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 55
Passage Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”

Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”

by Emma Marris

The author of this opinion article attended a symposium, or conference, in Missoula, Montana, at which biologists and other scientists discussed species of plants and animals that are not native to the areas in which they live.

Invasive species are scary. It was ecologist Charles Elton, back in the 1950s, who introduced the militaristic “invasion” metaphor to describe exotic plants and animals—but there’s no question some can be extremely destructive.

The brown tree snake has eaten a dozen kinds of forest birds in Guam to extinction; zebra mussels clog pipes around the Great Lakes; the common house cat turns out to be, in Australia, a mercilessly effective killer of cute, fluffy marsupials like the bilby and the numbat.

As scientists have sounded the alarm about these pests, the public has gotten the message. Citizen groups rip out non-native plants. Native gardens have become increasingly popular, both as ways to celebrate the unique flora of each region and as tiny hot spots of diversity. Native trees provide food for native bugs, which feed native birds. Food chains developed over thousands of years of co-evolution unfold in our backyards. . . .

So we’ve learned, scientists and laypeople alike, that native species are good and non-natives are bad.

Julian Olden, a biologist at the University of Washington, Seattle, who co-organized the symposium, recently polled nearly 2,000 ecologists. Among his findings: a substantial number of them said they would immediately eradicate a hypothetical non-native forest plant, even if it were shown to have no effect on the forest. Olden calls this the “guilty even when proven innocent” approach.

That kind of approach is not very useful on a rapidly changing planet.

Exotics Are Everywhere

Climate change is making it harder even to decide who the invaders are.

How, scientists at the symposium wondered, do you define “native” on a warming planet, when plants and animals are already moving toward the poles or up mountainsides in search of climate conditions they can tolerate? Should we consider them “invasive” in their new homes? Regardless of what we label them, conservationists will be reluctant to remove them from their new environs—to do so would stymie1 their chances of adapting to the warmer future we’re creating.

And then there are the non-natives that we actually like. Most domestic crops are exotic in most of the places they’re grown, but there are even wild exotics that “do good,” forming useful relationships with native species.

Edwin Grosholz of the University of California, Davis, told the recent symposium about one such relationship. On beaches in his state, non-native spartina grass has become important habitat for the endangered California clapper rail, a plump shorebird with a downward curving bill more at home on land than in the air. A project to rip out and poison the spartina—which grows in dense swaths that exclude many other shorebirds—saw clapper rail numbers go tumbling downward.

There are other examples like that. The endangered southwestern willow flycatcher nests in “invasive” tamarisk shrubs. Many native (and beautiful) Hawaiian flowers are now pollinated by the Japanese white-eye bird—because the native pollinators have been driven extinct by other non-native species.

Should we impose further risk on already endangered natives by severing these relationships? Or should we admire the resilience of nature and let such “well-behaved” exotics stay? . . .

Leave them alone, more and more conservationists are arguing, and stop focusing obsessively on categorizing species as native or non-native. Mark Davis, an ecologist at Macalester College in St. Paul, Minnesota, once considered himself an “invasion biologist”—but not anymore. “I am actively trying to get the field to retire the invader narrative,” he said in Missoula.

A Good Thing, Not the Only Thing

After all, nativeness is just one environmental value, and arguably not as important as preventing extinctions and preserving biodiversity. In some cases we can best serve biodiversity by leaving the non-natives alone or even—brace yourself, now—introducing them on purpose.

This is the thinking behind, for example, installing the Aldabra tortoise on the islands of Mauritius. The islands lost their own large tortoises, and the fruiting plants that formerly had their seeds moved around by these fruit-loving reptiles have been on the decline. A tortoise that’s related to the island’s large tortoises—a non-native from the Seychelles in the Indian Ocean that was intentionally introduced in 2004—is now handling some of that work.

Most of the time, for the time being, conserving species still means focusing on supporting them in their historical habitats, planting natives and removing non-natives. We can and should do that in places where it is feasible and important to us.

From “It’s Time to Stop Thinking That All Non-Native Species Are Evil” by Emma Marris from NATIONAL GEOGRAPHIC MAGAZINE, July 24, 2014. Copyright © 2014 by National Geographic Society.

