startling it earns them a free pass, the same way everyday life brakes for peacocks, parade floats. . . .

The dark mudflats loomed like wet, flattened dunes stretching deep into Skookumchuck Bay in front of our house. From a distance, they looked too barren to support sea life. Up close, they still did, unless you knew where to find the hearty clams, worms and tiny creatures that flourish in mud. . . . I’m not sure why I decided to take a look. It was still an hour before sunrise, and I knew exactly what the bars2 looked like in the moonlight, but for some reason, I couldn’t resist.

I heard it long before I saw it. It was an exhale, a release of sorts, and I instantly wondered if a whale was stranded again. We had a young minke3 stuck out there two summers prior, and it made similar noises until the tide rose high enough for rescuers to help free it. . . . I looked for a hulking silhouette but couldn’t find one. I waited, but there were no more sounds. Still, I went toward what I thought I’d heard, avoiding stepping into the mud until I had to. I knew the flats well enough to know I could get stuck just about anywhere. The general rule was you didn’t venture out past the shells and gravel with an incoming tide. I sank up to my knees twice, and numbing water filled my boots.

. . . I kept stepping toward the one sound I’d heard, a growing part of me hoping I’d find nothing at all. When I stopped to rest and yank up my socks, my headlamp crossed it. My first thought? A giant octopus.

Puget Sound has some of the biggest octopi in the world. They often balloon to a hundred pounds. Even the great Jacques Cousteau4 himself came to study them. But when I saw the long tubular shape of its upper body and the tangle of tentacles below it, I knew it was more than an octopus. I came closer, within fifty feet, close enough to see its large cylindrical siphon5 quiver. I couldn’t tell if it was making any sounds at that point, because it was impossible to hear anything over the blood in my ears. . . .

The creature’s body came to a triangular point above narrow fins that lay flat on the mud like wings, but it was hard to be sure exactly where it all began or ended, or how long its tentacles truly were, because I was afraid to pry my eyes off its jumble of arms for more than half a second. I didn’t know whether I was within reach, and its arms were as big around as my ankle and lined with suckers the size of half-dollars. If they even twitched I would have run. So, I was looking at it and not looking at it while my heart spangled my vision. I saw fragments, pieces, and tried to fuse them in my mind but couldn’t be certain of the whole. I knew what it had to be, but I wouldn’t allow myself to even think the two words. Then I gradually realized the dark shiny disc in the middle of the rubbery mass was too perfectly round to be mud or a reflection.

It was too late to smother my scream. Its eye was the size of a hubcap.6

From THE HIGHEST TIDE by Jim Lynch. Copyright © 2005 by Jim Lynch. Used by permission of Bloomsbury USA. All rights reserved.

1nudibranch: type of sea slug

2bars: sandbars

3minke: species of small whale

4Jacques Cousteau: renowned French oceanographer

5siphon: tube-like organ that is used for drawing in or removing fluids

6hubcap: removable cap over the end of a wheel axle

Question

Read these sentences from paragraph 8.

So, I was looking at it and not looking at it while my heart spangled my vision. I saw fragments, pieces, and tried to fuse them in my mind but couldn’t be certain of the whole.

The sensory language “spangled my vision,” “I saw fragments, pieces,” and “tried to fuse them in my mind” conveys the narrator’s

  • Aextreme excitement about making a great discovery.
  • Breluctant acceptance that he needs to leave the mudflats.
  • Cterrified confusion about the creature in the mudflats.
  • Dsudden concern about his personal safety.
Show the answer

Correct answer: C

The question asks what the sensory language in the sentences from paragraph 8 conveys about the narrator.

A. Incorrect. While the narrator does not leave the mudflats and is curious about what has been found, the main emotions described in paragraph 8 are fear and confusion as the narrator tries to comprehend the size of the animal.

B. Incorrect. The language focuses on the narrator’s inability to organize what he sees into useful thoughts and conclusions, and while the narrator feels fear in paragraph 8—“I was afraid” and “I would have run”—the narrator refuses to leave the mudflats out of curiosity.

C. CORRECT. The phrase “spangled my vision” illustrates that the narrator cannot fully recognize what has appeared on the mudflats. The sight is so amazing, the narrator is trying to “fuse” together “fragments” and “pieces” because seeing the creature has created so much emotion in the narrator that he feels confused.

D. Incorrect. While the narrator is feeling some fear, as expressed in paragraph 8, the phrases actually indicate that the narrator’s amazement causes him to struggle to take in the view of the creature before him.

Question analysis

This question about sensory language asks what three phrases, including “spangled my vision,” convey about the narrator as he stares at a huge creature in the mud in an excerpt from The Highest Tide. Students must interpret unusual imagery and choose among emotions that all seem possible at such a startling moment.

