3 English and 3 math
Here are 6 random questions to try. Takers earning below 75% are unlikely to receive an offer. You have 1 minute 48 seconds per question on the real exam.
Question 1 of 6
2026 Practice Test D English, question 8Passage Excerpt from “How We Made the First Flight”
Excerpt from “How We Made the First Flight”
by Orville Wright
In 1903 brothers Wilbur and Orville Wright conducted experiments related to flying machines. These experiments would eventually lead to air travel becoming a reliable form of transportation.
During the night of December 16, 1903, a strong cold wind blew from the north. When we arose on the morning of the 17th, the puddles of water, which had been standing about camp since the recent rains, were covered with ice. The wind had a velocity of 10 to 12 meters per second (22 to 27 miles an hour). We thought it would die down before long, and so remained indoors the early part of the morning. But when ten o’clock arrived, and the wind was as brisk as ever, we decided that we had better get the machine out and attempt a flight. We hung out the signal for the men of the Life Saving Station.1 We thought that by facing the flyer into a strong wind, there ought to be no trouble in launching it from the level ground about camp. We realized the difficulties of flying in so high a wind, but estimated that the added dangers in flight would be partly compensated for by the slower speed in landing.
Final Preparations
We laid the track on a smooth stretch of ground about one hundred feet north of the new building. The biting cold wind made work difficult, and we had to warm up frequently in our living room, where we had a good fire in an improvised stove made of a large carbide2 can. By the time all was ready, J. T. Daniels, W. S. Dough and A. D. Etheridge, members of the Kill Devil3 Life Saving Station; W. C. Brinkley of Manteo, and Johnny Moore, a boy from Nags Head,4 had arrived.
We had a “Richard” hand anemometer with which we measured the velocity of the wind. Measurements made just before starting the first flight showed velocities of 11 to 12 meters per second, or 24 to 27 miles per hour. . . .
Audacity—and Calculation
Wilbur having used his turn in the unsuccessful attempt on the 14th, the right to the first trial now belonged to me. After running the motor a few minutes to heat it up, I released the wire that held the machine to the track, and the machine started forward in the wind. Wilbur ran at the side of the machine, holding the wing to balance it on the track. Unlike the start on the 14th, made in a calm, the machine, facing a 27-mile wind, started very slowly. Wilbur was able to stay with it till it lifted from the track after a forty-foot run. One of the Life Saving men snapped the camera for us, taking a picture just as the machine had reached the end of the track and had risen to a height of about two feet. The slow forward speed of the machine over the ground is clearly shown in the picture by Wilbur’s attitude. He stayed along beside the machine without any effort.
Flight
The course of the flight up and down was exceedingly erratic, partly due to the irregularity of the air, and partly to lack of experience in handling this machine. The control of the front rudder was difficult on account of its being balanced too near the center. This gave it a tendency to turn itself when started; so that it turned too far on one side and then too far on the other. As a result the machine would rise suddenly to about ten feet, and then as suddenly dart for the ground. A sudden dart when a little over a hundred feet from the end of the track, or a little over 120 feet from the point at which it rose into the air, ended the flight. As the velocity of the wind was over 35 feet per second and the speed of the machine over the ground against this wind ten feet per second, the speed of the machine relative to the air was over 45 feet per second, and the length of the flight was equivalent to a flight of 540 feet made in calm air. This flight lasted only 12 seconds, but it was nevertheless the first in the history of the world in which a machine carrying a man had raised itself by its own power into the air in full flight, had sailed forward without reduction of speed and had finally landed at a point as high as that from which it started.
From “How We Made the First Flight” by Orville Wright—Public Domain/Federal Aviation Administration
1Life Saving Station: one of the rescue stations along the Atlantic coastline that provided assistance to mariners in distress
2carbide: a very hard material composed of carbon and other heavy metals
3Kill Devil: the town of Kill Devil Hills in eastern North Carolina
4Nags Head: a town in eastern North Carolina
Question
How does paragraph 1 introduce the idea that the Wright brothers knew that their flight attempt was risky?
- Athrough the mention of a signal to notify lifesaving experts that the flight attempt was about to begin
- Bby providing specific details about the speed of the wind and the Wright brothers’ response to the windy conditions
- Cby suggesting that a slower landing would be necessary at the end of the flight in order to maintain safety
- Dthrough the indication that the Wright brothers waited indoors for most of the morning because of the poor weather
Show the answer
Correct answer: A
The question asks how paragraph 1 introduces the idea that the Wright brothers knew that their flight attempt was risky.
A. CORRECT. Paragraph 1 describes the Wright brothers hanging out “the signal” to notify the lifesaving crew to stand by as they attempted flight; the need for lifesaving experts to be available in case of an accident introduces the idea that the attempted flight might crash.