Chart titled “Possible Management of Non-Native Species, Based on Extent of Invasion,” plotting Area Affected by Non-Native Species (vertical axis) against Time (horizontal axis) as an S-shaped curve that stays low, then rises steeply and levels off high, where it is labeled “Widespread and abundant throughout range.” The time line is divided into four shaded stages, left to right: Prevention, “Species absent”; Eradication, “Few, localized populations”; Containment, “Rapid increase in populations”; and Local Control and Management Only, “Eradication no longer feasible; can only protect small areas based on economic and ecological need.” Markers on the curve show “Species introduced” at the end of Prevention, “Detection” within Eradication and “Public awareness begins” near the end of Containment, and two large arrows read “Management = simple; eradication likely” across Prevention and Eradication and “Management = difficult and costly; eradication unlikely or impossible” across Containment and Local Control and Management Only.

1stymie: hinder or interfere with

Question

The details in the section “A Good Thing, Not the Only Thing” convey a central idea of the excerpt by suggesting that

  • Asome non-native species can replace native species that are unable to survive on their own.
  • Bdecisions about whether to keep non-native species should be considered on an individual basis.
  • Cthe scientists who study rapidly changing ecosystems agree that non-native species enhance biodiversity.
  • Da natural habitat that is healthy should be able to support a blend of native and non-native species.
Show the answer

Correct answer: B

The question asks how the details in the section “A Good Thing, Not the Only Thing” convey a central idea of the excerpt.

A. Incorrect. While paragraph 15 does discuss introducing non-native Aldabra tortoises to replace native tortoises that no longer exist, the real point of this section is to show that non-native species can sometimes help support native species that still exist but are struggling. In this case, the Aldabra tortoises are now moving seeds around for the fruiting plants on the islands where the tortoises have been introduced.

B. CORRECT. This section discusses situations in which non-native species should be kept (as in the example of the Aldabra tortoises in paragraph 15) but also asserts that “most of the time . . . conserving species still means focusing on supporting them in their historical habitats, planting natives and removing non-natives” (paragraph 16). This section makes the point that the issue of non-natives needs to be considered on a case-by-case basis.

C. Incorrect. This section does not claim that non-native species always or even usually enhance biodiversity; rather, it states that “in some cases we can best serve biodiversity by leaving the non-natives alone or even—brace yourself, now—introducing them on purpose” (paragraph 14), later adding that “most of the time . . . conserving species still means focusing on supporting them in their historical habitats, planting natives and removing non-natives” (paragraph 16).

D. Incorrect. While the section happens to give a good example of a habitat that supports both native and non-native species (the islands of Mauritius), it never suggests that being able to do so is a defining characteristic of healthy habitats.

Question analysis

This central-idea question asks how the details in the final section of an article on non-native species, titled “A Good Thing, Not the Only Thing,” convey a central idea of the excerpt. Students must sum up the section as a whole, including its example of a tortoise brought to the islands of Mauritius, and match it to the article's larger argument.

NYS standards
  • 7R2 theme or central idea
  • 7R5 structure and genre features
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Explaining how a section conveys a central idea is grade 7 work, but this section mixes an argument, an example and a closing paragraph, and the choices differ in how far they generalize from it, which demands more than typical.
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 11, 815 words; question and choices: about grade 11, 82 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 section's most memorable content is an example, the Aldabra tortoise doing the work of the islands' lost tortoises, and a choice built on it is the strongest pull. The central idea sits instead in the qualifiers at the start and end of the section: some cases favor non-natives, most still call for removing them. Students who summarize all three paragraphs in a sentence, including the last, arrive at the case-by-case reading.

  1. The right answer is reworded moderate Choosing the answer

    The right choice's “on an individual basis” appears nowhere in the section, while the wrong choices echo it: a non-native standing in for natives, “biodiversity”, natives alongside non-natives. (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)

  2. Evidence in several places moderate Working it out

    The case-by-case idea comes only from joining paragraph 14's “In some cases” to paragraph 16's “Most of the time” and “where it is feasible and important to us”. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: Sum up the section's three paragraphs in one sentence of your own, including its example and its final paragraph, then compare that sentence with each choice.

Traps

  • Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
  • Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
  • Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.

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

    A section is a part of an article under its own heading. This one runs from paragraph 14 to paragraph 16. You need to sum up the whole section, including its last paragraph. Then match that summary to a central idea.

  2. Read paragraph 14

    It says that “in some cases” we help nature most “by leaving the non-natives alone.” We might even bring them in “on purpose.” The words “in some cases” are the key. They mean sometimes, not always.