NYS standards
  • 7R4 word meaning and choice
  • 7L5 figurative language and word relationships
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Interpreting sensory language for a character's state of mind is grade 7 work, but spangled is an unusual verb, and the paragraph partly supports several of the emotions offered, so the choice must be matched precisely to the quoted phrases.
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 6, 902 words; question and choices: about grade 7, 92 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 quoted phrases are about perception, not feeling: the narrator sees fragments and cannot assemble them, while his heart pounds hard enough to blur his sight. The fear is clear from the surrounding sentences, where he is afraid to look away and ready to run, and that context makes the choice about personal safety very tempting. The answer must cover both the terror and the confusion, and the word “spangled” can mislead readers into hearing excitement.

  1. Figurative or literary language major Understanding the question

    The phrases describe seeing in pieces, “looking at it and not looking at it”, a heart that “spangled” his vision, “fragments” he cannot “fuse”, and the emotion has to be read from that broken sight. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  2. A very close wrong answer moderate Choosing the answer

    The right choice and the one about concern for his safety both name fear; they part on what the quoted phrases show, a mind unable to piece the creature together or a worry about its reach. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  3. Hard words minor Understanding the question

    “Spangled”, to scatter with glittering spots, is a rare word, and its sparkle can suggest delight, which opens a reading of excitement to students who miss the fear around it. (Perfetti, 2007; Freedle & Kostin, 1993)

Strategy: Ask what the three quoted phrases together say about how the narrator is seeing and thinking at this moment, then choose the emotion that accounts for all three, not just one.

Traps

  • True but not the answer: A choice says something accurate about the text that does not answer this question.
  • 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.

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

    Sensory language describes what a character sees, hears or feels. This asks what feeling the three quoted phrases show. Your answer must explain all three phrases, not just one.

  2. Explain the hard words

    To spangle means to cover with glittering spots. His heart pounds so hard that his sight seems to sparkle and blur. Fragments are small broken pieces. To fuse means to join together.

  3. Put the phrases together

    He sees only “fragments, pieces.” He tries “to fuse them in my mind” but “couldn’t be certain of the whole.” So he is confused, unable to tell what the creature really is. The sentences around them show he is also terrified. He is “afraid to pry my eyes off” its arms, and his heart is racing.

  4. Check each choice

    • C fits: “terrified confusion” covers both his fear and his broken, puzzled seeing.
    • A is wrong because “spangled” may sound happy, but he is frightened, not thrilled.
    • B is wrong because he never decides to leave, and he would run only if the arms moved.
    • D is wrong because the phrases show confused seeing, and his fear has been growing since paragraph 6.

    Watch out: D is close, since he is afraid. But it leaves out the confusion the phrases show.

  5. Choose the answer

    The phrases show a frightened narrator who cannot piece together what he sees. So the answer is C.

Why this answer and not the closest wrong one

D comes closest, because the narrator truly fears for his safety. But the quoted phrases are about how he sees: in pieces he can’t join. That is confusion. C names both the fear and the confusion, so it fits all three phrases.

The original DOE question
Question 49 as printed on page 67 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 67, question 49. Open page 67 of the handbook (PDF)
The passage “Excerpt from The Highest Tide” as printed (pages 64–65)The passage “Excerpt from The Highest Tide” as printed on page 64 of the DOE handbook.The passage “Excerpt from The Highest Tide” as printed on page 65 of the DOE handbook.

Question 2 of 6

2026 Practice Test B English, question 18
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

How does the interaction between the narrator and the professor in paragraphs 26–28 contribute to the development of the theme?

  • AIt illustrates the professor’s patience as the narrator argues against making the expedition.
  • BIt reveals the narrator’s frustration with his limited role in making decisions for the zoological society.
  • CIt emphasizes the professor’s desire to acquire new specimens for the zoological society at any cost.
  • DIt shows the narrator’s acceptance of his assignment despite his personal objections.
Show the answer

Correct answer: D

The question asks how the interaction between the narrator and the professor in paragraphs 26–28 contributes to the development of the theme.

A. Incorrect. Paragraphs 26–28 do not show the narrator arguing against making the expedition. He instead argues that it is unnecessary for the professor to pay to send extra men on the expedition. The narrator points out that he can ask for assistance if he does, in fact, find great auks (“ ‘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’ ” [paragraph 28]).

B. Incorrect. When the professor criticizes the narrator’s blind acceptance of the theory about the existence of the auks, the narrator is frustrated and embarrassed. This frustration does not stem from his inability to make decisions for the zoological society.

C. Incorrect. The professor states that “ ‘what I want you to do is to get those birds here safely’ ” (paragraph 27), which indicates that his main priority is the birds’ safety rather than acquiring specimens regardless of the consequences (i.e., at any cost).

D. CORRECT. Paragraph 26 describes the professor and the narrator making practical plans for the expedition (“we made out a list of articles necessary for me and itemized the expenses I might incur”), indicating the narrator’s acceptance of his assignment while also revealing that he does not anticipate a “successful termination to the expedition.” Paragraph 28 further describes the personal objections of the narrator, who believes that adding extra men to the expedition is pointless (“ ‘a useless expense’ ”), since he does not expect to find any great auks to bring back.

