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Question 1 of 6
2026 Practice Test C English, question 43Passage 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
With which statement would the author most likely agree?
- ASome plants are better adapted for growing in space than on Earth, and focus should be placed on them.
- BAttempting to grow plants in space the same way they are grown on Earth would not result in success.
- CPlants grown in space provide better nutritional value than plants grown on Earth.
- DSuccessfully growing plants in space is a challenge, so more research must first be completed on plants grown on Earth.
Show the answer
Correct answer: B
The question asks which statement the author would most likely agree with.
A. Incorrect. Although paragraphs 7 and 8 discuss plants that have been genetically engineered to “accommodate . . . the logistics of growing a plant in space,” the passage does not indicate that the plants are better adapted for growing in space rather than on Earth. Thus, the author is not likely to agree with this statement.
B. CORRECT. In paragraph 3, the author points out that growing plants in space “relies on highly specialized technology over 50 years in the making,” and in paragraph 4, the author explains that the Advanced Plant Habitat requires specialized controls and adaptations for light, moisture, and temperature. The author’s acknowledgment of the special conditions required to grow plants in space indicates that she would agree that growing methods used on Earth are unlikely to succeed in space.
C. Incorrect. Although paragraph 8 mentions that pepper plants were genetically engineered to meet “the nutritional needs of astronauts,” the passage gives no indication that astronauts have greater nutritional needs in space than they do on Earth or that plants grown in space are engineered to provide better nutrition than their counterparts on Earth. Thus, the author would not be likely to agree with this sentence.
D. Incorrect. Although the discussion in paragraph 4 of the rigorously controlled conditions indicates that growing plants in space is, indeed, challenging, the article indicates in paragraph 3 that NASA has been experimenting with growing plants in space “since 2014.” Because plant-growing experiments have already been under way in space for a number of years, it is unlikely that NASA or the author would agree that additional experiments on earth are necessary.
Question analysis
This inference question asks which statement the author of the space-farming excerpt, a Virginia farmer writing for WIRED about NASA’s pepper experiment, would most likely agree with. The author never states her view outright, so students must infer it from the way she reports the experiment, and every choice touches on a topic the article raises.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Inferring which statement an author would accept is regular grade 7 work, but this author mostly reports facts and quotes scientists, so her own view has to be pieced together from several paragraphs of technical description, more than grade 7 usually asks.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Reading between the lines major
- Evidence in several places moderate
- The right answer is reworded minor
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 10, 890 words; question and choices: about grade 6, 80 words.
- Corrected from the DOE handbook
- A misquotation of the excerpt in the explanation was corrected.
- 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
Because the article reports facts and quotes scientists, students must build the author’s view from her descriptions, and the key is a prediction she never makes outright. The half-right choice is the main trap: it begins with a view she does hold, that space farming is hard, then adds a demand for research on Earth that ignores NASA’s work in orbit since 2014. The other two turn the engineered variety and the nutrition theme into comparisons the article never draws.
Reading between the lines major Working it out
The author never states an opinion; her view must be drawn from how she describes the work, a habitat that “doesn’t aim to re-create Earth’s conditions” and technology “over 50 years in the making.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Evidence in several places moderate Working it out
The support is in paragraph 3’s description of the habitat and paragraph 4’s sensors and controls, while the wrong choices draw on paragraph 8’s engineered variety and paragraph 5’s supplements. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
The right answer is reworded minor Choosing the answer
The key’s “the same way they are grown on Earth would not result in success” restates paragraph 3 in new words, while wrong choices reuse “nutritional” and growing “in space.” (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
Strategy: Find the sentences where the author speaks in her own voice rather than quoting a scientist, then choose the statement those sentences support most directly, without adding claims the article never makes.
Traps
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
- Half right: One half of a two-part choice is right and the other is not.
- Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
The wrong answers, classified
A Reads too much in (Graesser, Singer & Trabasso, 1994)
Takes paragraph 8’s variety, bred to suit the logistics of growing in space, and paragraph 1’s upright plants as proof that some plants grow better in space than on Earth.
C Twists what the text says (King et al., 2004)
Turns the contrast between fresh crops and supplements that lose value into a claim that space-grown plants beat Earth-grown ones, though the excerpt never compares the two.
D Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Agrees that the complex habitat shows space farming is hard, then adds a need for more research on Earth first, though NASA has grown plants in space since 2014.
What was corrected from the DOE handbook, and why
- Explanation: The handbook’s explanation of Option A says the plants were genetically engineered “to accommodate the logistics of growing a plant in space.” Paragraph 8 says Bosland “cultivated a variety that could accommodate both the nutritional needs of astronauts as well as the logistics of growing a plant in space”: “to” is not in the excerpt, and eight words are left out without an ellipsis. The site now says genetically engineered to “accommodate . . . the logistics of growing a plant in space.”
