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Six SHSAT Questions

3 English and 3 math

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Question 1 of 6

2018 Test B English, question 31
Passage Excerpt from “Niagara Falls”

Excerpt from “Niagara Falls”

by Rupert Brooke

The real secret of the beauty and terror of the Falls is not their height or width, but the feeling of colossal power and of unintelligible disaster caused by the plunge of that vast body of water. If that were taken away, there would be little visible change, but the heart would be gone.

The American Falls do not inspire this feeling in the same way as the Canadian. It is because they are less in volume, and because the water does not fall so much into one place. By comparison their beauty is almost delicate and fragile. They are extraordinarily level, one long curtain of lacework and woven foam. Seen from opposite, when the sun is on them, they are blindingly white, and the clouds of spray show dark against them. With both Falls the colour of the water is the ever-altering wonder. Greens and blues, purples and whites, melt into one another, fade, and come again, and change with the changing sun. Sometimes they are as richly diaphanous1^1 as a precious stone, and glow from within with a deep, inexplicable light. Sometimes the white intricacies of dropping foam become opaque and creamy. And always there are the rainbows. If you come suddenly upon the Falls from above, a great double rainbow, very vivid, spanning the extent of spray from top to bottom, is the first thing you see. If you wander along the cliff opposite, a bow springs into being in the American Falls, accompanies you courteously on your walk, dwindles and dies as the mist ends, and awakens again as you reach the Canadian tumult. And the bold traveller who attempts the trip under the American Falls sees, when he dare open his eyes to anything, tiny baby rainbows, some four or five yards in span, leaping from rock to rock among the foam, and gambolling beside him, barely out of hand’s reach, as he goes. One I saw in that place was a complete circle, such as I have never seen before, and so near that I could put my foot on it. It is a terrifying journey, beneath and behind the Falls. The senses are battered and bewildered by the thunder of the water and the assault of wind and spray; or rather, the sound is not of falling water, but merely of falling; a noise of unspecified ruin. So, if you are close behind the endless clamour, the sight cannot recognise liquid in the masses that hurl past. You are dimly and pitifully aware that sheets of light and darkness are falling in great curves in front of you. Dull omnipresent foam washes the face. Farther away, in the roar and hissing, clouds of spray seem literally to slide down some invisible plane of air.

Beyond the foot of the Falls the river is like a slipping floor of marble, green with veins of dirty white, made by the scum that was foam. It slides very quietly and slowly down for a mile or two, sullenly exhausted. Then it turns to a dull sage green, and hurries more swiftly, smooth and ominous. As the walls of the ravine close in, trouble stirs, and the waters boil and eddy. These are the lower rapids, a sight more terrifying than the Falls, because less intelligible. Close in its bands of rock the river surges tumultuously forward, writhing and leaping as if inspired by a demon. It is pressed by the straits into a visibly convex form. Great planes of water slide past. Sometimes it is thrown up into a pinnacle of foam higher than a house, or leaps with incredible speed from the crest of one vast wave to another, along the shining curve between, like the spring of a wild beast. Its motion continually suggests muscular action. The power manifest in these rapids moves one with a different sense of awe and terror from that of the Falls. Here the inhuman life and strength are spontaneous, active, almost resolute. . . . A place of fear.

One is drawn back, strangely, to a contemplation of the Falls, at every hour, and especially by night, when the cloud of spray becomes an immense visible ghost, straining and wavering high above the river, white and pathetic and translucent. The Victorian lies very close below the surface in every man. There one can sit and let great cloudy thoughts of destiny and the passage of empires drift through the mind; for such dreams are at home by Niagara. I could not get out of my mind the thought of a friend, who said that the rainbows over the Falls were like the arts and beauty and goodness, with regard to the stream of life—caused by it, thrown upon its spray, but unable to stay or direct or affect it, and ceasing when it ceased. In all comparisons that rise in the heart, the river, with its multitudinous waves and its single current, likens itself to a life, whether of an individual or of a community. A man’s life is of many flashing moments, and yet one stream; a nation’s flows through all its citizens, and yet is more than they. In such places, one is aware, with an almost insupportable and yet comforting certitude, that both men and nations are hurried onwards to their ruin or ending as inevitably as this dark flood. Some go down to it unreluctant, and meet it, like the river, not without nobility. And as incessant, as inevitable, and as unavailing as the spray that hangs over the Falls, is the white cloud of human crying. . . . With some such thoughts does the platitudinous2^2 heart win from the confusion and thunder of a Niagara peace that the quietest plains or most stable hills can never give.

From LETTERS FROM AMERICA by Rupert Brooke—Public Domain

1^1diaphanous: sheer, translucent

2^2platitudinous: clichéd, common

Question

With which statement would the author of this excerpt most likely agree?