Question analysis

This theme question on In Search of the Unknown asks how paragraphs 26–28, in which the narrator and Professor Farrago talk over supplies, expenses and how many men to bring, contribute to the development of the theme. Students must decode formal, old-fashioned phrasing, then judge what the interaction shows. Every choice sounds like something the excerpt might say.

NYS standards
  • 7R5 structure and genre features
  • 7R2 theme or central idea
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 theme questions trace an idea through clear events. Paragraphs 26–28 are dense with formal phrasing such as “allowing no margin for a successful termination,” and each choice pairs a real detail with a claim, which pushes the task above grade 7.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Evidence
Answered from several paragraphs or stanzas
Reading level
Passage: about grade 9, 1066 words; question and choices: about grade 13, 76 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 choice pairs a real feature of the scene with a claim, and the claims must be checked against three short paragraphs of formal prose. The narrator does object, bluntly, so the choice that has him arguing against the trip draws strongly; what he rejects is the cost of extra men, while he plans the trip itself. Students who decode “allowing no margin for a successful termination” see the whole picture: he is going, and he expects to fail.

  1. Complex sentences moderate Understanding the question

    Paragraph 26 is a 36-word sentence that ends “allowing no margin for a successful termination to the expedition,” formal wording for planning as if the search will fail. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)

  2. Reading between the lines moderate Working it out

    The narrator never says he accepts the trip; his acceptance shows in the planning, and his objection in the blunt “None” and “a useless expense” of paragraph 28. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  3. How, not what minor Working it out

    The stem asks about the theme, yet every choice describes a character’s attitude, so students must judge which attitude these paragraphs show rather than look for a stated theme. (Anderson & Krathwohl, 2001)

Strategy: Translate each of paragraphs 26–28 into plain modern words, then check each choice’s claim about the narrator or the professor against exactly what those three paragraphs show.

Traps

  • Half right: One half of a two-part choice is right and the other is not.
  • Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
  • 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. Figure out what the question asks

    This asks how paragraphs 26–28 build the theme. A theme is a big message of a story. Read the three paragraphs. Decide what the narrator does and what he thinks.

  2. Read paragraph 26

    Paragraph 26 says “Together we made out a list of articles necessary for me and itemized the expenses I might incur.” Articles are supplies, and itemized means listed one by one. So the narrator is planning the trip. But he sets a return date “allowing no margin for a successful termination to the expedition.” A margin is extra room. He leaves no extra time in case he finds the birds. He plans as if he will find nothing.

  3. Read paragraphs 27 and 28

    The professor asks how many men he will take. The narrator answers bluntly, which means in a short, plain way. He takes none. Extra men would be “a useless expense, unless there is something to bring back.” He still thinks the birds are not real. Yet he does not refuse to go. He accepts the job while doubting it.

  4. Check each choice

    • A does not fit. The professor is patient, but the narrator never argues against going. He only refuses to take men.
    • B does not fit. Here the narrator makes decisions himself, like his return date and how many men to take.
    • C does not fit. They count the costs, and the professor wants the birds safe. That is not “at any cost.”
    • D fits. He plans the trip but shows he thinks it is pointless.

    Watch out: A is tempting because the professor does stay calm. But the narrator is planning the trip, not fighting it.

  5. Choose the answer

    The narrator does the job while making his doubts clear. So the answer is D, “It shows the narrator’s acceptance of his assignment despite his personal objections.”

Why this answer and not the closest wrong one

A is the closest wrong choice. The professor does answer calmly, “Never mind that.” But A says the narrator argues against making the trip. He does not. He helps plan it and only objects to taking men. D captures both parts: he goes, and he still doubts.

The original DOE question
Question 18 as shown on the DOE’s digital test, page 26 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test B English, page 26, question 18.
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 3 of 6

2026 Practice Test D English, question 5
Passage A Memory Revolution

A Memory Revolution

A high school senior logs on to a computer at the library to double-check the application due date listed on a college admissions website. Nearby, a librarian helps a group of biology students use a database to search for recent studies about mammals. In the past few decades, the Internet has become an integral component of daily life for many people. The seemingly limitless power of search engines made the Internet search extremely common, and today people increasingly rely on the Internet’s vast accumulation of sources to access all types of information. Scientists are beginning to examine how this reliance is modifying the strategies people use to store and prioritize information in their mind.

A Dependable and Valuable Asset

Psychologist Benjamin Storm from the University of California, Santa Cruz, and researchers Sean Stone and Aaron Benjamin devised an experiment to study students’ tendency to depend on the Internet for facts. To begin, the scientists divided sixty participants into multiple groups, including an “Internet” group and a “memory” group, and placed them in front of computers. The Internet group was required to use the search engine Google to answer eight challenging trivia questions. In contrast, participants in the memory group were permitted to use only their personal knowledge to answer the questions. In the second round, the researchers administered notably easier questions. This time, they allowed each group the option of using Google as they answered. Their results showed that 83 percent of the Internet group continued to consult Google in the second round, while only 63 percent of the memory group chose to do so.