- Explanation: The handbook’s explanation of Option B says “The author’s acknowledgment of the special conditions required to grow plants in space indicate that she would agree.” The subject is “acknowledgment,” so the site now says “indicates.”
Working it out, step by step
Figure out what the question asks
You need to figure out the author’s view. She never states it outright. She mostly reports facts and quotes scientists. So look at how she describes the work. Then pick the statement her own words support best, without adding ideas she never gives.
Find the author’s own words
In paragraph 3, the author says growing plants in space “relies on highly specialized technology over 50 years in the making.” She also says the habitat “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.” In paragraph 4, she adds that its “more than 180 sensors control and monitor temperature, humidity, and carbon dioxide.”
Explain what she means
Specialized means made for one special job. To re-create means to copy. A variable is one thing that can change, like light or heat. Clinical means very clean and controlled, like a hospital. So she is saying that space is not like a garden on Earth. Plants there need special tools that control every condition, one by one. Simply copying Earth’s way of growing would not be enough.
Check each choice
- A is wrong. Paragraphs 7 and 8 show a pepper bred to “accommodate” growing in space. But nothing says some plants grow better in space than on Earth.
- B is right. She stresses special technology and says the habitat doesn’t copy Earth. So Earth’s usual methods alone would fail.
- C is wrong. She never says space plants are healthier than Earth plants.
- D is wrong. She does show that growing in space is hard. But NASA has grown plants in space “since 2014.” Nothing says Earth research must come first.
Watch out: D starts with an idea she holds, that space farming is hard. Then it adds a demand she never makes.
Choose the answer
The author shows that space farming needs special tools, not Earth’s usual ways. So the answer is B, “Attempting to grow plants in space the same way they are grown on Earth would not result in success.”
Why this answer and not the closest wrong one
D is the closest wrong answer. Its first half fits the author: growing plants in space takes complex tools. But its second half says more research on Earth must come first. The article shows the opposite: NASA has grown plants in space for years. B sticks to what her words show.
More questions like this
The original DOE question
The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed (pages 50–51)
Question 2 of 6
2026 Practice Test B English, question 15Passage 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
Read this sentence from paragraph 3.
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.
What does the phrase “a faint trace of apology” convey about the professor?
- AIt indicates that the professor feels bad that he has to call the narrator to his office after work.
- BIt shows that the professor is hesitant to share his opinions with the narrator.
- CIt implies that the professor is uncomfortable criticizing the narrator’s work.
- DIt suggests that the professor knows that the conversation will be frustrating for the narrator.
Show the answer
Correct answer: D
The question asks what the phrase “a faint trace of apology” in paragraph 3 conveys about the professor.
A. Incorrect. The fact that the narrator had intended to leave the office for the day is not the source of the professor’s faintly apologetic manner, which is instead caused by the professor’s understanding that their conversation about the letter and the expedition is likely to cause an argument (“with a whimsical smile that suggested amusement, impatience, annoyance” [paragraph 3]). In paragraph 29, the professor asks the narrator if he can leave on an expedition that same evening, which indicates that the professor does not feel bad about taking up the narrator’s time after work.
B. Incorrect. The paragraphs that follow the sentence from paragraph 3 show the professor sharing his opinions without pause, even when his opinion of the narrator is unflattering (“ ‘Like swimming squirrels, you navigate with the help of Heaven and a stiff breeze, but you never land where you hope to—do you?’ ” [paragraph 17]).
C. Incorrect. The professor knows that the narrator will push back regarding the letter, but the professor is not uncomfortable challenging the narrator. Professor Farrago seems perfectly at ease and comfortable as he begins the discussion with the narrator.
D. CORRECT. The professor is both amused and annoyed by the narrator’s dismissal of the possibility that great auks still exist, and the professor knows that the narrator is likely to react negatively to being sent on what the narrator considers a “fool’s errand” (paragraph 25).
Question analysis
This question focuses on a single phrase in the excerpt from Robert W. Chambers’s In Search of the Unknown: as the professor looks up from a pile of letters, his whimsical smile shows “a faint trace of apology.” Students must work out what that hint of apology says about him. The phrase is brief and old-fashioned, and several explanations for it seem natural.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students often infer a character’s feelings from a description. Here the phrase ends a 46-word sentence of early-1900s prose, follows three other moods, and has to be interpreted from the scene as a whole, beyond typical grade 7 work.