B. Incorrect. The specifics on the speed of the wind by themselves do not emphasize the danger of the flight. While the brothers admitted that the strong wind posed certain risks, they also noted that the windy conditions might make landing safer (“estimated that the added dangers in flight would be partly compensated for by the slower speed in landing” [paragraph 1]).
C. Incorrect. A slower landing was expected as a result of the windy conditions, but it was not part of a plan to increase the safety of the flight.
D. Incorrect. While the Wright brothers’ initial decision to wait to see whether the wind would die down does suggest they were concerned about the safety of the flight, the explanation of their decision to proceed with the flight shows that they expected one benefit from the poor weather: “the slower speed in landing” (paragraph 1).
Question analysis
This question on Orville Wright’s account “How We Made the First Flight” asks how the opening paragraph, which describes a cold, windy December morning at the brothers’ camp, introduces the idea that the Wright brothers knew their flight attempt was risky. Students must judge which of four details from the paragraph does that work, and the paragraph mentions both dangers and reasons for confidence.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Finding how a paragraph introduces an idea is grade 7 work, but this paragraph is long and old-fashioned, every choice points to something it mentions, and students must decide which detail most clearly signals that the brothers saw a risk.
- 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 evaluate
- What makes it hard
- Reading between the lines moderate
- Every choice must be checked moderate
- Complex sentences minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 7, 816 words; question and choices: about grade 10, 93 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
Paragraph 1 states the danger outright only in its last sentence, and that sentence then weighs it against a gentler landing, so the choice built on the brothers’ response to the wind is the strongest pull. The key rests on a quieter detail whose meaning comes from a footnote: men from a rescue station were signaled before the attempt. Students must decide which detail shows the brothers preparing for trouble, not just noticing the weather, and that test is narrower than most expect.
Reading between the lines moderate Working it out
The key never says danger: students must connect “the signal for the men of the Life Saving Station” to footnote 1, rescue stations for “mariners in distress,” and see that summoning rescuers means expecting trouble. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Every choice must be checked moderate Choosing the answer
All four details come from paragraph 1, and its plainest admission of danger, “We realized the difficulties of flying in so high a wind,” sits inside a wrong choice, so each detail must be weighed for what it shows. (Embretson & Wetzel, 1987)
Complex sentences minor Understanding the question
The paragraph’s last sentence sets danger against benefit, “the added dangers in flight would be partly compensated for by the slower speed in landing,” and students must untangle it to see the brothers playing the risk down. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Strategy: Locate each of the four details in paragraph 1, reread the sentence it sits in, and ask what that detail on its own reveals about what the brothers feared could go wrong.
Traps
- Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
- 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
B Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Seizes on the wind speeds and “We realized the difficulties of flying in so high a wind,” but the response the paragraph describes is a calculation that a slower landing would offset the danger.
C Twists what the text says (King et al., 2004)
Turns the slower landing, a side effect of facing a strong wind, into a safety step the brothers needed, when the paragraph counts it as a partial offset to the added danger.
D Reads too much in (Graesser, Singer & Trabasso, 1994)
Reads the wait for calmer air as fear and stretches “the early part of the morning” into most of it, though at ten o’clock they decided to fly in the same brisk wind.
Working it out, step by step
Figure out what the question asks
This asks how paragraph 1 first shows that the Wright brothers knew their flight was risky. Risky means it could end badly. All four choices name details from paragraph 1. Your job is to find the detail that shows them getting ready for trouble.
Find the signal in paragraph 1
Paragraph 1 says “We hung out the signal for the men of the Life Saving Station.” The small number 1 after “Station” points to footnote 1 at the end of the excerpt. Read it. A Life Saving Station was “one of the rescue stations along the Atlantic coastline that provided assistance to mariners in distress.” Mariners are sailors. Distress means danger or trouble.
Work out what the signal means
The brothers called rescue workers before they tried to fly. People call rescuers only when someone might get hurt. So the signal shows the brothers knew the flight could go wrong. They wanted help close by in case of a crash.
Check each choice
- A fits. Signaling rescuers shows the brothers planned for trouble.
- B does not fit. The wind speeds are only numbers. The brothers’ response was to fly anyway, thinking “there ought to be no trouble in launching.”
- C does not fit. The slower landing was a side effect of the wind. They counted it as a plus, not as a safety step they needed.
- D does not fit. They stayed inside only “the early part of the morning,” hoping the wind would die down. Then they went out in the same wind.
Watch out: B is tempting because the paragraph says “We realized the difficulties of flying in so high a wind.” But that same sentence weighs those dangers against a slower landing. It plays the risk down.