People’s growing inclination to rely on the Internet in order to retrieve information, particularly facts and figures, is called cognitive offloading. Canadian researcher Evan F. Risko and British researcher Sam Gilbert, who have written extensively about the topic, say a similar process has been taking place for centuries. In the past, people used resources like encyclopedias to assist their memories; however, today the Internet, serving as a vast extended memory, allows people to digitally access and retrieve much larger volumes of information. Consequently, people’s minds are free for other cognitive feats, such as connecting data, learning new information, or solving problems.

Filing Information Away

The use of the Internet also appears to be modifying the strategies people use to store information in their mind. Researchers Betsy Sparrow from Columbia University, Jenny Liu from the University of Wisconsin-Madison, and Daniel Wegner from Harvard University conducted several studies to discover how people efficiently manage their information intake.

To begin, the researchers examined how people evaluate which information deserves their effort to remember. For this experiment, participants read forty trivia facts, such as “An ostrich’s eye is bigger than its brain,” and typed the statements into a computer file. Half the participants had been previously told the file would be saved, while half believed it would be erased. Next, the participants wrote down every fact they could recall. Those who believed the information would be erased and no longer available could recall 40 percent more facts than those who thought the information would be saved.

In another experiment, the same researchers tested the ability of study participants to remember where to access information. For this trial, participants read and typed trivia statements, which they saved in folders with generic names such as “Facts” and “Items.” After spending ten minutes writing down all the facts they could recall from memory, participants were asked which folder contained a particular fact based on a keyword. For example, “Which folder has the fact about ostriches?” Overall, participants recalled the information’s location more often than the content itself, correctly identifying 49 percent of the folders for specific facts while remembering only 23 percent of the actual trivia. The researchers concluded that our memory is adapting to the Internet age by prioritizing where to locate information even when the specific details are forgotten. According to Sparrow, the Internet has become an important form of transactive memory, an external source of the recollections and associative networks that constitute memory.

As the Internet’s resources continue to expand our “external” memory, some question whether the process may cause people to depend too heavily on technology. However, Steven Pinker, a professor of psychology at Harvard University, says, “Knowledge is increasing exponentially; human brainpower and waking hours are not. Fortunately, the Internet and information technologies are helping us manage, search and retrieve our collective intellectual output at different scales, from Twitter and previews to e-books and online encyclopedias. Far from making us stupid, these technologies are the only things that will keep us smart.”

Flow diagram titled “HOW MEMORY WORKS”: an arrow labeled “New Information” points down into a box labeled “Sensory Memory,” and an arrow labeled “Attention” leads down from that box to a box labeled “Short-Term Memory.” From Short-Term Memory, an arrow points right to the note “Unrehearsed information is forgotten,” and on its left a curved arrow labeled “Rehearsal” loops from the bottom of the box back into its top, beside the note “Information is maintained through repetition.” An arrow labeled “Storage” leads down from Short-Term Memory to a box labeled “Long-Term Memory,” a curved arrow labeled “Retrieval” leads from Long-Term Memory back up into Short-Term Memory, and an arrow points right from Long-Term Memory to the note “Some information may be forgotten over time.”

Question

How does the diagram provide additional support for the topic presented in the passage?

  • AIt reveals why human brains must adapt to obtaining information from the Internet as opposed to other sources.
  • BIt indicates how people can use the Internet to help improve their long-term recollection of information.
  • CIt shows how study participants’ brains distinguished between important and unimportant details.
  • DIt depicts the idea that repetition and rehearsal are necessary to recall information when tools such as search engines are unavailable.
Show the answer

Correct answer: D

The question asks how the diagram provides additional support for the topic presented in the passage.

A. Incorrect. While the diagram indicates that the human brain has the ability to maintain different types of memory, the diagram does not show the need for the brain to adapt to obtaining information from the Internet rather than from other sources.

B. Incorrect. The diagram enhances the reader’s understanding of how long-term memories are formed, but it does not provide details about how the Internet can be used to improve long-term recollection of information.

C. Incorrect. The diagram provides an understanding of how details that are important to people can become stored because of an effort made to recall them. However, the diagram does not show how people decide which information is important and which is not.

D. CORRECT. The diagram depicts the connections that the human brain maintains between the different forms of memory. It also illustrates the idea that repetition and rehearsal are important steps in creating memories, as unrehearsed information will be forgotten. This supports the passage by highlighting the idea that access to search engines and other tools leads people to skip rehearsal and repetition steps that create memories, because people know that the information is readily accessible.

Question analysis

This question pairs “A Memory Revolution” with its flow diagram, “How Memory Works,” which follows new information from sensory memory through short-term and long-term memory, and asks how the diagram supports the topic of the passage. Students must read the diagram’s boxes, arrows and notes and relate them to an article about the Internet that never refers to the diagram, so the connection has to be worked out.