- Estimated difficulty
- Among the hardest on the SHSAT: a non-obvious approach, heavy reading, or a well-hidden trap.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly analyze
- What makes it hard
- Reading between the lines major
- A very close wrong answer moderate
- Evidence in several places moderate
- Complex sentences minor
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 9, 1066 words; question and choices: about grade 10, 123 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 phrase comes before a word of the conversation is spoken, so the reason for the apology lies ahead in the text. Two natural guesses compete with it: the professor has called the narrator back just as he was leaving, and he is about to question one of the narrator’s replies. Only a reader who follows the scene to the narrator’s scorn for the letter and the errand sees that the professor, at ease throughout, is sorry for what he is about to put the narrator through.
Reading between the lines major Working it out
Nothing explains the apology; students must reason from the talk that follows, in which the professor sends the narrator after birds the narrator believes extinct, that the professor expects resistance. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
A very close wrong answer moderate Choosing the answer
The choice about criticizing the narrator’s work and the right one both tie the apology to the coming talk about a letter; one places discomfort in the professor, the other frustration in the narrator. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
What the professor anticipates appears only later: the narrator’s scorn for the letter in paragraphs 5–14 and his view of the trip as a “fool’s errand” in paragraph 25. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Complex sentences minor Understanding the question
The phrase closes a 46-word sentence, after a clause about the pile of letters and a run of three other moods, “amusement, impatience, annoyance.” (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Strategy: Read the full sentence and then the conversation it opens, and test each choice against how the professor actually speaks and acts in that conversation.
Traps
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
- Half right: One half of a two-part choice is right and the other is not.
- Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
The wrong answers, classified
A Reads too much in (Graesser, Singer & Trabasso, 1994)
Ties the apology to the timing, since Professor Lesard stopped the narrator as he was leaving Bronx Park, but the professor later asks him to leave on the trip that same night.
B Twists what the text says (King et al., 2004)
Reads the apology, and the “embarrassed smile” of paragraph 9, as reluctance to speak, though the professor states his belief in the letter plainly and even teases the narrator.
C Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Rightly senses that the professor is about to challenge the narrator’s reply to a letter, but he does it “placidly” and “coolly,” with no sign of discomfort.
Working it out, step by step
Figure out what the question asks
This asks what one phrase shows about the professor: “a faint trace of apology.” Faint means slight, and a trace is a small sign. So his smile looks a little bit sorry. Why would he feel sorry? You find out from the talk that follows.
Read the whole sentence
Paragraph 3 says the professor looked at the narrator “with a whimsical smile that suggested amusement, impatience, annoyance, and perhaps a faint trace of apology.” Whimsical means playful. He is amused by the narrator and a bit annoyed with him. Then he picks up a letter the narrator has already turned down.
See what the professor is about to do
The professor is about to defend that letter. Then he sends the narrator after the birds in it. The narrator thinks the birds are extinct, or all dead. In paragraph 25 he calls the trip “this fool’s errand,” a pointless job. The professor seems to know the narrator will hate this. That is why his smile looks a little sorry.
Check each choice
- A does not fit. He later asks, “Can you leave to-night?” (paragraph 29). He is not sorry about taking the narrator’s time.
- B does not fit. He shares his opinion plainly: “He isn’t—in mine” (paragraph 11).
- C does not fit. He does challenge the narrator, but calmly. He speaks “placidly” and “coolly,” with no sign of being uneasy.
- D fits. He knows the talk will annoy the narrator.
Watch out: C is tempting because the professor is about to disagree with the narrator. But nothing shows that he is uncomfortable about it.
Choose the answer
The slight apology shows that the professor expects the narrator to be frustrated. So the answer is D, “It suggests that the professor knows that the conversation will be frustrating for the narrator.”
Why this answer and not the closest wrong one
C is the closest wrong choice. Both C and D link the apology to the talk about the letter. But C puts the bad feeling in the professor, as if he were nervous. He is not. He speaks “placidly,” which means calmly. D puts the bad feeling in the narrator, and the narrator does get upset.
More questions like this
The original DOE question
The passage “Excerpt from In Search of the Unknown” as printed (page 21)
Question 3 of 6
2018 Test B English, question 52Passage Invention of the Telegraph
Samuel Morse, an American inventor, is credited with creating the electronic telegraph, a communication device that allows users to send messages using a system of short and long pulses that represent letters, numbers, and punctuation. In 1843 the United States Congress passed the Telegraph Bill, which provided Morse with the funds to build an electric telegraph system.