  3. Read the example and the ending

    Paragraph 15 gives an example. A non-native tortoise was brought to Mauritius to spread the seeds of fruiting plants. Then paragraph 16 says that “most of the time,” saving species still means “planting natives and removing non-natives.” We should do that “where it is feasible and important to us.” Feasible means possible.

  4. Put the section together

    Sometimes it is best to keep a non-native species. Most of the time it is best to remove it. So each case has to be judged on its own. That is what “on an individual basis” means.

  5. Check each choice

    • B fits: deciding case by case matches both “in some cases” and “most of the time.”
    • A is wrong because the tortoise is one example, and the section ends by saying removal is still the usual choice.
    • C is wrong because the section never says scientists agree, and “in some cases” is far from always.
    • D is wrong because the section never says what a healthy habitat should hold.

    Watch out: A is built on the section’s most memorable detail. But the main idea comes from the words that limit the claim.

  6. Choose the answer

    The section says to keep non-natives in some cases and remove them in others. So the answer is B.

Why this answer and not the closest wrong one

A comes closest, because the Aldabra tortoise really does take over work the lost tortoises once did. But that is one case. The section ends by saying that most of the time we still remove non-natives. B covers both sides: some cases call for keeping them, and others call for removing them.

The original DOE question
Question 55 as printed on page 71 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 71, question 55. Open page 71 of the handbook (PDF)
The passage “Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”” as printed (pages 68–70)The passage “Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”” as printed on page 68 of the DOE handbook.The passage “Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”” as printed on page 69 of the DOE handbook.The passage “Excerpt from “It’s Time to Stop Thinking That All Non-Native Species Are Evil”” as printed on page 70 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 A English, question 17
Passage Excerpt from A Voice in the Wilderness

Excerpt from A Voice in the Wilderness

by Grace Livingston Hill

With a lurch the train came to a dead stop and Margaret Earle, hastily gathering up her belongings, hurried down the aisle and got out into the night.

It occurred to her, as she swung her heavy suit-case down the rather long step to the ground, and then carefully swung herself after it, that it was strange that neither conductor, brakeman, nor porter had come to help her off the train, when all three had taken the trouble to tell her that hers was the next station; but she could hear voices up ahead. Perhaps something was the matter with the engine that detained them and they had forgotten her for the moment.

The ground was rough where she stood, and there seemed no sign of a platform. Did they not have platforms in this wild Western land, or was the train so long that her car had stopped before reaching it?

She strained her eyes into the darkness, and tried to make out things from the two or three specks of light that danced about like fireflies in the distance. She could dimly see moving figures away up near the engine, and each one evidently carried a lantern. The train was tremendously long. A sudden feeling of isolation took possession of her. Perhaps she ought not to have got out until some one came to help her. Perhaps the train had not pulled into the station yet and she ought to get back on it and wait. Yet if the train started before she found the conductor she might be carried on somewhere and he justly blame her for a fool.

There did not seem to be any building on that side of the track. It was probably on the other, but she was standing too near the cars to see over. She tried to move back to look, but the ground sloped and she slipped and fell in the cinders1^1, bruising her knee and cutting her wrist.

In sudden panic she arose. She would get back into the train, no matter what the consequences. They had no right to put her out here, away off from the station, at night, in a strange country. If the train started before she could find the conductor she would tell him that he must back it up again and let her off. He certainly could not expect her to get out like this.

She lifted the heavy suit-case up the high step that was even farther from the ground than it had been when she came down, because her fall had loosened some of the earth and caused it to slide away from the track. Then, reaching to the rail of the step, she tried to pull herself up, but as she did so the engine gave a long snort and the whole train, as if it were in league against her, lurched forward crazily, shaking off her hold. She slipped to her knees again, the suit-case, toppled from the lower step, descending upon her, and together they slid and rolled down the short bank, while the train . . . ran giddily off into the night.

The horror of being deserted helped the girl to rise in spite of bruises and shock. She lifted imploring hands to the unresponsive cars as they hurried by her—one, two, three, with bright windows, each showing a passenger, comfortable and safe inside, unconscious of her need.

A moment of useless screaming, running, trying to attract some one’s attention, a sickening sense of terror and failure, and the last car slatted itself past with a mocking clatter, as if it enjoyed her discomfort.