  • AA sense of ease and assurance comes with accepting one’s fate.
  • BNo matter where one’s path goes in life, one will always have regrets.
  • CThe best way to overcome fear is to recognize it and then defy it.
  • DReason will die out with humanity, but art will remain immortal.
Show the answer

Correct answer: A

The question asks for the statement the author would agree with most. In paragraph 4, the author states that the Falls make a person feel “with an almost insupportable and yet comforting certitude, that both men and nations are hurried onwards to their ruin or ending.” Later, the final sentence says, “With some such thoughts does the platitudinous heart win from the confusion and thunder of a Niagara peace.” This sentence supports the author’s belief that a person can find peace in accepting the certainty of his or her own ending, as expressed in Option A.

Option B is incorrect because the author does not discuss regrets in the excerpt.

Option C is incorrect because, while the excerpt discusses fear when looking at the power of the Falls, the excerpt does not support the idea that one should defy fear.

Option D is incorrect because the excerpt states in paragraph 4 that art and beauty are “caused by” the stream of life and end with it, “ceasing when it ceased.”

Question analysis

This question asks students to infer which statement about life the author of “Niagara Falls” would most likely agree with, based on the reflections that close his essay. It is hard because the evidence sits in long, abstract sentences of century-old prose and must be pieced together from more than one place in the final paragraph.

NYS standards
  • 7R6 point of view and author position
  • 7R1 textual evidence and inferences
Grade level
Grade 9 reading and task
Compared with grade 7
Above grade 7 Grade 7 point-of-view questions usually rest on a clearly stated opinion. Here the author’s view must be pieced together from abstract reflection on lives, nations and the river, with words like “insupportable” and “platitudinous,” which is closer to high school reading.
Estimated difficulty
Among the hardest on the SHSAT: a non-obvious approach, heavy reading, or a well-hidden trap.
Evidence
Answered from one paragraph or stanza
Reading level
Passage: about grade 9, 987 words; question and choices: about grade 6, 61 words.
Corrected from the DOE handbook
  • A misreading of a word in the passage was corrected in the explanation.
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

This question asks for the author’s outlook, which he reaches only in the closing sentences of a long, abstract paragraph. The mood there is gloomy, with ruin, a dark flood and human crying, so students who read the mood but not the argument choose regret. The comfort and peace he finds in that certainty are easy to miss in the inverted final sentence, and they are exactly what the answer rests on.

  1. Reading between the lines major Working it out

    The author never states a belief; students must combine “comforting certitude,” people who meet their end “unreluctant” and “not without nobility,” and the closing “peace” into an attitude of accepting fate. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  2. Complex sentences major Understanding the question

    The last sentence inverts normal order, “With some such thoughts does the platitudinous heart win from the confusion and thunder of a Niagara peace,” so its subject and object are hard to find. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)

  3. The right answer is reworded moderate Choosing the answer

    The right statement uses none of the passage’s words, turning “certitude” into “assurance” and “peace” into “ease,” while wrong choices pick up “fear” and “art.” (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)

  4. Hard words moderate Understanding the question

    “Certitude,” “unreluctant,” “unavailing” and “platitudinous” carry the author’s attitude, and the glossary defines only the last of them. (Perfetti, 2007; Freedle & Kostin, 1993)

Strategy: Reread the second half of paragraph 4 slowly, translating each long sentence into plain words, then choose the statement those lines support without adding ideas the author never mentions.

Traps

  • Outside knowledge: A choice is plausible in the real world but not supported by this text.
  • Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: The handbook rejects Option D because paragraph 4 says art is “unable to stay.” In the passage, art and beauty are “unable to stay or direct or affect” the stream of life: “stay” means to stop or hold back the stream, not to last. What shows that art is not immortal is that it is “caused by” the stream of life and ends with it, “ceasing when it ceased,” which the site now quotes.

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 which statement the author would most likely agree with. He never states his belief outright, so you must infer it from his words, especially at the end of paragraph 4.

  2. Find what he says about endings

    In paragraph 4, he says that at Niagara one feels “with an almost insupportable and yet comforting certitude” that people and nations reach an end. He adds: “Some go down to it unreluctant, and meet it, like the river, not without nobility.” His last sentence says the heart can “win from the confusion and thunder of a Niagara peace.”

  3. Put his words in plain English

    “Certitude” means being sure. “Insupportable” means too hard to bear. So knowing that everything ends is hard, yet it is also comforting. “Unreluctant” means willing. Some people meet their end willingly, with dignity. And the Falls give the heart peace. Put together: accepting what must happen brings calm.

  4. Check each choice

    • A is right. He finds comfort and peace in accepting fate. That is “ease and assurance.”
    • B is wrong. He never mentions regrets.
    • C is wrong. He talks about accepting what must happen, not about fighting fear.
    • D is wrong. Art and beauty are “caused by” life and end with it, “ceasing when it ceased.” So art does not last forever.

    Watch out: “The white cloud of human crying” sounds sad, so B may tempt you. But sadness is not regret, and the author ends on peace.

  5. Choose the answer

    The author finds calm and comfort in accepting what must come. So the answer is A.

Why this answer and not the closest wrong one

B is the closest wrong answer, because paragraph 4 mentions human crying and ruin. But the author never talks about regret. He calls the certainty of an ending “comforting,” and the essay closes on the word “peace.” Feeling calm by accepting fate is what A says.