Invention of the Telegraph
Earlier Signal Systems
Long before Samuel F. B. Morse electrically transmitted his famous message “What hath God wrought?” from Washington to Baltimore on May 24, 1844, there were signaling systems that enabled people to communicate over distances. Most were visual or “semaphore” systems using flags or lights. In the eighteenth century, such systems used an observer who would decipher a signal from a high tower on a distant hill and then send it on to the next station. The young American republic wanted just such a system along its entire Atlantic coast and offered a prize of $30,000 for a workable proposal. The framers of this legislation had no way of knowing that when they used the word “telegraph” to refer to this visual semaphore system, they would be offered an entirely new and revolutionary means of communication—electricity.
The Growth of an Idea
The idea of using electricity to communicate over distance is said to have occurred to Morse during a conversation aboard ship when he was returning from Europe in 1832. Michael Faraday’s recently invented electromagnet was much discussed by the ship’s passengers, and when Morse came to understand how it worked, he speculated that it might be possible to send a coded message over a wire. While a student at Yale College years before, he had written his parents a letter about how interesting he found the lectures on electricity. Despite what he had learned at Yale, Morse found when he began to develop his idea that he had little real understanding of the nature of electricity, and after sporadic attempts to work with batteries, magnets, and wires, he finally turned for help to a colleague at the University of the City of New York, Leonard D. Gale.
Gale was a professor of chemistry and familiar with the electrical work of Princeton’s Joseph Henry, a true pioneer in the new field. Well before Morse had his shipboard idea about a telegraph, Henry rang a bell at a distance by opening and closing an electric circuit. In 1831, he had published an article, of which Morse was unaware, that contained details suggesting the idea of an electric telegraph. Gale’s help and his knowledge of this article proved crucial to Morse’s telegraph system because Gale not only pointed out flaws in the system but showed Morse how he could regularly boost the strength of a signal and overcome the distance problems he had encountered by using a relay system Henry had invented. Henry’s experiments, Gale’s assistance, and, soon after, hiring the young technician Alfred Vail were keys to Morse’s success.
Obstacles and Opportunities
By December 1837, Morse had enough confidence in his new system to apply for the federal government’s appropriation, and during the next year he conducted demonstrations of his telegraph both in New York and Washington.
However, when the economic disaster known as the Panic of 1837 took hold of the nation and caused a long depression, Morse was forced to wait for better times. It was during this period that Morse visited Europe again and tried not only to secure patent protection overseas but to examine competing telegraph systems in England. . . .
By 1843, the country was beginning to recover economically, and Morse again asked Congress for the $30,000 that would allow him to build a telegraph line from Washington to Baltimore, forty miles away. The House of Representatives eventually passed the bill containing the Morse appropriation, and the Senate approved it in the final hours of that Congress’s last session. With President Tyler’s signature, Morse received the cash he needed and began to carry out plans for an underground telegraph line.
Realizing a Great Invention
Morse had hired the ingenious construction engineer Ezra Cornell to lay the pipe carrying the wire, and although Cornell did his job superbly, one of Morse’s partners, Congressman F. O. J. Smith, had purchased wire with defective insulation. Too much time had been wasted laying bad wire, and with the project on a rigid deadline, something had to be done quickly. Cornell suggested that the fastest and cheapest way of connecting Washington and Baltimore was to string wires overhead on trees and poles. The desperate Morse gave the go-ahead, and the line was completed in time for the dramatic and spectacularly successful link between the Supreme Court chamber of the Capitol building and the railroad station in Baltimore.
Soon, as overhead wires connected cities up and down the Atlantic coast, the dots-and-dashes method that recorded messages on a long moving strip of paper was replaced by the operator’s ability to interpret the code in real time. . . . Telegraph lines soon extended westward, and within Morse’s own lifetime they connected the continents of Europe and America.
“Invention of the Telegraph”—Public Domain/Library of Congress
legislation: Telegraph Bill
dots-and-dashes method: the short and long pulses of Morse code that are sent and received by telegraph operators
The first transatlantic electric telegraph message was sent in 1858, and by 1902 the British All-Red Line connected most of the world.
Source: U.S. Bureau of the Census. Historical Statistics of the United States, Colonial Times to 1970, Bicentennial Edition, Part 2. Washington, D.C., 1975.
Question
The details of the section “The Growth of an Idea” convey a central idea of the passage by suggesting that
- Athe collaborative efforts of colleagues resulted in successful communication over a wire.
- Ba great deal of interest and work was devoted to understanding how to use electricity to send signals.
- CFaraday’s invention of the electromagnet inspired the invention of the telegraph.
- Dcolleges like Yale played a great role in making new discoveries about electricity and its applications.