Margaret stood dazed, reaching out helpless hands, then dropped them at her sides and gazed after the fast-retreating train, the light on its last car swinging tauntingly, blinking now and then with a leer in its eye, rapidly vanishing from her sight into the depth of the night.

She gasped and looked about her for the station that but a short moment before had been so real to her mind; and, lo! on this side and on that there was none!

The night was wide like a great floor shut in by a low, vast dome of curving blue set with the largest, most wonderful stars she had ever seen. Heavy shadows of purple-green, smoke-like, hovered over earth darker and more intense than the unfathomable blue of the night sky. It seemed like the secret nesting-place of mysteries wherein no human foot might dare intrude. It was incredible that such could be but common sage-brush, sand, and greasewood wrapped about with the beauty of the lonely night.

No building broke the inky outlines of the plain, nor friendly light streamed out to cheer her heart. Not even a tree was in sight, except on the far horizon, where a heavy line of deeper darkness might mean a forest. Nothing, absolutely nothing, in the blue, deep, starry dome above and the bluer darkness of the earth below save one sharp shaft ahead like a black mast throwing out a dark arm across the track.

As soon as she sighted it she picked up her baggage and made her painful way toward it, for her knees and wrist were bruised and her baggage was heavy.

A soft drip, drip greeted her as she drew nearer; something plashing down among the cinders by the track. Then she saw the tall column with its arm outstretched, and looming darker among the sage-brush the outlines of a water-tank. It was so she recognized the engine’s drinking-tank, and knew that she had mistaken a pause to water the engine for a regular stop at a station.

1^1cinders: track bed made from the residue of burnt coal

From A VOICE IN THE WILDERNESS by Grace Livingston Hill—Public Domain

Question

How do Margaret’s earlier interactions with the conductor, brakeman, and porter affect the plot?

  • AThey prompt Margaret to get off the train without further assistance.
  • BThey cause Margaret to think that she knows what to do once she gets off the train.
  • CThey compel Margaret to wonder whether the train has not pulled all the way into the station.
  • DThey lead Margaret to believe that train stations in rural areas lack platforms.
Show the answer

Correct answer: A

The question asks how Margaret’s earlier interactions with the conductor, brakeman, and porter affect the plot.

A. CORRECT. Because the conductor, brakeman, and porter have all “taken the trouble to tell her that hers was the next station” (paragraph 2), Margaret assumes that the next time the train stops, she will have reached her station. This assumption causes Margaret to get off the train at the next stop without waiting for help or confirmation, but the stop turns out to be just “a pause to water the engine” (paragraph 15). This mistaken assumption creates the main problem that Margaret confronts in the passage.

B. Incorrect. Although Margaret’s earlier interactions with the three railroad employees cause her to think that she knows when to get off the train, it is clear from paragraph 4 that Margaret is deeply confused and does not know what to do once she has exited the train car. She muses uneasily, “Perhaps she ought not to have got out until some one came to help her. Perhaps the train had not pulled into the station yet and she ought to get back on it and wait” (paragraph 4).

C. Incorrect. Margaret wonders in paragraph 3 whether the train is “so long that her car had stopped before reaching [the station]” and speculates in paragraph 4 that “the train had not pulled into the station yet.” These thoughts reflect her assumption (based on her interactions with the three railroad employees) that the next stop is her station. However, Margaret’s speculation that the train has not fully pulled into the station does not significantly affect the plot.

D. Incorrect. Margaret wonders in paragraph 3 whether they “have platforms in this wild Western land” and is expecting to see a platform because her interactions with the three railroad employees have led her to believe that she has reached a station. However, it is unclear whether Margaret really believes that rural stations all lack platforms, and her speculation on this point is not further developed in the passage and does not affect the plot.

Question analysis

This plot question on A Voice in the Wilderness asks how Margaret’s earlier dealings with the conductor, brakeman and porter, mentioned only in passing in paragraph 2, affect what happens to her. Students must connect that brief remark to later events in the excerpt. Several choices describe things that do happen, so students must judge which one those conversations truly cause.