NYS standards
  • 7R1 textual evidence and inferences
  • 7R2 theme or central idea
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 students regularly connect a diagram to a text. This flow diagram of memory never mentions the Internet, so students must build the bridge to the article’s studies themselves, and every choice claims something the diagram alone cannot show.
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 14, 763 words; question and choices: about grade 12, 81 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 diagram is a general model of memory, and every choice, even the right one, goes beyond it by bringing in the Internet, search engines or the study participants. The way through is to ask which choice rests on something the diagram really shows, and only one names its rehearsal loop and the forgetting of unrehearsed information. The strongest pull uses the diagram’s long-term memory and retrieval but claims the Internet improves recollection, the opposite of what paragraph 5’s experiment found.

  1. Combines ideas moderate Working it out

    The diagram never mentions the Internet and the article never mentions the diagram, so students must join its rehearsal loop to paragraph 5’s finding that people who expected the facts to be saved remembered fewer. (Embretson, 1998; Daniel & Embretson, 2010)

  2. Reading a figure, table or graph moderate Understanding the question

    Students must follow the arrows from “Attention” into short-term memory and find the “Rehearsal” loop beside “Information is maintained through repetition,” with “Unrehearsed information is forgotten” on the other side. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)

  3. Every choice must be checked minor Choosing the answer

    Three choices tie the diagram to the Internet, adaptation or the study participants, and even the key mentions search engines, so each claim must be held against the boxes and arrows actually drawn. (Embretson & Wetzel, 1987)

Strategy: Trace the diagram’s arrows from new information to long-term memory and say what each label shows, then ask which choice links that process to the studies without crediting the diagram with ideas it never shows.

Traps

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 diagram supports the article. The diagram is the flow chart called “HOW MEMORY WORKS” at the end of the passage. It never mentions the Internet. So you must find what it shows, then link that to the article.

  2. Follow the arrows in the diagram

    Start at the top. An arrow labeled “New Information” goes into the box “Sensory Memory.” The “Attention” arrow leads to “Short-Term Memory.” From there, two things can happen. On the left, a loop labeled “Rehearsal” sits beside the note “Information is maintained through repetition.” On the right, a note says “Unrehearsed information is forgotten.” A “Storage” arrow leads down to “Long-Term Memory,” and a “Retrieval” arrow leads back up.

  3. Explain what the diagram means

    To rehearse information is to repeat it, the way you practice lines for a play. To maintain something is to keep it. So the diagram says that information you repeat stays with you. Information you don’t repeat is lost. Repeating takes effort.

  4. Link the diagram to the passage

    Paragraph 5 describes people who typed forty facts. Some thought the file would be saved. Others thought it would be erased. Those who thought it would be erased “could recall 40 percent more facts.” They knew they could not look the facts up later. So they made the effort to remember. The diagram shows that effort: rehearsal. When search engines are at hand, people may skip it.

  5. Check each choice

    • A does not fit. The diagram never mentions the Internet. It does not say brains must adapt.
    • B does not fit. The diagram shows nothing about using the Internet. Paragraph 5 even found that people remembered less when they expected the facts to be saved.
    • C does not fit. The diagram shows memory in general. It shows no study participants and no sorting of important facts.
    • D fits. The “Rehearsal” loop shows that repeating information keeps it. Without a tool to look things up, that repeating is what lets you recall.

    Watch out: B is tempting because the diagram has “Long-Term Memory” and “Retrieval,” and the article calls the Internet an outside memory. But the diagram is about the brain, not the Internet.

  6. Choose the answer

    The diagram shows rehearsal keeping information and unrehearsed information being forgotten. That explains why people who can’t look facts up must work to remember them. So the answer is D, “It depicts the idea that repetition and rehearsal are necessary to recall information when tools such as search engines are unavailable.”

Why this answer and not the closest wrong one

B is the closest wrong choice. It uses the diagram’s “Long-Term Memory” and “Retrieval” labels. But the diagram never shows the Internet improving recall. The passage says the opposite: expecting the facts to be saved made people remember fewer. D rests on what the diagram really shows, the “Rehearsal” loop and the note “Unrehearsed information is forgotten.”

The original DOE question
Question 5 as shown on the DOE’s digital test, page 9 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test D English, page 9, question 5.
The passage “A Memory Revolution” as printed (pages 3–4)The passage “A Memory Revolution” as printed on page 3 of the DOE handbook.The passage “A Memory Revolution” as printed on page 4 of the DOE handbook.

Question 4 of 6

2018 Test B Math, question 42

Question

There are 1,000 cubic centimeters in 1 liter, and 1,000 cubic millimeters in 1 milliliter. How many cubic millimeters are there in 1,000 cubic centimeters?