Show the answer
Correct answer: B
The question asks how a passage section helps convey a central idea of the passage. Paragraph 3 states that “Henry’s experiments, Gale’s assistance, and, soon after, hiring the young technician Alfred Vail were keys to Morse’s success.” The level of interest inspired Morse and others to work together to find a way to use electricity to send long-distance messages.
Option B is correct; the section helps convey a central idea because, overall, the section focuses on what fascinated Morse enough to begin his work and how others were just as interested and willing to work to achieve this goal.
Option A is incorrect because, although the word collaborative suggests that multiple people contributed to the telegraph’s success, the option does not clarify the research and effort needed in order to understand how to use electricity to send signals.
Option C is incorrect because when Morse came to understand how Faraday’s electromagnet worked, Morse wondered if it might be possible to send a coded message over a wire, but that thought later evolved into the telegraph only after more research and experimentation.
Option D is incorrect because the influence of what Morse learned at Yale was only a minor factor in his development of the telegraph.
Question analysis
This central idea question asks what the details in the section “The Growth of an Idea” suggest about the passage “Invention of the Telegraph.” The section covers Faraday’s electromagnet, Morse’s Yale lectures, and help from Gale, Henry and Vail, so students must judge which statement those details support as a group, and more than one choice sounds right.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 central-idea questions usually have one clearly best summary. Here two paragraphs of names and events must be weighed, and several choices restate true details, so judging which fits the whole section is unusually demanding.
- Estimated difficulty
- Among the hardest on the SHSAT: a non-obvious approach, heavy reading, or a well-hidden trap.
- Thinking it demands
- Depth of knowledge 3, strategic thinking · mainly understand
- What makes it hard
- A very close wrong answer major
- Evidence in several places moderate
- The right answer is reworded moderate
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 11, 910 words; question and choices: about grade 12, 77 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
This is among the hardest questions in the set because the most tempting wrong choice reads like a paraphrase of the section’s final sentence. Rejecting it means noticing that the section never shows a message getting through and never shows Henry working with Morse, who had not even read his article. The right choice is vague by design, and only a summary of both paragraphs together shows that it fits better.
A very close wrong answer major Choosing the answer
The colleagues choice and the interest-and-work choice both describe effort spent on sending signals by wire; they part on one claim, that the effort “resulted in successful communication,” which the section never shows, the working line arriving in paragraph 7. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The idea emerges only from details across two paragraphs, passengers discussing the electromagnet, Morse’s Yale letter, his failed attempts, Henry’s bell and article, Gale’s relay advice, taken together. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
The right answer is reworded moderate Choosing the answer
The key names none of the section’s people, while the wrong choices echo its “colleague,” “over a wire,” Faraday’s electromagnet and Yale, and so look more firmly rooted in the text. (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
Strategy: Summarize paragraphs 2 and 3 together in one sentence of your own before reading the choices, then choose the statement closest to your summary, checking that every part of it is true of this section.
Traps
- Half right: One half of a two-part choice is right and the other is not.
- 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.
The wrong answers, classified
A Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Rightly sees teamwork in the section’s close, but successful communication over Morse’s wire comes later, under “Realizing a Great Invention,” and the passage never shows Henry working with Morse.
C Too narrow (King et al., 2004)
Treats the spark as the whole story: Faraday’s electromagnet gave Morse the idea, but the section goes on to years of failed attempts and help from others.
D Too broad or too strong (King et al., 2004)
Inflates a passing mention: Morse’s Yale lectures appear once, and the section notes that despite them he had “little real understanding of the nature of electricity.”
Working it out, step by step
Figure out what the question asks
This asks what the section “The Growth of an Idea” says about a central idea, or main message. The section is paragraphs 2 and 3. Sum up both paragraphs together before you look at the choices.
List the section’s details
On the ship, Faraday’s electromagnet “was much discussed by the ship’s passengers.” Morse had found the electricity lectures at Yale interesting. He made “sporadic attempts” on his own. In paragraph 3, Henry “rang a bell at a distance by opening and closing an electric circuit.” Gale showed Morse how to use Henry’s relay system.
Find what the details share
Look at what links these details. Passengers talked about electricity. Morse was curious and kept trying. Henry ran tests and wrote an article. Gale gave advice. All of it is people taking an interest in electricity and working to send signals with it. That is the section’s main point. A working telegraph line does not appear until paragraph 7.
Check each choice
- A is close but wrong. Morse’s telegraph does not send a message until paragraph 7. Also, Henry never worked with Morse. At first, Morse did not even know about Henry’s article.
- B fits. It covers the interest and the work in both paragraphs.
- C is wrong. The electromagnet gave Morse the idea, but that is only the start of the section.
- D is wrong. Yale is only a small part of paragraph 2. And “Despite what he had learned at Yale,” Morse still knew little.