NYS standards
  • 7R3 plot elements and ideas
  • 7R1 textual evidence and inferences
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 plot questions ask how story elements affect one another, usually through an event and its result. Here the cause is a clause inside a long sentence of century-old prose, and students must trace its effect across the excerpt rather than within one paragraph.
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 8, 981 words; question and choices: about grade 7, 72 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 talks with the trainmen are mentioned once, in the middle of a long sentence, and the question asks students to see them as the start of the whole plot. Several choices describe thoughts Margaret really has right after she steps down, which makes them feel connected, but those thoughts change nothing. The point goes to students who trace cause to consequence: told her stop was next, she gets off alone at a water tank.

  1. Evidence in several places moderate Working it out

    The cause sits in paragraph 2, where all three men had told her “hers was the next station,” and the effect shows only in paragraph 15, when the stop proves to be a water tank. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

  2. Reading between the lines moderate Working it out

    The excerpt never says the men’s words made her step off; students must infer that their assurance is why she left the train at the first stop without waiting for anyone. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  3. Complex sentences minor Understanding the question

    The interactions appear in a 66-word sentence in paragraph 2, tucked into a “when” clause after a run of commas, so they read as a passing detail rather than a cause. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)

Strategy: Reread paragraph 2 to find what the three men told Margaret, then trace how that information shapes the events that follow, and choose the effect that matters most to the plot.

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 something from earlier affects the plot. The plot is the chain of events in a story. What did the three train workers tell Margaret, and what did that cause?

  2. Find what the workers told her

    Paragraph 2 says it was strange that “neither conductor, brakeman, nor porter had come to help her off the train, when all three had taken the trouble to tell her that hers was the next station.” A conductor, a brakeman and a porter are all people who work on a train.

  3. Trace what happened because of it

    Three workers told her that her stop was next. So when the train stopped, she was sure she had arrived. She got off alone, without waiting for anyone to help. But in paragraph 15 she learns it was only “a pause to water the engine.” Their words set off the whole problem: she is left alone in the dark.

  4. Check each choice

    • A fits. Their words led her to get off by herself.
    • B does not fit. They told her when to get off, not what to do next. In paragraph 4 she is lost: “Perhaps she ought not to have got out until some one came to help her.”
    • C does not fit. She does wonder this, but the thought changes nothing in the story.
    • D does not fit. She only asks a question about platforms. She never decides anything about country stations.
  5. Choose the answer

    The workers’ words made Margaret step off the train on her own at the wrong stop. So the answer is A.

Why this answer and not the closest wrong one

C is the closest wrong choice. The workers’ words do make her guess that the train has not reached the station yet. But that guess goes nowhere. What changes the story is that she gets off alone at a stop that is not a station. That is A.

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 A English, page 25, question 17.
The passage “Excerpt from A Voice in the Wilderness” as printed (pages 128–129)The passage “Excerpt from A Voice in the Wilderness” as printed on page 128 of the DOE handbook.The passage “Excerpt from A Voice in the Wilderness” as printed on page 129 of the DOE handbook.

Question 4 of 6

2024 Test A Math, question 6

Question

Mr. Jones has 550 goats, which is 10% more than Mr. King has. How many more goats does Mr. Jones have than Mr. King?

  • A50
  • B55
  • C495
  • D500
Show the answer

Correct answer: A

First, set up a proportion to determine x, the number of goats Mr. King has.

KingJones=x550\frac{\text{King}}{\text{Jones}} = \frac{x}{550}

x550=100%100%+10%\frac{x}{550} = \frac{100\%}{100\% + 10\%}

Then solve the proportion for x.

x550=100%100%+10%\frac{x}{550} = \frac{100\%}{100\% + 10\%}

550(100%)=x(100%+10%)550(100\%) = x(100\% + 10\%)

550(100%)=x(110%)550(100\%) = x(110\%)

550(1)=x(1.10)550(1) = x(1.10)

550=1.10x550 = 1.10x

550÷1.10=(1.10÷1.10)x550 \div 1.10 = (1.10 \div 1.10)x

500=x500 = x

Finally, determine the difference between the number of goats Mr. Jones has, 550, and the number of goats Mr. King has, 500.

550−500=50550 - 500 = 50

Mr. Jones has 50 more goats than Mr. King.

Question analysis

A percent word problem: Mr. Jones has 550 goats, which is 10% more than Mr. King has, and students find how many more goats Mr. Jones has. It asks students to work with a percent increase when only the larger amount is known. The tricky part is deciding which amount the 10% is taken of.