  • A1,000
  • B10,000
  • C100,000
  • D1,000,000
Show the answer

Correct answer: D

If 1 L = 1,000 cu cm, then 1 L = 1,000 mL. Set up a proportion, letting xx = the amount of cubic millimeters in 1,000 cubic centimeters.

1,000 cu mm1 mL=x cu mm1,000 mL\frac{1{,}000\text{ cu mm}}{1\text{ mL}}=\frac{x\text{ cu mm}}{1{,}000\text{ mL}}

Solve for xx: 1,000,000 cubic millimeters are in 1,000 cubic centimeters.

Question analysis

The question gives two metric facts, cubic centimeters per liter and cubic millimeters per milliliter, and asks how many cubic millimeters are in 1,000 cubic centimeters. It tests chaining unit conversions with volume units. The hard part is that the two facts do not connect without a link the question leaves out.

NYS standards
  • 6.RP.3d converting measurement units
Grade level
Grade 6 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 6 and 7 students convert units with one given factor. This needs three linked conversions, one using a fact the question does not state, and involves cubic units, which most grade 7 students find unfamiliar.
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 13, 20 words.
Corrected from the DOE handbook
  • The units in the explanation’s proportion were 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 question gives two conversion facts that do not connect until the student supplies the link between liters and milliliters. Students who instead reach for 1 centimeter = 10 millimeters often scale a volume like a length or an area and land short by a factor of 10 or 100. Writing the unit at every step, so the units cancel, keeps both factors of 1,000 in view.

  1. Something you must already know moderate Working it out

    The chain needs 1 liter = 1,000 milliliters, which the stem never states, yet it is the only link between its two conversion facts. (Anderson & Krathwohl, 2001)

  2. Many steps moderate Working it out

    Three conversions in a row, cubic centimeters to liters, liters to milliliters and milliliters to cubic millimeters, multiply out to 1,000 × 1,000. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)

Strategy: Build a chain from cubic centimeters to liters, liters to milliliters, and milliliters to cubic millimeters, writing the units at every step so they cancel.

Traps

  • Units or scale: The answer is wanted in other units, or a rate or scale must be converted first.
  • Stops one step early: A choice is a number from partway through the solution.

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: The handbook’s proportion is 1,000 cu mm / 1 L = x cu mm / 1,000 cu mm. But 1,000 cubic millimeters make 1 milliliter, not 1 liter, and the second denominator should be the 1,000 mL that equal 1,000 cubic centimeters. The site uses 1,000 cu mm / 1 mL = x cu mm / 1,000 mL, which gives x = 1,000,000 cubic millimeters.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Volume of a cube
V=s×s×sV = s \times s \times s
V is the volume, the space inside the cube. s is the length of one side. A cube has the same length, width and height, so you multiply the side by itself three times.
  1. Sort out what you know

    You are told two facts. 1 liter (L) is 1,000 cubic centimeters (cu cm). 1 milliliter (mL) is 1,000 cubic millimeters (cu mm). You need the number of cu mm in 1,000 cu cm.

    One fact is missing. 1 liter is 1,000 milliliters. The word milli means one thousandth.

  2. Change cubic centimeters to liters

    The first fact says 1,000 cu cm is exactly 1 liter. So the amount in the question is 1 liter of space.

  3. Change liters to milliliters

    One liter is 1,000 milliliters. So 1,000 cu cm is the same as 1,000 mL.

    Watch out: you are not done yet. The question asks for cubic millimeters. Stopping at 1,000 gives choice A.

  4. Change milliliters to cubic millimeters

    Each milliliter is 1,000 cu mm. There are 1,000 milliliters, so multiply.

    1,000×1,000=1,000,0001{,}000 \times 1{,}000 = 1{,}000{,}000

    So 1,000 cu cm is 1,000,000 cu mm. The answer is D, 1,000,000.

Check your answer

Use the cube formula. A cube 1 cm on each side is 10 mm on each side. Its volume is V=10×10×10=1,000V = 10 \times 10 \times 10 = 1{,}000 cu mm. So 1,000 cu cm is 1,000×1,000=1,000,0001{,}000 \times 1{,}000 = 1{,}000{,}000 cu mm. Using only one 10 gives choice B. Using two 10s gives choice C.

The original DOE question
Question 99 as printed on page 160 of the DOE handbook.
As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 160, question 99. Open page 160 of the handbook (PDF) This is the DOE’s version, before the corrections listed in the analysis.

Question 5 of 6

2024 Test B Math, question 49

Question

Suppose that w, x, y, and z are integers, none of which are zero. Under which set of conditions would the product x2yz3|w|x^{2}yz^{3}|w| always be positive?

  • Ax is positive and w is positive.
  • Bx is negative and w is negative.
  • Cy is negative and z is negative.
  • Dx and y are negative, and z and w are positive.
Show the answer

Correct answer: C

First, analyze the role of each variable in the expression x2yz3|w|x^{2}yz^{3}|w|.

x2x^{2} will always be a positive number.

y can be a positive or a negative number.

z3z^{3} can be a positive or a negative number.

|w||w| will always be a positive number.