Choose the answer
The call to the rescue station is the detail that shows the brothers preparing for danger. So the answer is A, “through the mention of a signal to notify lifesaving experts that the flight attempt was about to begin.”
Why this answer and not the closest wrong one
B is the closest wrong choice. The paragraph does admit the wind made flying harder. But the brothers then argue the danger down: a slower landing would partly make up for it. A shows them acting on the risk. They called in rescuers before they flew. You only do that if you think something could go wrong.
More questions like this
The original DOE question
The passage “Excerpt from “How We Made the First Flight”” as printed (pages 13–14)
Question 2 of 6
2025 Practice Test A English, question 12Passage Excerpt from “Scribe Like an Egyptian”
Excerpt from “Scribe Like an Egyptian”
by Hilary Wilson
In ancient Egypt, literacy was the key to success. However, contrary to popular belief, not all Egyptian scribes understood hieroglyphs. Many relied instead on the simpler hieratic script for the multitude of everyday documents generated by the Egyptian bureaucracy.
Hieroglyphs—“the Words of God”—compose a writing system with more than 1,000 distinct characters, the meanings of which were lost for 1,500 years before they were deciphered by Jean-François Champollion in 1822. Including both ideograms (which convey a whole word or idea, either concrete or abstract, in a single sign) and phonograms (representing either an alphabetic sound or a group of consonants), [the writing system] was used in formal inscriptions on tomb and temple walls as well as on elaborate funerary papyri. For everyday purposes, however, scribes used a shorthand version of the hieroglyphic script known as hieratic, which was quicker to write and more economical of space. The two writings existed side by side for at least 2,500 years.
Scraps of ancient hieratic writing, mostly penned by student scribes on limestone flakes called ostraca, suggest that no matter how humble his origins, an educated Egyptian could achieve almost anything. Horemheb (d.1292 B.C.) is a good example. Born of middle-ranking parents, his scribal training led to an army career. From Scribe of Recruits, during the reign of Akhenaten (1353–1336 B.C.), Horemheb rose through the military ranks and, by the rule of Tutankhamun (1332–1323 B.C.), he was commander in chief of the Egyptian forces. As a close adviser of the young Pharaoh, Horemheb was appointed “Deputy of the King throughout the Two Lands,” and might have expected to succeed to the throne should the king die childless. He had to wait a few years, but eventually Horemheb achieved the pinnacle of his career by becoming the last king of the 18th Dynasty, making his mark by instituting dramatic reforms to the organisation of the army, the judiciary and administration in general. The lasting success of these changes owed much to his scribal background. . . .
But education was not available to all. Government departments and major temples supported schools, where boys commenced their training at six or seven, sometimes earlier. To these boarding establishments . . . family or household servants delivered the students’ food and drink rations daily for several years, during which time the student was not contributing to the family’s income. Boys from poorer families could only hope to be educated with support from a wealthier relative or patron, or through apprenticeship to an older scribe, perhaps the local clerk or land agent, who would teach them the basics of the scribe’s craft. This limited the scope for employment but such “on the job” training allowed apprentices to help out at home while learning. . . .
Scribal education began with the elementary principles of the hieratic script. The lowliest scribes, who trained for just five or six years, probably learned only the rudiments of the hieroglyphic script. Students were set exemplar documents and extracts from popular texts to copy, to practice their hieratic handwriting on basic-format letters, reports and contracts, while absorbing the good advice contained in the texts. Surviving examples of copy-work sometimes include tutors’ corrections added in red. Some significant Egyptian literary works survive almost exclusively from student copies.
A schoolboy “dictionary” of hieroglyphs with their hieratic equivalents shows that a knowledge of more than 450 signs was required for everyday writing purposes. Lessons in record-keeping and filing and labelling enabled any half-competent scribe to perform that most essential of all scribal functions: the making and updating of lists. For professions such as those of government official, priest or lawyer, a scribe would train for several more years, increasing his vocabulary to perhaps a thousand or more signs. Those with the best handwriting or drawing skills might follow the craft of creating beautifully illustrated copies of funerary texts, commonly called Books of the Dead. Others could become draughtsmen, artists or architects. Doctors compiled their own collections of medication recipes, treatments and associated incantations, many copied from texts found in the House of Life, the temple library. Lawyers had to be familiar with the corpus of civil and religious laws and precedents found in the official records, which were administered by archivists. Egypt’s bureaucratic society depended on the skills of an army of scribes of all ranks from filing clerk to tax assessor. For young Egyptians, “be a scribe” was the best of career advice.