NYS standards
  • 7.RP.3 multistep ratio and percent problems
  • 6.RP.3c percent as a rate per 100
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students usually find a percent increase from a known original amount. This runs the task backward: the increased amount is given, and the original must be recovered before the difference can be found, a step many do not expect.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Solution
2 steps
Reading level
Question and choices: about grade 1, 22 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 arithmetic is one division and one subtraction, so the question is really about the base of a percent. The sentence gives the bigger number and calls it 10% more, and the reflex is to take 10% of the number on the page. That shortcut lands on a listed choice five goats from the answer. Students who find King's herd first, 550 ÷ 1.1, still have to remember that the question wants the difference, not the herd.

  1. Turning words into math major Understanding the question

    The clause "which is 10% more than" makes King's unknown herd the base of the 10%, so 550 is 110% of his number rather than the amount the 10% is taken of. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

  2. A very close wrong answer moderate Choosing the answer

    The choices 50 and 55 are only 5 goats apart, and both are 10% of a herd; only taking the percent of King's 500 rather than of 550 separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

Strategy: Mr. Jones's 550 is 110% of Mr. King's number, so divide 550 by 1.10 to find Mr. King's goats, then subtract that from 550.

Traps

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Percent increase
new=original×(1+p100)\text{new} = \text{original} \times \left(1 + \frac{p}{100}\right)
The original is the amount you start from, the one the percent is taken of. p is the percent of increase. The new amount is all of the original, which is 100%, plus p% more. For 10% more, you multiply by 1.10.
  1. Sort out the question

    Mr. Jones has 550 goats. That is “10% more than Mr. King has”. You need how many more goats Mr. Jones has than Mr. King. That is the difference between the two herds, not the size of a herd.

  2. Decide what the 10% is of

    The words “10% more than Mr. King” mean the 10% is a part of Mr. King’s herd. So Mr. King’s herd is the original. Mr. Jones has all of Mr. King’s goats, 100%, plus 10% more. That is 110% of Mr. King’s herd. Watch out: do not take 10% of 550. That gives 55, choice B. It uses the wrong herd. Taking those 55 away from 550 gives 495, choice C, which is also wrong.

  3. Find Mr. King’s herd

    Call Mr. King’s number of goats K. Use the percent increase formula with p = 10. The new amount is 550.

    new=original×(1+p100)\text{new} = \text{original} \times \left(1 + \frac{p}{100}\right)

    550=K×1.10550 = K \times 1.10

    K=550÷1.10=500K = 550 \div 1.10 = 500

    Mr. King has 500 goats. Watch out: 500 is Mr. King’s herd, choice D. It is not the difference.

  4. Find the difference

    550−500=50550 - 500 = 50

    Mr. Jones has 50 more goats than Mr. King. So the answer is A, 50.

Check your answer

Check the 10%. 10% of 500 is 0.10×500=500.10 \times 500 = 50, and 500+50=550500 + 50 = 550, Mr. Jones’s herd. So 550 really is 10% more than 500. If King had 495, then 10% more would be about 545, not 550.

The original DOE question
Question 63 as printed on page 77 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 77, question 63. Open page 77 of the handbook (PDF)

Question 5 of 6

2024 Test B Math, question 53

Question

Which graph represents the solution to |x+1|≥2|x+1|\geq 2?

  • ANumber line from −3 to 3 with a tick at every integer. Closed dots at −3 and 1. The line is shaded from −3 to the left, ending in an arrow, and from 1 to the right, ending in an arrow.
  • BNumber line from −3 to 3 with a tick at every integer. Closed dots at −1 and 1. The line is shaded from −1 to the left, ending in an arrow, and from 1 to the right, ending in an arrow.
  • CNumber line from −3 to 3 with a tick at every integer. Closed dots at −3 and 1, with the segment between them shaded.
  • DNumber line from −3 to 3 with a tick at every integer. Closed dots at −3 and 3. The line is shaded from −3 to the left, ending in an arrow, and from 3 to the right, ending in an arrow.
Show the answer

Correct answer: A

Since |x+1|≥2|x+1|\geq 2, either x+1≤−2x+1\leq -2 or x+1≥2x+1\geq 2.

Solving x+1≤−2x+1\leq -2 for x gives x≤−3x\leq -3.

Solving x+1≥2x+1\geq 2 for x gives x≥1x\geq 1.

A filled circle on a number line represents “or equal to.” So the correct number line representation has filled circles at −3 and 1, with the number line filled to the left of −3 for “less than” and to the right of 1 for “greater than.”