More questions like this

The original DOE question
Question 31 as printed on page 137 of the DOE handbook.
As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 137, question 31. Open page 137 of the handbook (PDF) This is the DOE’s version, before the corrections listed in the analysis.
The passage “Excerpt from “Niagara Falls”” as printed (pages 134–135)The passage “Excerpt from “Niagara Falls”” as printed on page 134 of the DOE handbook.The passage “Excerpt from “Niagara Falls”” as printed on page 135 of the DOE handbook.

Question 2 of 6

2026 Practice Test C English, question 45
Passage New York City and the Hudson Valley Brickmaking Industry

New York City and the Hudson Valley Brickmaking Industry

(1) Residents of New York City cannot help but notice that the buildings they are surrounded by are predominantly made of brick. (2) Indeed, one author described the bricks that make up some of New York City’s most recognizable landmarks, including the Empire State Building and the arches of the Brooklyn Bridge, as “an inescapable presence.” (3) Nearly 65 million people visit New York City every year to see these and other attractions. (4) Why was so much brick used in buildings constructed during the century before World War II? (5) The answer involves an explosion in New York City’s population that caused an increase in demand for bricks starting in the mid-1800s and lasting into the 1940s that affected the area more than 100 miles up the Hudson River Valley toward Albany. (6) When demand later declined, the industry would entirely disappear.

(7) New York City’s appetite for brick was fueled by surging population and demand for safer building materials. (8) The city’s population ballooned from about 313,000 people in 1840 to more than 7 million a century later. (9) Following large, destructive fires in the 1830s, the city had enacted laws requiring the use of fire-resistant materials. (10) Bricks turned out to be an inexpensive way for builders to quickly throw together a lot of structures while keeping building owners and safety inspectors happy.

(11) The brickmaking industry in the Hudson Valley skyrocketed. (12) At the industry’s peak, approximately 130 brick factories crammed themselves into a 120-mile stretch along the Hudson River. (13) These factories employed much of the region’s population. (14) Population growth in the Hudson River Valley after the mid-1800s was substantial, though percentage increases were smaller than those in New York City. (15) Even though the factories operated only during the summers, their production was immense. (16) Hudson Valley factories shipped over a billion bricks on barges down the river to New York City annually. (17) In fact, The New York Times declared, “It’s fairly safe to assume that any brick building constructed between 1800 and 1950 includes some form of sediment from the banks of the Hudson River.”

(18) History has proven, however, that boom times eventually end. (19) Shifting architectural trends halted not only the Hudson Valley’s brickmaking boom, but its entire industry. (20) Starting early in the twentieth century, architects and builders increasingly favored steel, glass, and concrete instead of brick. (21) By 1979, reduced demand for brick had driven every Hudson Valley brick factory out of business.

(22) The Hudson Valley’s brickmaking legacy lives on in the architecture of New York City. (23) Throughout the city, famous and ordinary buildings stand as evidence of the remarkable productivity achieved by the Valley’s brickmakers. (24) The brick buildings surrounding New Yorkers today serve as a reminder that, as one amateur brick historian put it, “The skyline of New York City used to be the landscape of the Hudson River Valley.”

Question

Which two sentences present information irrelevant to the ideas in the passage and should be deleted?

Move the two correct answers to the box.

Should Be Deleted

On the test you drag tiles into the box; here, choose them below. The DOE has not published how answers with several parts are scored; this site counts one right only when every part is right.

  • A“Nearly 65 million people visit New York City every year to see these and other attractions.” (sentence 3)
  • B“The city’s population ballooned from about 313,000 people in 1840 to more than 7 million a century later.” (sentence 8)
  • C“Population growth in the Hudson River Valley after the mid-1800s was substantial, though percentage increases were smaller than those in New York City.” (sentence 14)
  • D“History has proven, however, that boom times eventually end.” (sentence 18)
  • E“Throughout the city, famous and ordinary buildings stand as evidence of the remarkable productivity achieved by the Valley’s brickmakers.” (sentence 23)
Show the answer

Correct answer: A and C

The question asks which two sentences present information irrelevant to the ideas of the passage and should be deleted.

CORRECT. “Nearly 65 million people visit New York City every year to see these and other attractions” (sentence 3) presents irrelevant information and should be deleted. While the statistic is interesting, it focuses on tourism, which is not relevant to either the topic of the passage—the growth and decline of the brickmaking industry—or to the ideas in the first paragraph (sentences 1–6), which focus on the prominence of brick in New York City’s buildings.

Incorrect. “The city’s population ballooned from about 313,000 people in 1840 to more than 7 million a century later” (sentence 8) is relevant to the ideas of the passage and should not be deleted. The numerical details in sentence 8 about the rapid growth in New York City provide relevant evidence that supports a central idea of the passage: that the brickmaking industry of the Hudson River Valley expanded quickly to supply the demands of builders who were, in turn, meeting the demands of a booming population.