Choose the answer
The section shows lots of interest and effort aimed at sending signals with electricity. So the answer is B, “a great deal of interest and work was devoted to understanding how to use electricity to send signals.”
Why this answer and not the closest wrong one
A sounds like a summary of the section’s last sentence, which is why it tempts. But it claims the teamwork “resulted in successful communication,” and that only happens in a later section. B claims less, so every detail in paragraphs 2 and 3 fits it.
More questions like this
The original DOE question
The passage “Invention of the Telegraph” as printed (pages 146–148)
Question 4 of 6
2026 Practice Test D Math, question 48Question
The perimeter of square W is twice the perimeter of equilateral triangle X. What is the ratio of the length of one side of square W to the length of one side of equilateral triangle X?
- A3:8
- B2:3
- C3:2
- D2:1
Show the answer
Correct answer: C
First, set up the ratio of the perimeter of the square to the triangle as 2:1 because the question states that the perimeter of the square is twice the perimeter of the triangle.
Recognizing that the square has 4 equal sides and that an equilateral triangle has 3 sides, use division to find the ratio of the sides.
Perimeter:
Sides:
Question analysis
The perimeter of square W is twice the perimeter of equilateral triangle X, and students find the ratio of a side of the square to a side of the triangle. This ratio question uses perimeters of regular shapes with no lengths given. Turning a comparison of perimeters into one of sides, and keeping the ratio in the order asked, are the tricky parts.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 ratio problems usually supply numbers to work with. This one gives only a relationship between two perimeters, so students must bring in the number of sides of each shape themselves and keep the ratio in the order asked.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math moderate
- Variables instead of numbers moderate
- A very close wrong answer minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 9, 36 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The question turns a statement about perimeters into a ratio of sides, and the natural guess, that the sides keep the perimeters’ 2 to 1, ignores that the square shares its perimeter among 4 sides and the triangle among 3. Choosing a triangle perimeter such as 12 makes the comparison concrete. The order of the ratio still has to be checked at the end, because its reverse is listed too.
Turning words into math moderate Understanding the question
“The perimeter of square W is twice the perimeter of equilateral triangle X” must become 4s = 2 × 3t, with the 2 on the triangle’s side; written backward, it gives the triangle the larger perimeter. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Variables instead of numbers moderate Understanding the question
No side length is given, so students must either work with letters for the two sides or choose a convenient perimeter themselves, such as 12 for the triangle. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
A very close wrong answer minor Choosing the answer
The ratios 3:2 and 2:3 use the same two numbers, so only keeping the square’s side first, as the question orders it, separates the answer from its reverse. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Pick an easy side length for the triangle, find its perimeter, double that for the square, divide by the square's number of sides, and write square to triangle.
Traps
- Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.
- Wrong operation: Adds instead of multiplying, divides the wrong way round, turns a ratio or rate upside down, or undoes a step in the wrong direction (subtracts what should be added back).
- Equation written backwards: Writes a comparison the wrong way round, word for word: "six times as many students as professors" as 6S = P. The bigger quantity gets the bigger number.
The wrong answers, classified
A Equation written backwards (Clement, Lochhead & Monk, 1981)
Writes the comparison backward, 2 × 4s = 3t, giving the triangle the larger perimeter, so the ratio of the sides comes out 3:8.
B Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Finds the right relationship but turns the ratio upside down, giving the triangle’s side to the square’s instead of the square’s side first.
D Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Assumes the sides are in the same ratio as the perimeters, 2:1, ignoring that the square has 4 sides and the triangle only 3.
Worked solution, step by step
Formulas used
- Perimeter of a square
- P is the perimeter, the distance around the shape. s is the length of one side. A square has 4 equal sides, so its perimeter is 4 times one side.
- Perimeter of an equilateral triangle
- An equilateral triangle has 3 equal sides. t is the length of one side. So its perimeter is 3 times one side.
- Ratio
- A ratio compares two amounts in order. a : b means a compared with b. The order matters, so write the amounts in the order the question names them.
Sort out the question
Square W has a perimeter twice as long as the perimeter of triangle X. Equilateral means all 3 sides of X are equal.
You need the ratio of one side of the square to one side of the triangle, in that order. No lengths are given, so you can pick a size to try.
Pick a size for the triangle
Choose an easy side length for the triangle, such as 2 units. All 3 sides are 2, so its perimeter is:
Find the square’s side
The square’s perimeter is twice the triangle’s:
The square has 4 equal sides, so divide by 4:
Each side of the square is 3 units.
Write the ratio in order
The square comes first, then the triangle. Their sides are 3 and 2, so the ratio is 3 : 2.