Question analysis

Students choose the number line graph that shows every solution of an inequality in which x + 1 sits inside absolute value bars. It tests absolute value as distance and graphing inequalities. The tricky part is turning one absolute value statement into two pieces and placing each boundary point and shaded ray correctly.

NYS standards
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students solve and graph two-step inequalities and know absolute value as distance. An inequality with an absolute value has to be split into two cases, which is outside the grade 6 to 8 standards and well above 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 9, 7 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

Reading |x + 1| as the distance from x to −1 makes this quick: the points 2 units away are −3 and 1, and greater than or equal means outside them. Students who solve only one case and mirror it across 0 land on graphs centered on 0, and students who find both endpoints may still shade between them. The graphs differ in just one dot or one shading choice, so each must be read carefully.

  1. Something you must already know moderate Working it out

    Solving |x + 1| ≥ 2 needs two cases, x + 1 ≤ −2 or x + 1 ≥ 2, joined by or; absolute value inequalities go beyond grade 7, and the stem gives no hint. (Anderson & Krathwohl, 2001)

  2. A very close wrong answer moderate Choosing the answer

    The right graph and the segment from −3 to 1 share both filled endpoints, so only deciding between outside and between the boundaries separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  3. Reading a figure, table or graph minor Understanding the question

    Four number lines must be read for filled dots and arrow directions, and two of them differ from the right one only in where a single dot sits. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)

Strategy: Read the absolute value as distance from −1 on the number line, find the points exactly 2 units away, and decide whether the solutions lie between or outside them.

Traps

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

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Absolute value as distance
|x−a|=distance from x to a|x - a| = \text{distance from } x \text{ to } a
x and a are points on the number line. The bars mean absolute value. |x − a| is how far apart the two points are, which is never negative. Since x + 1 = x − (−1), |x + 1| is the distance from x to −1.
  1. Sort out the question

    You need the graph of every x that makes |x+1|≥2|x + 1| \geq 2 true. The sign ≥ means greater than or equal to. The bars mean absolute value.

    On a number line, a filled dot means that point counts. A thick line with an arrow means all the numbers that way count too.

  2. Read it as a distance

    Adding 1 is the same as subtracting −1, so x+1=x−(−1)x + 1 = x - (-1). By the formula, |x+1||x + 1| is the distance from x to −1.

    So the inequality says that x is at least 2 units away from −1.

  3. Find the two boundary points

    Start at −1 and go 2 units each way.

    −1−2=−3-1 - 2 = -3

    −1+2=1-1 + 2 = 1

    At −3 and at 1, the distance is exactly 2. The words or equal to let them count, so they get filled dots.

  4. Decide which side to shade

    Being at least 2 away means being farther out. Numbers between −3 and 1 are too close to −1. For example, 0 is only 1 unit away. So shade to the left of −3 and to the right of 1.

    In algebra, that is x+1≤−2x + 1 \leq -2 or x+1≥2x + 1 \geq 2. These give x≤−3x \leq -3 or x≥1x \geq 1.

  5. Match the graph

    Choice A has filled dots at −3 and 1, with arrows going outward. That matches.

    Watch out: Choice C shades between −3 and 1. Those are the points within 2 of −1, the answer to |x+1|≤2|x + 1| \leq 2. Choices B and D are centered on 0, but the center here is −1.

    So the answer is A, the graph shaded outward from −3 and 1.

Check your answer

Test a point from each part. For x = 2, |2+1|=3|2 + 1| = 3, and 3 is at least 2. For x = 0, |0+1|=1|0 + 1| = 1, which is less than 2. For x = −3, |−3+1|=2|-3 + 1| = 2, which counts. Graph A agrees with all three.

The original DOE question
Question 110 as printed on page 214 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 214, question 110. Open page 214 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 16

Question

A truck rental company charges a one-time fee of $40 plus $1 per mile driven. Dalia rented a truck and used a coupon for 20% off the total rental cost. After the coupon was applied, she spent a total of $60. How many miles did she drive?

  • A8
  • B20
  • C32
  • D35
Show the answer

Correct answer: D

Let m equal the miles driven during Dalia’s rental. The total cost, c, can be expressed as an equation.

c=40+mc = 40 + m

Dalia spent a total of $60, which included a 20% off coupon. Find the cost before the coupon by dividing the final cost ($60) by the percentage paid (80%):

6080%=600.80=75\frac{60}{80\%} = \frac{60}{0.80} = 75

Use $75 as the total cost to find m.