CORRECT. “Population growth in the Hudson River Valley after the mid-1800s was substantial, though percentage increases were smaller than those in New York City” (sentence 14) presents irrelevant details and should be deleted. The information in sentence 14 comparing population growth rates between the region and New York City is not needed to develop the passage’s central focus on the rise and decline of the Hudson River Valley’s brickmaking industry. The sentence also does not support ideas in the third paragraph (sentences 11–17). Although it mentions that brick factories employed much of the Hudson River Valley population, the productivity of the factories, rather than the Valley’s population, is the topic of the paragraph.

Incorrect. “History has proven, however, that boom times eventually end” (sentence 18) is relevant to the ideas of the passage and should not be deleted. Sentence 18 effectively introduces the central idea of the passage: the decline of the Hudson River Valley brickmaking industry. The sentence also serves as a clear transition from the third paragraph (sentences 11–17), which provides evidence of the industry’s boom, to the fourth paragraph (sentences 18–21), which provides details about how the industry came to an end.

Incorrect. “Throughout the city, famous and ordinary buildings stand as evidence of the remarkable productivity achieved by the Valley’s brickmakers” (sentence 23) is relevant to the ideas of the passage and should not be deleted. The mention of famous and ordinary buildings provides an effective link to introductory sentences 1 and 2, strengthening the passage’s conclusion, while also emphasizing the productivity of the Hudson Valley brickmaking industry detailed in the third paragraph (sentences 11–17).

Question analysis

This revising question asks which two of five sentences from the passage on the Hudson Valley brickmaking industry present irrelevant information and should be deleted. On the test students move two sentence tiles into a box labeled Should Be Deleted, and both must be right. The five sentences come one from each paragraph, so each must be judged against its own paragraph and the whole passage.

NYS standards
  • 7W2b developing a topic
Grade level
Grade 7 reading and task
Compared with grade 7
Above grade 7 Grade 7 revision usually asks for one off-topic sentence within one paragraph. Here students check five sentences spread over the whole passage, must find two, and get credit only if both are right, a broader demand than typical grade 7 work.
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 12, 465 words; question and choices: about grade 10, 114 words.
Corrected from the DOE handbook
  • A missing hyphen in a quotation in the explanation was restored.
  • A grammatical error in the explanation was corrected.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Sentence 3 announces itself: tourism has nothing to do with brick. The second deletion is the trap, because sentence 14 sits after a sentence about factories employing the region’s population and looks like a continuation. Students who reject population as a topic often delete sentence 8 instead, which measures a cause the passage names, and students who judge by sound cut the general “boom times eventually end,” which turns the passage toward the industry’s decline.

  1. A very close wrong answer moderate Choosing the answer

    Sentences 8 and 14 are both population statistics; what separates them is that sentence 8 measures the “surging population” sentence 7 names as a cause, while the Valley’s growth in sentence 14 explains nothing. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  2. How sentences fit together moderate Working it out

    Each kept sentence earns its place by its links: sentence 18 turns from boom to decline, sentence 23 echoes the landmarks of sentences 1–2, and sentence 14 merely follows sentence 13’s “region’s population.” (Halliday & Hasan, 1976)

  3. Much to keep track of minor Working it out

    Five tiles, one from each paragraph, are judged against both their paragraph and the whole passage, and both picks must be right, so two relevance tests run side by side. (Sweller, 1988; Carpenter, Just & Shell, 1990)

Strategy: Sum up the passage’s topic in one phrase, then read each of the five sentences in its paragraph and ask whether removing it would leave a gap in the ideas around it; delete only sentences that leave none.

Traps

  • Fixes what isn't broken: Changes a part of the sentence that was already correct, while the real error stays; or, where the question asks which sentence has an error or should go, picks one that is correct and belongs.
  • Off the point: Adds or keeps something that does not support the paragraph's or the passage's focus, or an introduction or conclusion that misses the main point.

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: The handbook’s explanation quotes sentence 14 as “Population growth in the Hudson River Valley after the mid 1800s was substantial.” The passage and the tile say “mid-1800s,” so the site now quotes it that way.
  • Explanation: The handbook’s explanation says “The information in sentence 14 comparing population growth rates between the region and New York City are not needed.” The subject is “information,” so the site now says “is not needed.”

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    You need to find two sentences that don’t belong. A sentence is irrelevant when it has nothing to do with the main ideas. You can delete it without leaving a gap. On the test you drag two tiles into the Should Be Deleted box. Here, you choose two of the five. Both must be right.

  2. Name the topic of the passage

    The passage explains why New York City has so many brick buildings. It tells how the Hudson Valley brick industry grew to meet that demand, then died out. Each paragraph has its own job. Paragraph 1 asks why so much brick was used. Paragraph 2 gives the causes. Paragraph 3 shows how much the factories made. Paragraph 4 tells how the industry ended. Paragraph 5 sums up.