From “Scribe Like an Egyptian” by Hilary Wilson from HISTORY TODAY, August 8, 2019. Copyright © 2019 by History Today Ltd. Company.
bureaucracy: an administrative staff of government officials
funerary papyri: a sheet or scroll of papyrus containing religious images and hieroglyphs meant to help the deceased be reborn in the afterlife
rudiments: basics
schoolboy: slang that refers to materials used during the course of receiving an education
draughtsmen: people who draw plans of machinery or structures
corpus: a collection of writings
Question
Which claim is best supported by the information presented in paragraphs 3 and 4?
- AEducation was difficult for the common citizens of Egypt to obtain.
- BOnce students began studying to become scribes, their future held more possibilities.
- CIf someone wanted to become a scribe, support from outside sources such as the government or a temple was necessary.
- DBecoming a successful scribe required a student’s family to sacrifice time and money in order to ensure the best education.
Show the answer
Correct answer: B
The question asks for the claim that is best supported by the details in paragraphs 3 and 4.
A. Incorrect. While paragraph 4 does explain that boys from poorer families had more challenges in receiving an education, the paragraph also provides examples of obtaining a patron or getting an apprenticeship as ways that these aspiring scribes could attain an education. Furthermore, the details in paragraph 3 do not provide any support for the claim that “common citizens” had difficulty getting an education because that paragraph focuses on the example of one person who was able to become a king as a result of his background as a scribe.
B. CORRECT. In paragraph 3, the author provides an example of a person who used his skills as a scribe to rise through the ranks of society by describing the achievements of Horemheb to support the idea that “no matter how humble his origins, an educated Egyptian could achieve almost anything.” The author continues in paragraph 4 to explain that with the proper support, some young Egyptians could become educated, thereby opening more opportunities for themselves.
C. Incorrect. Paragraph 4 explains that schools were supported by the government and religious institutions, but it also explains that apprenticeships were a method of learning the craft of the scribe. As the paragraph indicates, boys could also be helped in their education by support from “a wealthier relative or patron.”
D. Incorrect. In paragraph 4, the author details the sacrifices that families made to keep their sons at the schools, while boys from poorer families could only hope for a patron or an apprenticeship. Paragraph 4 also explains that apprentices could help out at home while learning, so the sacrifice of time and money was not required of every family.
Question analysis
This inference question asks which claim is best supported by paragraphs 3 and 4 of “Scribe Like an Egyptian,” which tell the story of the scribe Horemheb and describe who could get a scribal education in ancient Egypt. Students must weigh each claim against both paragraphs together, and several claims echo a single sentence closely enough to look supported.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Choosing the claim a passage best supports is core grade 7 work. Here the claim must fit two paragraphs that do different jobs, one telling a single man’s story and one explaining access to schooling, and some choices fit only part of that.
- 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 evaluate
- What makes it hard
- Evidence in several places moderate
- The right answer is reworded moderate
- Reading between the lines minor
- Evidence
- Answered from several paragraphs or stanzas
- Reading level
- Passage: about grade 12, 810 words; question and choices: about grade 10, 75 words.
- Corrected from the DOE handbook
- A misdescription of the passage in the explanation of one wrong answer 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
The trap is a claim that paragraph 4 seems to state almost word for word, which makes it feel safer than the right one. But the question asks for support from both paragraphs, and Horemheb’s story points the other way, toward what schooling made possible. The two other wrong claims harden paragraph 4’s details into rules, a necessary sponsor or a required family sacrifice, so words like “necessary” and “required” are the ones to test.
Evidence in several places moderate Working it out
The claim must fit two paragraphs that do different work: paragraph 3 follows Horemheb from army scribe to king, and paragraph 4 explains who could pay for schooling and what the alternatives were. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
The right answer is reworded moderate Choosing the answer
The right claim restates paragraph 3’s “an educated Egyptian could achieve almost anything” in new words, while the most tempting wrong one nearly copies paragraph 4’s opening, “education was not available to all.” (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)
Reading between the lines minor Working it out
Students must connect Horemheb’s rise with paragraph 4’s account of who got schooling to see that both paragraphs are about education opening doors, a link the author leaves implicit. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Strategy: Sum up paragraph 3 and paragraph 4 in a sentence each, then test every claim against both summaries, watching for words that make a claim stronger than the text.
Traps
- Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
- Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
- Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.
The wrong answers, classified
A Too narrow (King et al., 2004)
Rests on paragraph 4’s opening, “education was not available to all,” and ignores paragraph 3, whose Horemheb shows an educated man rising from modest origins to the throne.
C Too broad or too strong (King et al., 2004)
Makes the government and temple schools of paragraph 4 “necessary,” overlooking its other routes: help from “a wealthier relative or patron,” or apprenticeship to a working scribe.