40+m=7540 + m = 75

m=35m = 35

Dalia drove 35 miles.

Question analysis

A multistep word problem about a truck rental that costs a $40 fee plus $1 per mile, with a 20% off coupon applied to the total. Given that Dalia paid $60 after the coupon, students find how many miles she drove. Undoing the discount correctly before removing the fixed fee is the hard part.

NYS standards
  • 7.EE.4a two-step equations
  • 7.RP.3 multistep ratio and percent problems
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students solve two-step equations and work with discounts, usually separately. This combines them and makes students undo a 20% discount starting from the price paid, a reversal many grade 7 students have not practised.
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 5, 43 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

Two ordinary skills, undoing a discount and solving a two-step equation, are stacked, and the first runs in reverse. The natural way to undo 20% off is to add 20% back, which gives $72 instead of $75 and a choice three miles from the answer. Students who check by applying the coupon to the full cost of 40 + 35 = 75 dollars see at once that 80% of it is 60.

  1. Turning words into math moderate Understanding the question

    The sentence "After the coupon was applied, she spent a total of $60" makes 60 the price after 20% off, so it is 80% of the full cost, 40 + m. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

  2. Combines ideas moderate Working it out

    A percent discount has to be undone before the fee-plus-mileage equation can be solved: 60 ÷ 0.8 = 75, then 75 − 40 = 35 miles. (Embretson, 1998; Daniel & Embretson, 2010)

  3. A very close wrong answer moderate Choosing the answer

    The choices 32 and 35 are three miles apart, too close to tell apart by estimate; only dividing 60 by 0.8, rather than adding 20% of 60, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

Strategy: Since $60 is 80% of the full cost, divide 60 by 0.80 to find the cost before the coupon, then subtract the $40 fee to get the miles.

Traps

  • Percent of the wrong amount: Finding the whole from a part, or a percent change measured from the wrong starting amount.
  • Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Rental cost
c=40+1×mc = 40 + 1 \times m
c is the full cost in dollars, before any coupon. 40 is the one-time fee, paid once no matter how far you drive. m is the number of miles, and each mile costs 1 dollar.
Price after a discount
price paid=full cost×(1−p100)\text{price paid} = \text{full cost} \times \left(1 - \frac{p}{100}\right)
The full cost is the price before the discount. p is the percent taken off. You pay what is left: 100% minus p%. For 20% off you pay 80%, so you multiply by 0.80.
  1. Sort out the question

    The truck costs a $40 fee, plus $1 for each mile. Dalia’s coupon took 20% off the total. After the coupon, she paid $60. You need how many miles she drove. The $60 is the price after the discount, not the full cost.

  2. Write what she paid

    20% off means she paid what was left of the full cost.

    100%−20%=80%100\% - 20\% = 80\%

    As a decimal, 80% is 0.80.

    price paid=full cost×(1−p100)\text{price paid} = \text{full cost} \times \left(1 - \frac{p}{100}\right)

    60=full cost×0.8060 = \text{full cost} \times 0.80

  3. Undo the discount

    To undo times 0.80, divide by 0.80. Move the decimal point one place in both numbers to make it easier.

    full cost=60÷0.80=600÷8=75\text{full cost} = 60 \div 0.80 = 600 \div 8 = 75

    The full cost was $75. Watch out: the 20% was taken off the full cost, not off $60. Adding 20% of $60 gives $72 and leads to 32 miles, choice C. Taking 20% off $60 again leads to 8 miles, choice A.

  4. Find the miles

    c=40+1×mc = 40 + 1 \times m

    75=40+m75 = 40 + m

    m=75−40=35m = 75 - 40 = 35

    She drove 35 miles. Watch out: do not skip the coupon. Using $60 as the full cost gives 20 miles, choice B. So the answer is D, 35.

Check your answer

Go forward. 35 miles cost $35. Add the $40 fee to get $75. The coupon takes off 20% of $75, which is 0.20×75=150.20 \times 75 = 15 dollars. Then 75−15=6075 - 15 = 60. That is exactly what she paid.

The original DOE question
Question 73 as printed on page 79 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 79, question 73. Open page 79 of the handbook (PDF)

Sample #191181