  3. Test sentences 3 and 14

    Sentence 3 says: “Nearly 65 million people visit New York City every year to see these and other attractions.” That is about tourists, not bricks. Sentence 14 says: “Population growth in the Hudson River Valley after the mid-1800s was substantial, though percentage increases were smaller than those in New York City.” Paragraph 3 is about how much the factories made, “over a billion bricks” a year. How fast the Valley grew explains nothing about bricks.

  4. Test the other three sentences

    • Sentence 8 stays. Sentence 7 says the hunger for brick was “fueled by surging population.” Sentence 8 gives the numbers that show it.
    • Sentence 18 stays. It turns the passage from the boom to the decline. A boom is a time of fast growth.
    • Sentence 23 stays. It links back to the famous buildings in sentences 1 and 2 and praises the brickmakers.

    Watch out: Sentence 14 comes right after one about factories that “employed much of the region’s population.” So it seems to fit. But it changes the topic from factories to population.

  5. Choose the answers

    Sentences 3 and 14 add facts that don’t help explain the brick industry. So the answers are A and C. Move these two tiles into the Should Be Deleted box. A is “Nearly 65 million people visit New York City every year to see these and other attractions.” (sentence 3). C is “Population growth in the Hudson River Valley after the mid-1800s was substantial, though percentage increases were smaller than those in New York City.” (sentence 14).

Why this answer and not the closest wrong one

B is the closest wrong answer, since sentences 8 and 14 are both about population. But sentence 8 measures the “surging population” that sentence 7 names as a cause of the demand for brick. Sentence 14 explains nothing about bricks. So delete 14 and keep 8.

More questions like this

The original DOE question
Question 45 as shown on the DOE’s digital test, page 66 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test C English, page 66, question 45. This is the DOE’s version, before the corrections listed in the analysis.
The passage “New York City and the Hudson Valley Brickmaking Industry” as printed (page 64)The passage “New York City and the Hudson Valley Brickmaking Industry” as printed on page 64 of the DOE handbook.

Question 3 of 6

2026 Practice Test C English, question 39
Passage Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”

Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”

by Melanie Canales

The author, Melanie Canales, is a first-generation Peruvian American farmer and beekeeper based in Virginia’s Shenandoah Valley, on lands of the indigenous Monacan and Manahoac tribes. Her work focuses on creating healthy relationships between people and their surrounding ecosystems.

Unburdened by the constraints of gravity, red and green peppers jut out at 45-degree angles inside the Advanced Plant Habitat (APH), a sort of space terrarium not much larger than a microwave. Four chile pepper plants stand effortlessly upright, despite the dozens of glossy fruits weighing them down. These plants have lived entirely in space; their leaves have never been chewed on by insects or rustled by a summer breeze, [and] their stems are unfamiliar with bending toward the sun’s arc across the sky. Scissors glint under the tank’s white and blue lights as astronaut Mark Vande Hei and his team snip the stems of those that are ready for harvest. The peppers whirl around their heads until the astronauts catch them and tape them against a board to photograph.

Back on Earth, the Plant Habitat-04 team of engineers and plant scientists are observing and conferring with the astronauts. Of the 26 peppers in this batch, only the 14 finest will stay on the International Space Station [ISS] for consumption. The rest will be wrapped in foil, sealed in a Ziploc bag, then frozen at a brisk −80 degrees, until they can come roaring back to Earth in the next cargo capsule to be studied later. Now, after a 137-day growth cycle, the astronauts remove the plants from the module and trash them. Project Plant Habitat-04 is complete. It’s taco night on the ISS.

Since 2014, NASA1 has experimented with growing lettuces, brassicas,2 and zinnias3 in space, an endeavor that relies on highly specialized technology over 50 years in the making. [Fall 2021’s] two successful pepper harvests . . . will provide data on the nutritional and psychological benefits of growing vegetables on-craft, as well as a crop’s ability to reliably produce long-term in microgravity. While controlled environmental agriculture is not new, the APH experiment represents an evolution in specialized growth habitats. It doesn’t aim to re-create Earth’s conditions, but to perfect each isolated variable of plant growth in the clinical environment of a spaceship.

“The Advanced Plant Habitat is the most complex plant growth system on orbit today,” says Lashelle Spencer, a plant scientist at NASA’s Kennedy Space Center. Its more than 180 sensors control and monitor temperature, humidity, and carbon dioxide. The astronauts can adjust the color and intensity of the light, and how much moisture the plants’ roots are getting. It waters itself.

It’s the day after Thanksgiving, and Spencer has been at Kennedy since 5 a.m. to facilitate the peppers’ final harvest. As part of the project team, she played a crucial role in preparing the seeds that were sent hurtling into space in June and guiding the astronauts through maintaining the plants in orbit. . . . Though astronauts can spend upwards of 100 days in space, their on-mission meals come dehydrated and pre-packaged; their vitamins and minerals are isolated in supplements, which lose nutritional value the longer they’re stored. Spencer’s goal is to create the conditions necessary for cultivating healthy plants in space, so those plants can sustain healthy astronauts on long-term missions. Astronaut food is great, she says—“especially the shrimp cocktail. But you’re missing that crunch. You’re missing that fresh pop of flavor, the green flavor that’s not there in that packaged food.”