Watch out: 2 : 1, choice D, compares the perimeters, not the sides. The square splits its perimeter into 4 sides, the triangle into only 3. Choice B, 2 : 3, puts the triangle first. Choice A, 3 : 8, comes from giving the triangle the bigger perimeter.
So the answer is C, 3:2.
Check your answer
Try a different size. Give the triangle sides of 4. Its perimeter is 12, so the square’s is 24. Each side of the square is . The ratio 6 : 4 simplifies to 3 : 2. The size does not change the ratio.
More questions like this
The original DOE question
Question 5 of 6
2018 Test A Math, question 5Question
The sum of two consecutive integers is −15. If 1 is added to the smaller integer and 2 is subtracted from the larger integer, what is the product of the two resulting integers?
Grid-in question: work out the answer and enter it as a number.
Show the answer
Correct answer: 63
If x is the smaller consecutive integer, then
is the larger consecutive integer. Use their sum (−15) to find x:
The two consecutive integers are −8 and −7. One is added to the smaller integer:
and 2 is subtracted from the larger integer:
Find the product:
Question analysis
A grid-in problem about two consecutive integers whose sum is −15. Students find the two integers, add 1 to the smaller and subtract 2 from the larger, then multiply the results. Deciding which negative integer is the smaller one, and keeping signs straight through every step, are what make it tricky.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 A typical grade 7 task solves one two-step equation or multiplies signed numbers. This links both: set up a consecutive-integer equation, solve it with negatives, adjust each integer, and multiply, with no choices to check against.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- Turning words into math moderate
- Many steps moderate
- Solution
- 4 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
Every step is routine, yet the question collects most of the ways students lose points with negatives. The crucial judgment is which of −8 and −7 is the smaller; a student who picks −7 still produces a tidy, wrong product. Gridding the product of the original pair, or giving a negative product, are the other usual losses. Writing each intermediate pair down, rather than holding them in mind, protects against all three.
Error-prone arithmetic moderate Working it out
Every number in play is negative: −8 and −7, then −7 and −9, and a product of two negatives that must come out positive. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Turning words into math moderate Understanding the question
"1 is added to the smaller integer and 2 is subtracted from the larger" depends on knowing that −8, not −7, is the smaller, since it lies farther below zero. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Many steps moderate Working it out
Four linked steps: set up x + (x + 1) = −15, solve for x, adjust each integer, then multiply; an error early in the chain carries through to the product. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Strategy: Halve the sum to see which two integers sit on either side of it, remember that the smaller negative is farther from zero, then adjust each and multiply.
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.)
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
60 Negatives and direction (Brown & Burton, 1978)
Takes −7 as the smaller integer because 7 is less than 8, so adjusts to −7 + 1 = −6 and −8 − 2 = −10, and multiplies to 60.
56 Misreads the question (Hegarty, Mayer & Monk, 1995)
Finds −8 and −7 and multiplies them to get 56, skipping the sentence that adds 1 to one integer and subtracts 2 from the other.
-63 Negatives and direction (Brown & Burton, 1978)
Finds the adjusted integers −7 and −9 correctly but gives their product a negative sign, gridding −63.
Worked solution, step by step
Formulas used
- Consecutive integers
- Integers are whole numbers and their opposites, like −2, −1, 0, 1 and 2. Consecutive integers come one right after another. If n is the smaller one, the next one is n + 1, because each step up the number line adds 1.
- Multiplying two negative numbers
- a and b are positive numbers, so −a and −b are negative. When you multiply two negative numbers, the answer is positive. The two minus signs cancel out.
Sort out the question
Two consecutive integers add up to −15. Integers are whole numbers and their negatives. Consecutive means one comes right after the other, like 4 and 5. You need to do three things:
- Find the two integers.
- Add 1 to the smaller one. Subtract 2 from the larger one.
- Find the product of the two new numbers. The product is the answer when you multiply.
Find the two integers
Call the smaller integer n. Then the larger one is n + 1. Their sum is −15.
Subtract 1 from both sides. Then divide both sides by 2.
So the integers are −8 and −7.
Decide which one is smaller
On a number line, −8 is to the left of −7. Numbers to the left are smaller. So −8 is the smaller integer, and −7 is the larger one. Watch out: 8 is bigger than 7, but −8 is smaller than −7. Mixing them up gives −6 and −10, and the wrong answer 60.
Change each integer
Add 1 to the smaller integer.
Subtract 2 from the larger integer.
The two new numbers are −7 and −9.
Multiply the new numbers
Both numbers are negative, so their product is positive.