D Reads too much in (Graesser, Singer & Trabasso, 1994)
Turns the rations and lost income that some families bore in paragraph 4 into a requirement for every successful scribe, and adds “the best education,” which the paragraph never mentions.
What was corrected from the DOE handbook, and why
- Explanation: The DOE’s explanation of D said paragraph 4 details sacrifices “necessary for some poorer families,” and that paragraph 3’s Horemheb, born of middle-ranking parents, shows the sacrifice was not required of all families. In paragraph 4 the rations and lost income are those of families whose sons were at the schools; poorer boys could only hope for a patron or an apprenticeship; and paragraph 3 says nothing about what Horemheb’s family gave up. The explanation now says so: D is wrong because apprentices could help out at home while learning, so not every family made the sacrifice.
Working it out, step by step
Figure out what the question asks
This asks which claim is best supported by paragraphs 3 and 4 together. A claim is a statement that someone says is true. The right claim must fit both paragraphs. Watch for strong words, like “necessary,” that go further than the text.
Sum up paragraph 3
Paragraph 3 tells about Horemheb. His parents were middle-ranking, not rich or powerful. His training as a scribe led to a job in the army. He rose to lead the army, then to serve the young king, and in the end he became king himself. The author uses him to show that “no matter how humble his origins, an educated Egyptian could achieve almost anything.” Humble origins means an ordinary family background.
Sum up paragraph 4
Paragraph 4 opens by saying that not everyone could get an education. Government offices and big temples ran schools. Families sent food and drink for years, while the boy earned nothing for them. Poorer boys could hope for help from “a wealthier relative or patron.” A patron is someone who pays for another person’s training. Or they could learn on the job from a working scribe. That path led to fewer jobs.
Put the two paragraphs together
Both paragraphs are about what schooling could do for a boy. Paragraph 3 shows a man rising all the way to king because he trained as a scribe. Paragraph 4 shows that, with the right support, boys could get that schooling. It even notes that the on-the-job path led to fewer jobs. So education opened doors. That is what choice B says.
Check each choice
- A does not fit. It matches only the start of paragraph 4. Paragraph 4 also gives ways in for poorer boys, and paragraph 3 shows a man from an ordinary family rising to the top.
- B fits. Both paragraphs show schooling leading to more possibilities.
- C does not fit. A government or temple school was not “necessary.” A relative, a patron or an apprenticeship could also work.
- D does not fit. Apprentices could help out at home while they learned, so not every family gave up time and money. And the paragraphs never mention “the best education.”
Choose the answer
The claim that fits both paragraphs is that schooling gave a boy more possibilities. So the answer is B.
Why this answer and not the closest wrong one
A is the closest wrong choice, because paragraph 4 begins by saying not everyone could get an education. But the question asks about paragraphs 3 and 4. Paragraph 3 tells of a scribe from an ordinary family who became king. Paragraph 4 shows ways around the cost. Both point to what education made possible, which is B.
More questions like this
The original DOE question
The passage “Excerpt from “Scribe Like an Egyptian”” as shown on the test
Question 3 of 6
2024 Test B English, question 1Question
What is the best way to combine these sentences to clarify the relationship between ideas?
(1) The International Space Station has been inhabited by crew members since 2000.
(2) Tourists will soon be allowed to pay for visits to the space station.
(3) Because the cost is $52–$58 million round trip, few people will be able to take advantage of the opportunity to have a vacation in outer space.
- AThe International Space Station has been inhabited by crew members since 2000, but tourists will soon be allowed to pay for visits to the space station, which cost $52–$58 million round trip, so few people will be able to take advantage of the opportunity to have a vacation in outer space.
- BThe International Space Station has been inhabited by crew members since 2000 and will soon allow tourists to pay for visits, but because the cost is $52–$58 million round trip, few people will be able to take advantage of the opportunity to have a vacation in outer space.
- CThe International Space Station has been inhabited by crew members since 2000, but tourists will soon be allowed to pay for visits to the space station, though the cost is $52–$58 million round trip, so few people will be able to take advantage of the opportunity to have a vacation in outer space.
- DThe International Space Station has been inhabited by crew members since 2000, and tourists will soon be allowed to pay for visits to the space station because the cost is $52–$58 million round trip, therefore few people will be able to take advantage of the opportunity to have a vacation in outer space.
Show the answer
Correct answer: B
The question asks for the best way to combine the sentences.