The sensory experience of growing productive crops can also help mitigate4 the psychological effects of long-term space travel. . . . Spencer says the team cracked open the door of the APH every day to observe their vegetable companions with all the tenderness of home gardeners. When harvest day came, they batted their bounty around the ISS, taking selfies and delighting in watching the fruits pirouetting around the spacecraft. . . .

“We were thinking no heat, so that [the peppers] wouldn’t be dangerous, but maybe the astronauts need a little spice in their life,” says Paul Bosland, who along with his colleagues at the Chile Pepper Institute genetically engineered5 the NuMex Española Improved chile pepper seeds grown in Plant Habitat-04. . . .

Working with NASA, Bosland cultivated a variety that could accommodate both the nutritional needs of astronauts as well as the logistics of growing a plant in space. . . .

. . . The experiment is helping gather the data necessary to determine the nutritional content of crops grown in space, and therefore how many people they can feed, and for how long. Though much is still unknown, Spencer is certain of one thing that future astronauts will need to do: “I think in an optimal world, a scientist like me would say that they would be growing plants from day one. From the day they left to the day they came back, they would be growing them.”

From “Growing Peppers on the ISS Is Just the Start of Space Farming” by Melanie Canales from WIRED, December 21, 2021. Copyright © 2021 Condé Nast. All rights reserved.

1NASA: National Aeronautics and Space Administration

2brassicas: a large genus of herbs, such as broccoli and cabbage

3zinnias: a genus of herbs and low shrubs that have flowers at their heads

4mitigate: to make something less severe or harmful

5genetically engineered: combined parts of DNA from different plants to produce a new plant

Question

The description in paragraph 5 of Lashelle Spencer’s goal develops a central idea of the excerpt by

  • Aillustrating that certain types of packaged foods available in space lack particular flavors.
  • Bsupporting the notion that spending more than 100 days in space is detrimental to astronauts’ health.
  • Coffering an example of how the limited selection of on-mission meals becomes less appealing over time.
  • Dmaking an important point about the astronauts’ current reliance on supplements for vitamins and minerals.
Show the answer

Correct answer: D

The question asks how the description of Lashelle Spencer’s goal in paragraph 5 develops a central idea of the excerpt.

A. Incorrect. Although Spencer mentions how astronauts miss certain eating experiences like the “fresh pop” and “green flavor” not found in packaged and dehydrated food, a central idea of the excerpt is that there is a need to provide fresh, healthy foods for long missions, not that food flavor should be improved.

B. Incorrect. While the excerpt focuses on how spending more than 100 days in space affects nutrition, it does not discuss specific ways in which spending long periods of time in space is detrimental to the health of astronauts.

C. Incorrect. Although paragraph 5 states that astronauts “can spend upwards of 100 days in space,” the excerpt does not develop a central idea that existing meals in space become less appealing over time.

D. CORRECT. The paragraph explains that astronauts currently rely on supplements for vitamins and minerals, which lose their nutritional value over time. Spencer’s goal for growing plants in space is to “sustain healthy astronauts,” supporting a central idea that astronauts need more nutritionally valuable food to sustain them while in space for long periods of time.

Question analysis

Lashelle Spencer’s goal for growing plants in space is described in paragraph 5 of the WIRED excerpt, and this central-idea question asks how that description develops a central idea of the whole excerpt. Students must connect a single sentence about a scientist’s aim to the article’s larger point, and every choice draws on details from that same paragraph.

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 Grade 7 students trace how a central idea develops, usually through a plainly stated example. Here the goal’s connection to the central idea runs through the sentences around it, and the choices are abstract restatements, which asks more than typical grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from several paragraphs or stanzas
Reading level
Passage: about grade 10, 890 words; question and choices: about grade 12, 75 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

Every choice draws on paragraph 5, and none mentions growing plants, which leaves students looking for the goal without finding it. The flavor quotation that follows the goal is the most memorable detail and the easiest wrong pick. The key works only through context: the goal answers the problem the previous sentence sets out, crews depending on supplements that weaken in storage, which is why it serves the article’s case for fresh food on long missions.

  1. Reading between the lines moderate Working it out

    Spencer’s goal names healthy plants and healthy astronauts but no supplements; its link to the key runs through the sentence before it, where vitamins sit in supplements that “lose nutritional value the longer they’re stored.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  2. Every choice must be checked moderate Choosing the answer

    No choice restates the goal of growing plants itself, so none can be matched at a glance; each must be tested for whether it ties the goal to the excerpt’s concern with nutrition on long missions. (Embretson & Wetzel, 1987)

  3. How, not what minor Working it out

    The question asks how the description develops a central idea, its role in the article, so knowing what Spencer wants is only the first step toward the answer. (Anderson & Krathwohl, 2001)

  4. Evidence in several places minor Working it out

    The central idea must come from the whole excerpt: paragraph 3’s “nutritional and psychological benefits,” paragraph 8’s “nutritional needs of astronauts” and paragraph 9’s “nutritional content of crops.” (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: State a central idea of the whole excerpt in your own words, reread Spencer’s goal with the sentences around it in paragraph 5, and pick the option that connects the goal to that central idea.