Watch out: the answer is not −63, because two negatives make a positive. Also, don’t multiply the first pair, −8 and −7. That gives 56 and skips the changes. So you would grid 63.
Check your answer
Check the pair: , and they are one apart. Half of −15 is −7.5, and −8 and −7 sit on either side of it. Then , and the sign is positive.
More questions like this
The original DOE question
Question 6 of 6
2026 Practice Test D Math, question 19Question
A store manager purchases a piece of furniture for $456.00. To determine the selling price, the manager increases the purchase cost by 125%. A customer buys the furniture and pays an additional 8% sales tax. How much does the customer pay for the furniture?
- A$615.60
- B$627.48
- C$1,108.08
- D$1,846.80
Show the answer
Correct answer: C
Given a purchase price of $456.00, the 125% increase in price is calculated as:
The selling price equals the purchase price plus the increase, or:
The sales tax on the selling price is:
The customer pays the selling price plus the sales tax:
Question analysis
A store manager buys a piece of furniture for $456.00 and raises the price by 125% to set the selling price, and the customer also pays 8% sales tax. Students find the total the customer pays. It tests percent increase and sales tax in sequence, and reading an increase of more than 100% correctly is the main challenge.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students find markups and sales tax, usually with increases under 100%. An increase of more than 100% is unusual and easy to misread, and two percent changes must be applied in order, which goes beyond routine grade 7 work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math moderate
- Many steps moderate
- Error-prone arithmetic minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 7, 41 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
A percent above 100 is unusual in grade 7 work, and it is the center of the question: the markup more than doubles the price. Students who treat “by 125%” as “125% of” still find a listed answer after adding tax, and so do students who add $125. A rough check helps: the selling price must be more than twice $456, about $1,000, and the tax adds less than a tenth of that.
Turning words into math moderate Understanding the question
“Increases the purchase cost by 125%” adds 125% of $456 to the $456 itself, a multiplier of 2.25; reading it as 125% of the cost leaves the original price out. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Many steps moderate Working it out
Four steps in a row, the increase, the selling price, the tax and the total, each depend on the one before, and two of them are easy to merge or skip. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Error-prone arithmetic minor Working it out
Taking 8% of $1,026 means multiplying by 0.08, and a decimal point one place off, 0.8, makes the tax ten times too large. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Strategy: Turn each percent change into a multiplier, remembering that an increase by a percent is added to the original amount, apply the markup and then the tax, and estimate to check the size.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- 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.
- An arithmetic slip: The right method with a plausible arithmetic error: a digit, a place value or a times-table fact.
The wrong answers, classified
A Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds the increase, 125% of $456 = $570, and uses it as the selling price without adding back the $456 cost, then adds 8% tax.
B Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Reads the 125% increase as $125, a fixed amount, so the selling price is $581, and then adds 8% tax correctly to reach $627.48.
D An arithmetic slip (Junker & Sijtsma, 2001)
Finds the $1,026 selling price correctly but writes 8% as 0.8, adding $820.80 in tax instead of $82.08.
Worked solution, step by step
Formulas used
- Percent of a number
- n is the starting amount, and p is the percent. Percent means out of 100, so 125% is 125/100 = 1.25 and 8% is 8/100 = 0.08. Multiply n by that decimal to find the part.
- Price after an increase
- The old price is what you start with. The increase is the amount added on. To increase by a percent, find that percent of the old price, then add it to the old price. Sales tax is added the same way.
Sort out the question
The manager pays $456.00 for the furniture. The selling price is that cost increased by 125%. The customer then pays 8% sales tax on top. Sales tax is an extra charge, a percent of the price. You need the total the customer pays.
Find the increase
Find 125% of $456. As a decimal, 125% is 1.25, which is 1 and a quarter. A quarter of 456 is 114:
The increase is $570.
Find the selling price
Increases by means the increase is added to the cost:
The selling price is $1,026.
Watch out: $570 is only the increase. Using it as the price gives $615.60, choice A. And 125% is a percent, not $125. Adding $125 leads to $627.48, choice B.
Find the sales tax
As a decimal, 8% is 0.08. Find 8% of the selling price:
The tax is $82.08.
Watch out: 8% is 0.08, not 0.8. Using 0.8 makes the tax ten times too big and gives $1,846.80, choice D.
Add the tax to the price
The customer pays the selling price plus the tax:
So the answer is C, $1,108.08.
Check your answer
Estimate. The price more than doubles: $456 plus $570 is about $1,000. Tax of 8% adds about $80. So the total should be a bit over $1,080, and only $1,108.08 is close. Or multiply in one go: 456 × 2.25 × 1.08 = 1,108.08.
More questions like this
The original DOE question