A. Incorrect. Although the option combines the sentences in a way that accurately reflects the meaning of each individual sentence, the combined sentence is a string of clauses that do not effectively cohere. Because it is poorly structured, the combined sentence does not clarify the relationship of ideas as effectively as the correct response does. The sentence incorrectly uses “but tourists,” and “which cost” modifies “the space station” but does not modify the trip. Compared with the correct response, the combined sentence in this option is also imprecise and unnecessarily wordy.
B. CORRECT. The option uses a complex sentence to present ideas clearly and precisely, and it shows the relationship between the ideas in the original sentences. In the first part of the sentence, the conjunction “and” correctly joins the first and second sentences by indicating a relationship, rather than a contrast, between the two. In the second part of the sentence, the conjunction “but” adds additional emphasis to the fact that while tourists will be allowed to visit the space station, the cost of the trip will likely prohibit most people from visiting.
C. Incorrect. Although the option combines the sentences in a way that accurately reflects the meaning of each individual sentence, the combined sentence is a string of clauses that do not effectively cohere. Because it is so poorly structured, the combined sentence does not clarify the relationship of ideas as effectively as the correct response does. Compared with the correct response, the combined sentence in this option is also imprecise and unnecessarily wordy.
D. Incorrect. The combination of the sentences contains an illogical relationship between ideas with the statement that tourists will be allowed to pay for visits to the space station because the cost is $52–$58 million round trip. The connection between the idea that “tourists will soon be allowed to pay for visits” and the subsequent “therefore few people will be able to take advantage of the opportunity” is also illogical.
Question analysis
This sentence-combining question gives three sentences about the International Space Station, its crew and the high price of a tourist trip, and asks for the best way to join them into one. Every version keeps the same facts, so students must judge which connecting words show how the ideas relate while the sentences stay long and nearly identical.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 students practice joining two short sentences with a fitting conjunction. Here three sentences become one long sentence in four nearly identical versions, so students must weigh every connecting word and clause rather than spot one error.
- 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 evaluate
- What makes it hard
- How sentences fit together major
- Complex sentences moderate
- Every choice must be checked moderate
- Evidence
- Answered from one sentence or line
- Reading level
- Question and choices: about grade 15, 261 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
None of the wrong versions drops a fact, and two of them are loose rather than plainly ungrammatical, so the ear is little help. Students lose the point by accepting the smoothest chain of clauses without asking what each connector claims: whether the crew and the tourists really contrast, what the price belongs to, and what the price explains. The question rewards deciding the three links before reading the versions, then checking them one connector at a time.
How sentences fit together major Working it out
Sentence 2 simply adds to sentence 1, while sentence 3’s price works against the tourist plan and explains why few will go, so every “but,” “though,” “because” or “so” in a version must fit one of those links. (Halliday & Hasan, 1976)
Complex sentences moderate Understanding the question
Each version is one sentence of 48 to 53 words with four clauses, and at that length a “which cost” hanging on the wrong noun or a comma before “therefore” is easy to read past. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Every choice must be checked moderate Choosing the answer
All four versions keep the same facts in the same order and share most of their words, so none can be ruled out by content; each connecting word has to be tested in turn. (Embretson & Wetzel, 1987)
Strategy: Before reading the choices, decide how each sentence relates to the next: added fact, contrast, or cause and result. Then check every connecting word in each version against those links.
Traps
- Misplaced modifier: A describing word or phrase that attaches to the wrong word, or to nothing in the sentence.
- Wordy, vague or informal: A revision is grammatical but wordy, imprecise or too casual for the passage.
- Wrong transition: A connecting word or phrase that signals the wrong relationship, such as contrast where the idea continues.
The wrong answers, classified
A Misplaced modifier (Connors & Lunsford, 1988)
Keeps the price as the reason few can go, marked by “so,” but misses that “which cost” hangs on “the space station” and that “but” sets crew against tourists.
C Wordy, vague or informal (Connors & Lunsford, 1988)
Keeps every fact in order, but stacking “but,” “though” and “so” in one sentence turns the price into an aside instead of plainly the reason few people will go.
D Wrong transition (Halliday & Hasan, 1976)
Keeps sentence 3’s “because the cost is” word for word, but here it explains why tourists are allowed, and “therefore” after a comma splices on the result.
Working it out, step by step
Figure out what the question asks
You need to join three sentences into one. The best version shows clearly how the ideas connect. Joining words do that job. A conjunction is a joining word, like and, but, so or because. Each one tells the reader something. And adds a fact. But shows a contrast (two ideas that pull against each other). Because and so show a cause and its result.
Decide how the three sentences connect
Sentence 1 says crews have lived on the station since 2000. Sentence 2 adds a new fact: tourists will soon be able to visit. That is not a contrast, so it needs and. Sentence 3 works against sentence 2. The trip costs “$52–$58 million round trip.” That price is also the reason few people will go. So you need a contrast and a reason. Example: The pool is open to all, but because it costs $90, few kids swim there.