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.
  • Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
  • 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. Figure out what the question asks

    A central idea is a main point the whole article keeps coming back to. This question asks how Spencer’s goal, in paragraph 5, helps build one of those main points. So first, find the goal. Then connect it to the big idea.

  2. Find the goal and the sentence before

    Paragraph 5 says: “Spencer’s goal is to create the conditions necessary for cultivating healthy plants in space, so those plants can sustain healthy astronauts on long-term missions.” Cultivating means growing. The sentence just before it shows why she has this goal. Astronauts’ “vitamins and minerals are isolated in supplements, which lose nutritional value the longer they’re stored.”

  3. Connect the goal to the big idea

    Today astronauts get vitamins from pills, called supplements. Those pills lose their health value as they sit. Spencer wants fresh plants grown in space to keep astronauts healthy instead. So her goal points to a problem: relying on weak pills. The article returns to food and health again and again. Paragraph 8 mentions “the nutritional needs of astronauts.” Nutritional means having to do with healthy food.

  4. Check each choice

    • A is wrong. The “fresh pop of flavor” line comes after the goal. It is about taste, a side point.
    • B is wrong. The article never says long trips in space harm astronauts’ health.
    • C is wrong. It is the stored supplements that lose value over time, not meals that get less tasty.
    • D is right. The goal answers a problem: astronauts depend on supplements that weaken in storage. That ties to the article’s idea that astronauts need healthy fresh food on long trips.

    Watch out: Spencer’s flavor quote is the most memorable line nearby, so A pulls hard. But her goal is about health, not taste.

  5. Choose the answer

    Spencer wants healthy plants because pills are not enough. So the answer is D, “making an important point about the astronauts’ current reliance on supplements for vitamins and minerals.” Reliance means depending on something.

Why this answer and not the closest wrong one

A is the closest wrong answer. Spencer really does miss the crunch and flavor of fresh food. But her goal is to “sustain healthy astronauts,” which is about health. Health is the big idea the article keeps returning to. D connects the goal to that idea through the supplements that lose value.

More questions like this

The original DOE question
Question 39 as shown on the DOE’s digital test, page 57 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test C English, page 57, question 39.
The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed (pages 50–51)The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed on page 50 of the DOE handbook.The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed on page 51 of the DOE handbook.

Question 4 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.

More questions like this

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 5 of 6

2018 Test A Math, question 40

Question

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

  • A5
  • B6
  • C13
  • D15
Show the answer

Correct answer: B

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

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

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

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

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

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

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

Question analysis

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

NYS standards
  • 6.NS.4 common factors and multiples
Grade level
Grade 6 content, by NYS standard
Compared with grade 7
Above grade 7 Multiples are sixth-grade content, but grade 7 problems rarely ask students to count a set under two overlapping conditions. The inclusive range and the numbers that are multiples of both make this longer and trickier than usual.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Solution
3 steps
Reading level
Question and choices: about grade 9, 30 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The question gives the overlap, four multiples of both 2 and 3, which invites a subtraction method with three places to go wrong: the count of the set, the overlap, and the final complement. Each of those errors has its own choice. Listing the 19 numbers and crossing out evens and then odd multiples of 3 is slower to describe but faster and safer to do.

  1. Much to keep track of moderate Working it out

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

  2. A very close wrong answer moderate Choosing the answer

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

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

Traps

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

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

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

  1. Sort out the question

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

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

  2. Count the numbers in the set

    n=30−12+1=19n = 30 - 12 + 1 = 19

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

  3. Cross out the even numbers

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

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

    That is 9 numbers.

  4. Cross out the multiples of 3

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

    13, 17, 19, 23, 25, 29

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

  5. Count what is left

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

Check your answer

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

More questions like this

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

Question 6 of 6

2024 Test A Math, question 39

Question

Triangle with its two slanted sides each labeled 13 in. and its base labeled 10 in. Beside it, a vertical arrow as tall as the triangle, from its base to its top vertex, is labeled 12 in.

Raquel is cutting out pieces of cardboard to make a pyramid. She will use a square piece for the base and identical triangular pieces for the sides. The figure above shows the dimensions of the triangle for each side. What will be the total surface area, in square inches, of the pyramid, including the square base?

  • A280
  • B295
  • C340
  • D360
Show the answer

Correct answer: C

Surface area is found by calculating the area of each side, including the base, and adding them all together.

The base of the pyramid measures 10 inches on each side, so the area of the base is

10×10=10010 \times 10 = 100

Each triangular face has a base of 10 inches and a height of 12 inches, so the area of each face is

12×10×12=60\frac{1}{2} \times 10 \times 12 = 60

There are 4 triangular faces (because the square base has 4 edges, each of which will have a triangular face). So the total surface area of the pyramid is the sum of the areas of 4 triangles and 1 square.