The expressions x2x^{2} and |w||w| will always be positive. Therefore, making the values of y and z negative would result in the expression yz3yz^{3} being positive, since a negative multiplied by a negative is positive. Thus the given product would always be positive.

Question analysis

Four nonzero integers appear in a product that includes a square, a cube and an absolute value. Students choose the set of conditions that makes the product positive every time. It tests the sign rules for multiplication together with exponents and absolute value, and the trap is judging the sign by counting negative variables without looking at what is done to each.

NYS standards
  • 7.NS.2a rational number multiplication
  • 6.EE.1 whole-number exponent expressions
  • 6.NS.7c absolute value as distance
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students learn sign rules for products of signed numbers. Here they must reason about four unknown integers under an even power, an odd power and an absolute value, and decide what is always true, which is more abstract than typical 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 6, 58 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

One insight decides the question: x² and |w| are positive whatever x and w are, so only the signs of y and z³ matter. Students who count negative letters instead of negative factors pick conditions that look balanced but leave y as the only negative factor. Students who test a single set of values can be fooled by a choice that leaves y and z unspecified.

  1. Variables instead of numbers moderate Understanding the question

    There are four variables and no numbers, and always positive must hold for every allowed value, so one test case can rule a choice out but never confirm it. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)

  2. Every choice must be checked moderate Choosing the answer

    Each set of conditions has to be checked against all four factors; the first two fix only x and w and leave y and z free to make the product negative. (Embretson & Wetzel, 1987)

  3. Something you must already know minor Working it out

    Students must know that a nonzero square and an absolute value are always positive, while an odd power such as z³ keeps the sign of z. (Anderson & Krathwohl, 2001)

Strategy: Work out, factor by factor, which signs each part of the product can take, then test each set of conditions against every factor rather than counting negatives.

Traps

  • 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.)
  • 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.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Signs in multiplication
(−a)×(−b)=a×b(-a) \times (-b) = a \times b
a and b are positive numbers, so −a and −b are negative. A negative times a negative is positive. A negative times a positive is negative. So a product is positive when it has an even number of negative factors.
  1. Sort out the question

    w, x, y and z are integers, meaning whole numbers or their negatives. None of them is 0. The product x2yz3|w|x^2 y z^3 |w| means x2×y×z3×|w|x^2 \times y \times z^3 \times |w|.

    You need the conditions that make the product positive every time, for every number that fits them.

  2. Look at x squared and |w|

    x2x^2 means x × x. Two positives or two negatives multiply to a positive. So x2x^2 is always positive.

    |w||w| is the absolute value of w, its distance from 0. It is always positive, since w is not 0.

    So x and w never change the sign of the product. Their signs do not matter.

  3. Look at y and z cubed

    y can be positive or negative. z3z^3 means z × z × z, and it has the same sign as z. For example, (−2)3=−8(-2)^3 = -8.

    So the sign of the whole product is the sign of y×z3y \times z^3. It depends only on y and z.

  4. Test each choice

    • A and B say nothing about y and z. If y = −1 and z = 1, the product is negative. So they do not always work.
    • C: y is negative, and z3z^3 is negative. A negative times a negative is positive. This always works.
    • D: y is negative and z is positive. So the product is always negative.

    Watch out: D has two negative letters, x and y. But x2x^2 is positive anyway, so y is the only negative factor.

    So the answer is C, y is negative and z is negative.

Check your answer

Try numbers for C. Let x = −2, y = −3, z = −1 and w = −5. Then x2×y×z3×|w|=4×(−3)×(−1)×5=60x^2 \times y \times z^3 \times |w| = 4 \times (-3) \times (-1) \times 5 = 60, which is positive. Even with x and w negative, the product stays positive.

The original DOE question
Question 106 as printed on page 213 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 213, question 106. Open page 213 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).

Question 6 of 6

2024 Test A Math, question 18

Question

Each number in a sequence is formed by doubling the previous number and then adding 1. If the 9th number in the sequence is 63, what is the 10th number minus the 7th number?

  • A96
  • B111
  • C112
  • D127
Show the answer

Correct answer: C

First, write an equation based on the rule described in the item. Let x be the previous number in the sequence and y be the number in the sequence. The ninth number in the sequence is 63.

2x+1=y2x + 1 = y

Determine the 10th number in the sequence, y, by making x=63x = 63 and solving:

2(63)+1=y2(63) + 1 = y

126+1=y126 + 1 = y

127=y127 = y

Determine the 8th number in the sequence, x, by making y=63y = 63 and solving:

2x+1=632x + 1 = 63

Subtract one from both sides of the equation.