Test each choice
- B uses “and will soon allow tourists” to add the new fact. Then “but because the cost is” shows the contrast and the reason. Every link is right.
- A joins sentence 2 with “but tourists,” as if crews and tourists were opposites. Also, “which cost” comes right after “the space station.” So it sounds like the station costs that much, not the trip.
- C stacks “but,” “though” and “so” in one long chain. The price turns into a side note instead of the clear reason.
- D says tourists may visit “because the cost is” so high. That makes no sense. And “therefore” after a comma joins two sentences the wrong way.
Pick the answer
Watch out: A is the most tempting. It keeps the price as the reason, with “so.” But its “but” and its “which” send the reader the wrong way. Only one choice links every idea correctly. So the answer is B.
Why this answer and not the closest wrong one
A is the closest wrong answer. Like B, it says the price keeps most people away. But A sets crews against tourists with “but tourists.” Its “which cost” also seems to give the price of the station. B uses and for the added fact and but because for the price, so each link is clear.
More questions like this
The original DOE question
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 30Question
Today, Tien’s age is of Jordan’s age. In 2 years, Tien’s age will be of Jordan’s age. How old is Jordan today?
- A4 years old
- B6 years old
- C12 years old
- D16 years old
Show the answer
Correct answer: D
First, set up an equation to express Tien’s age () and Jordan’s age () today:
Two years from now, Tien’s age will be , and Jordan’s age will be .
Set up an equation about the relationship between Tien’s age and Jordan’s age in two years:
Solve the above equation for :
Now set the two equations equal to each other and solve for :
Question analysis
This age word problem says Tien is one fourth of Jordan's age today and will be one third of Jordan's age in two years, then asks for Jordan's current age. Students must turn two fractional relationships into equations and solve them together. Both people age by the same two years, and it is easy to solve for the wrong person.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 equations have one unknown on one side, like 3x + 5 = 20. This one links two unknown ages with fractional coefficients and leads to a variable on both sides, which is grade 8 algebra.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math major
- Error-prone arithmetic moderate
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 1, 31 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
The difficulty is in the setup: two fractional relationships at two different times, with both people aging. Once the equations are right, the algebra is short, but it ends with two ages and only one is asked for. Testing the choices against both conditions is a reliable alternative that avoids the algebra entirely.
Turning words into math major Understanding the question
The second sentence must become T + 2 = (J + 2)/3; writing J/3, or forgetting that Jordan also ages two years, breaks the equation. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Error-prone arithmetic moderate Working it out
Substituting J/4 for T leaves J/4 + 2 = (J + 2)/3, an equation with fractions on both sides that must be cleared, usually by multiplying by 12. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Strategy: Let Jordan's age be J, write Tien's age as J/4, and set J/4 + 2 equal to one third of (J + 2); or test each choice against both conditions.
Traps
- Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
The wrong answers, classified
A Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Solves the equations correctly but reports Tien's age today, 4, which is one fourth of Jordan's 16, instead of Jordan's age.
B Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Gives Tien's age two years from now, 4 + 2 = 6, answering for the wrong person and the wrong time.
C Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Picks 12 because it is a multiple of both 4 and 3, but then Tien would be 3 and later 5, not a third of 14.
Worked solution, step by step
Formulas used
- Distributive property
- a, b and c are any numbers. To multiply a sum by a number, multiply each part of the sum, then add. It works because a groups of (b + c) is the same as a groups of b plus a groups of c.
Sort out what you know
Today, Tien’s age is of Jordan’s age. That means Jordan is 4 times as old as Tien.
In 2 years, both of them will be 2 years older. Then Tien’s age will be of Jordan’s. So Jordan will be 3 times as old as Tien. You need Jordan’s age today.
Name the ages with a letter
Let t stand for Tien’s age today. Jordan is 4 times as old, so his age is 4t, which means 4 times t. Add 2 years to each age:
Person Today In 2 years Tien Jordan Watch out: Jordan gets 2 years older too. Do not forget to add 2 to his age.
Write an equation for later
In 2 years, Jordan’s age will be 3 times Tien’s age. Write that as an equation:
Use the distributive property on the right side. Multiply both t and 2 by 3:
Solve for Tien’s age
Take 3t away from both sides. Doing the same thing to both sides keeps them equal:
Now take 2 away from both sides:
So Tien is 4 years old today. Watch out: 4 is Tien’s age, not Jordan’s. Choice A, 4 years old, is a trap.
Find Jordan’s age
Jordan is 4 times as old as Tien:
So the answer is D, 16 years old.