(4×60)+100=240+100(4 \times 60) + 100 = 240 + 100

So the total surface area is 340 square inches.

Question analysis

This surface area word problem shows one triangular face, with sides of 13 inches, a base of 10 inches and a height of 12 inches, that Raquel will use to build a cardboard pyramid with a square base. Students find the total area of the base and all the triangular sides. Picturing the solid and choosing the right measurements from the figure are the tricky parts.

NYS standards
  • 7.G.6 area, surface area, and volume
  • 6.G.4 nets and surface area
  • 6.G.1 area of polygons
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students find the surface area of a pyramid from a drawn net or solid. Here only one triangular face is shown, so students must picture the whole pyramid, count its faces, and choose which labeled length belongs in the area formula.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
4 steps
Reading level
Question and choices: about grade 6, 56 words.
Corrected from the DOE handbook
  • A wrong unit in the explanation was corrected.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Students have to build the pyramid in their heads from one flat triangle, then choose the right measurement from three labels. The 13-inch sides look like the natural height, and using them gives a listed total; picturing a pyramid with three sloping faces gives another. Sketching the square base with a triangle on each edge, and marking 12 as the height, settles both the face count and the formula.

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

    The figure gives one triangle with three length labels, 13, 13 and 10, and puts its height, 12, on a separate arrow beside it, where it is easy to overlook. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)

  2. Combines ideas moderate Working it out

    The solid is never drawn: students must see that the square's side equals the triangle's 10-inch base, count four triangles, and add triangle and square areas. (Embretson, 1998; Daniel & Embretson, 2010)

  3. Something you must already know minor Working it out

    A triangle's area uses its perpendicular height, not a slanted side, and a pyramid on a square base has four triangular faces; neither fact is given. (Anderson & Krathwohl, 2001)

Strategy: Sketch the pyramid: a square base whose side is the triangle's base, and one triangular face on each side of the square. Find each area with the matching formula, then add them all.

Traps

  • Misreads the figure: Reads a value, label or tick spacing in a figure, table or graph wrongly.
  • Information you don't need: The question gives numbers or facts that play no part in the answer.
  • 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

What was corrected from the DOE handbook, and why

  • Explanation: The handbook ends “So the total surface area is 340 square feet.” The triangle’s dimensions are in inches and the question asks for square inches, so the site now reads “340 square inches.”

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Area of a triangle
A=12×b×hA = \frac{1}{2} \times b \times h
A is the area. b is the base, the side the triangle sits on. h is the height: the straight-up distance from the base to the top corner, at a right angle to the base. You take half because a triangle is half of a rectangle with the same base and height.
Area of a square
A=s×sA = s \times s
A is the area and s is the length of one side. All four sides of a square are equal, so the area is side times side.
Surface area
surface area=sum of the areas of all the faces\text{surface area} = \text{sum of the areas of all the faces}
A face is one flat side of a solid shape. The surface area is the total area of the outside. Picture unfolding the solid into flat pieces. Then add up the area of every piece.

  1. Sort out the question

    Raquel’s pyramid has a square base. Each side is a triangle like the one in the figure. The triangle’s base is 10 in. Its two slanted sides are 13 in. Its height, the arrow beside it, is 12 in. You need the total surface area, including the square base, in square inches.

  2. Picture the pyramid

    Surface area is the total area of all the flat sides, called faces. Each triangle stands on one edge of the square. So each edge of the square is 10 inches, the same as the triangle’s base. A square has 4 edges, so the pyramid has 4 triangles.

    surface area=sum of the areas of all the faces\text{surface area} = \text{sum of the areas of all the faces}

    Here that is 4 triangles plus 1 square. Watch out: counting only 3 triangles gives 280, choice A.

  3. Find the area of one triangle

    A=12×b×hA = \frac{1}{2} \times b \times h

    A=12×10×12=60A = \frac{1}{2} \times 10 \times 12 = 60

    Each triangle is 60 square inches. Watch out: the height is 12 in., the straight-up arrow. It is not 13 in., the slanted side. Using 13 gives 65 for each triangle and 360 in all, choice D.

  4. Find the area of the base

    The base is a square with sides of 10 inches, the same as each triangle’s base.

    A=s×sA = s \times s

    A=10×10=100A = 10 \times 10 = 100

    The square base is 100 square inches.

  5. Add all five faces

    surface area=4×60+100=240+100=340\text{surface area} = 4 \times 60 + 100 = 240 + 100 = 340

    The four triangles and the square together cover 340 square inches.

    So the answer is C, 340 square inches.

Check your answer

Each triangle is half of a 10 by 12 rectangle, which has an area of 120. So two triangles make 120, and four make 240. Add the base: 240+100=340240 + 100 = 340. The units fit too: inches times inches gives square inches.

More questions like this

The original DOE question
Question 96 as printed on page 86 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 86, question 96. Open page 86 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). This is the DOE’s version, before the corrections listed in the analysis.

Sample #73886