2x+(1−1)=63−12x + (1 - 1) = 63 - 1

2x=622x = 62

2x2=622\frac{2x}{2} = \frac{62}{2}

x=31x = 31

Determine the 7th number in the sequence, x, by making y=31y = 31 and solving:

2x+1=312x + 1 = 31

2x+(1−1)=31−12x + (1 - 1) = 31 - 1

2x=302x = 30

2x2=302\frac{2x}{2} = \frac{30}{2}

x=15x = 15

Subtract the 7th number in the sequence from the 10th number:

127−15=112127 - 15 = 112

The difference is 112.

Question analysis

A sequence question: each number is found by doubling the one before it and adding 1, and the 9th number is 63. Students find the 10th number minus the 7th. That means running the rule forward once and backward twice, while keeping track of which position each number holds.

NYS standards
  • 7.EE.4a two-step equations
  • 6.EE.2c evaluating expressions and order of operations
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students solve two-step equations but rarely have to run a rule backward through a sequence. This mixes forward and backward steps with position counting, so it asks for more planning than a typical grade 7 task.
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 7, 32 words.
Corrected from the DOE handbook
  • A misplaced parenthesis in the explanation’s working 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

Applying the rule forward is routine; running it backward is not, and the question needs both. Students must also count positions carefully, since the 9th number is given and the 7th is two steps back, not one. Each listed wrong answer stops or slips at a different stage, so writing the four numbers in a row, 15, 31, 63 and 127, before subtracting is the reliable way.

  1. No obvious method moderate Working it out

    The rule is stated only forward, double and add 1, but the 7th and 8th numbers come before the given 9th, so the rule must be undone: subtract 1, then halve. (Schoenfeld, 1985)

  2. Many steps moderate Working it out

    One forward step reaches the 10th number, 127, two backward steps reach the 8th and 7th, 31 and 15, and a final subtraction finishes. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)

  3. Much to keep track of minor Working it out

    Four positions and their values, 7th to 10th, have to be kept straight, and the 8th number is easy to mistake for the 7th. (Sweller, 1988; Carpenter, Just & Shell, 1990)

Strategy: Apply the rule to 63 to get the 10th number; to go back a position, subtract 1 and halve, doing it twice to reach the 7th; then subtract.

Traps

  • 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).
  • Stops one step early: A choice is a number from partway through the solution.

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: Finding the 7th number, the handbook writes “2x + (1 − 1 = 31 − 1)”, with the closing parenthesis after the whole equation, so the line reads as an equation inside an expression (and 1 − 1 = 31 − 1 is false). The site now reads 2x + (1 − 1) = 31 − 1, the same step the handbook writes correctly for the 8th number (2x + (1 − 1) = 63 − 1). It leads to 2x = 30 and x = 15 as before.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

The sequence rule
y=2x+1y = 2x + 1
A sequence is a list of numbers that follows a rule. x is a number in the list, and y is the next number. To get the next number, double x and then add 1.
Going back one number
x=(y−1)÷2x = (y - 1) \div 2
y is a number in the list, and x is the one just before it. To go back, undo the rule in reverse order. The rule doubles and then adds 1. So first subtract 1, then divide by 2.
  1. Sort out the question

    Each number is “formed by doubling the previous number and then adding 1”. Previous means the one just before. The 9th number is 63. You need the 10th number minus the 7th number. So you go forward one number and back two numbers.

  2. Find the 10th number

    Use the rule with x = 63.

    y=2x+1y = 2x + 1

    y=2×63+1=126+1=127y = 2 \times 63 + 1 = 126 + 1 = 127

    The 10th number is 127. Watch out: remember to add 1. Doubling only gives 126 and leads to 111, choice B.

  3. Plan how to go back

    The 7th number comes before the 9th, so you must undo the rule. The rule doubled, then added 1. Undo the last step first: subtract 1. Then undo the doubling: divide by 2.

    x=(y−1)÷2x = (y - 1) \div 2

  4. Find the 8th number

    x=(63−1)÷2=62÷2=31x = (63 - 1) \div 2 = 62 \div 2 = 31

    The 8th number is 31. Watch out: 31 is the 8th number, not the 7th. Using it gives 127−31=96127 - 31 = 96, choice A.

  5. Find the 7th number

    Step back once more, from the 8th number. Use the same rule with y = 31.

    x=(31−1)÷2=30÷2=15x = (31 - 1) \div 2 = 30 \div 2 = 15

    The 7th number is 15.

  6. Subtract the 7th from the 10th

    127−15=112127 - 15 = 112

    Watch out: 127 alone is choice D. You still have to subtract the 7th number. So the answer is C, 112.

Check your answer

Go forward from 15 using the rule. 2×15+1=312 \times 15 + 1 = 31, then 2×31+1=632 \times 31 + 1 = 63, then 2×63+1=1272 \times 63 + 1 = 127. You land on 63 as the 9th number, so the list is right. And 127−15=112127 - 15 = 112.

The original DOE question
Question 75 as printed on page 80 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 80, question 75. Open page 80 of the handbook (PDF) This is the DOE’s version, before the corrections listed in the analysis.

Sample #8