Check your answer
Put 16 back into the story. Today, Tien is 16 ÷ 4 = 4. In 2 years, Tien is 6 and Jordan is 18. Is 6 one third of 18? Yes, because 18 ÷ 3 = 6. Choice C fails: Tien would be 3, then 5, and 5 is not a third of 14.
More questions like this
The original DOE question
Question 6 of 6
2024 Test A Math, question 16Question
A truck rental company charges a one-time fee of $40 plus $1 per mile driven. Dalia rented a truck and used a coupon for 20% off the total rental cost. After the coupon was applied, she spent a total of $60. How many miles did she drive?
- A8
- B20
- C32
- D35
Show the answer
Correct answer: D
Let m equal the miles driven during Dalia’s rental. The total cost, c, can be expressed as an equation.
Dalia spent a total of $60, which included a 20% off coupon. Find the cost before the coupon by dividing the final cost ($60) by the percentage paid (80%):
Use $75 as the total cost to find m.
Dalia drove 35 miles.
Question analysis
A multistep word problem about a truck rental that costs a $40 fee plus $1 per mile, with a 20% off coupon applied to the total. Given that Dalia paid $60 after the coupon, students find how many miles she drove. Undoing the discount correctly before removing the fixed fee is the hard part.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students solve two-step equations and work with discounts, usually separately. This combines them and makes students undo a 20% discount starting from the price paid, a reversal many grade 7 students have not practised.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Turning words into math moderate
- Combines ideas moderate
- A very close wrong answer moderate
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 5, 43 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Two ordinary skills, undoing a discount and solving a two-step equation, are stacked, and the first runs in reverse. The natural way to undo 20% off is to add 20% back, which gives $72 instead of $75 and a choice three miles from the answer. Students who check by applying the coupon to the full cost of 40 + 35 = 75 dollars see at once that 80% of it is 60.
Turning words into math moderate Understanding the question
The sentence "After the coupon was applied, she spent a total of $60" makes 60 the price after 20% off, so it is 80% of the full cost, 40 + m. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Combines ideas moderate Working it out
A percent discount has to be undone before the fee-plus-mileage equation can be solved: 60 ÷ 0.8 = 75, then 75 − 40 = 35 miles. (Embretson, 1998; Daniel & Embretson, 2010)
A very close wrong answer moderate Choosing the answer
The choices 32 and 35 are three miles apart, too close to tell apart by estimate; only dividing 60 by 0.8, rather than adding 20% of 60, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Since $60 is 80% of the full cost, divide 60 by 0.80 to find the cost before the coupon, then subtract the $40 fee to get the miles.
Traps
- Percent of the wrong amount: Finding the whole from a part, or a percent change measured from the wrong starting amount.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
A Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Takes 20% off the $60 again, 60 × 0.8 = 48, instead of undoing the discount, then subtracts the $40 fee to get 8 miles.
B Misreads the question (Hegarty, Mayer & Monk, 1995)
Ignores the coupon and treats the $60 as the full cost, so it subtracts the $40 fee and gets 20 miles.
C Percent of the wrong amount (Parker & Leinhardt, 1995)
Undoes the coupon by adding 20% of $60 to get $72, though the 20% was taken of the larger pre-coupon cost, then subtracts the $40 fee.
Worked solution, step by step
Formulas used
- Rental cost
- c is the full cost in dollars, before any coupon. 40 is the one-time fee, paid once no matter how far you drive. m is the number of miles, and each mile costs 1 dollar.
- Price after a discount
- The full cost is the price before the discount. p is the percent taken off. You pay what is left: 100% minus p%. For 20% off you pay 80%, so you multiply by 0.80.
Sort out the question
The truck costs a $40 fee, plus $1 for each mile. Dalia’s coupon took 20% off the total. After the coupon, she paid $60. You need how many miles she drove. The $60 is the price after the discount, not the full cost.
Write what she paid
20% off means she paid what was left of the full cost.
As a decimal, 80% is 0.80.
Undo the discount
To undo times 0.80, divide by 0.80. Move the decimal point one place in both numbers to make it easier.
The full cost was $75. Watch out: the 20% was taken off the full cost, not off $60. Adding 20% of $60 gives $72 and leads to 32 miles, choice C. Taking 20% off $60 again leads to 8 miles, choice A.
Find the miles
She drove 35 miles. Watch out: do not skip the coupon. Using $60 as the full cost gives 20 miles, choice B. So the answer is D, 35.
Check your answer
Go forward. 35 miles cost $35. Add the $40 fee to get $75. The coupon takes off 20% of $75, which is dollars. Then . That is exactly what she paid.
More questions like this
The original DOE question
