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 40Passage Martial Arts for the Mind and Body
Martial Arts for the Mind and Body
(1) The martial arts blend a series of physical movements with strategic mental discipline so that practitioners can defend themselves, physically defeat an opponent, or both. (2) Historians are unsure of exactly when and where martial arts were first used. (3) Martial arts have been practiced by several different societies for many centuries. (4) Martial arts such as karate, kung fu, tae kwon do, and judo are still taught and practiced as methods of self-defense, but they offer students more than that. (5) The study of martial arts can provide students with a way to enhance their mental discipline as well as their physical fitness.
(6) Discipline, focus, and respect are important qualities for everyone to have. (7) However, for most people these qualities are not innate; they must be learned and practiced. (8) The study of martial arts can provide an opportunity to develop these skills. (9) Students are rewarded for their dedication by passing tests and advancing to higher ranks or levels. (10) For example, in a typical tae kwon do class, students learn discipline by diligently practicing moves, improve focus by listening carefully, and demonstrate respect by bowing to the instructor and following directions.
(11) For teenagers, martial arts classes provide a safe and structured environment for gaining physical skills, building confidence, and enjoying a sense of community. (12) A lot of teens go through hard situations as they try to do well in school and in life. (13) A martial arts class can provide teens with a physical outlet for stress while also challenging them mentally. (14) Participating in a martial arts program also helps children and teens focus on self-improvement rather than on competition. (15) Progressing through levels of achievement involves mastering more physically demanding techniques. (16) It requires students to take responsibility and be accountable for achieving set goals. (17) Students gain confidence and experience companionship with other students who are progressing through the ranks.
(18) Adults who practice martial arts can experience many of the same benefits that younger people do, but perhaps the greatest of these is health and fitness. (19) Adult martial arts students often see changes in their body within weeks of beginning a program.
(20) For people interested in studying a martial art, there are many ways to learn and practice. (21) In addition to private studios, community recreation centers often offer low-cost or free martial arts classes. (22) There are even online videos that introduce students to the basic concepts. (23) People should study martial arts.
Question
Which concluding sentence should replace sentence 23 to best support the topic presented in the passage?
- AWith so many ways to begin studying martial arts, people can easily discover how the skills needed to progress in rank may help them in life.
- BBy taking advantage of opportunities to practice martial arts, people can experience the satisfaction of achieving goals while also improving themselves.
- CBecause people are eager to reap the mental and physical benefits of studying martial arts, enrollment in martial arts courses has increased.
- DWhile taking martial arts classes can improve health for both young people and adults, the effects are clearly more immediate for adults.
Show the answer
Correct answer: B
The question asks for the concluding sentence that best replaces sentence 23 and supports the topic presented in the passage.
A. Incorrect. The phrase “the skills needed to progress in rank” is vague, and progressing in rank is not related to the overall topic of the passage, which is the benefits of studying martial arts. The topic of the passage is not the “many ways to begin studying martial arts” or how “people can easily discover” the benefits of martial arts.
B. CORRECT. This option is correct because it best supports the topic of the passage—the benefits of studying martial arts—by stating two reasons why people should study martial arts: to “experience the satisfaction of achieving goals while also improving themselves.”
C. Incorrect. Some readers may choose this option because it refers to the benefits of martial arts, but the word “because” and the detail that “enrollment in martial arts courses has increased” make this sentence unrelated to the overall topic of the passage, which is about the benefits of studying martial arts, not the number of people who participate.
D. Incorrect. Although the benefits of studying martial arts are described for both teens (in the third paragraph) and adults (in the fourth paragraph), the topic of the passage is the overall benefits of studying martial arts, which include mental discipline (discussed in the first, second, and third paragraphs) in addition to health benefits. Furthermore, the passage does not compare the health effects of studying martial arts across age groups.
Question analysis
This conclusion question asks which sentence should replace sentence 23, the bare closing line “People should study martial arts,” to best support the topic of the passage. Students must keep all five paragraphs in view, from mental discipline to fitness to ways of getting started, because every choice sounds like a reasonable final line when read on its own.
- NYS standards
- 7W2e concluding informative writing
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 writers choose conclusions that follow from a passage’s topic. This passage covers mental and physical benefits for different ages, and each long choice picks up a real thread, so judging the best fit takes more than typical 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 evaluate
- What makes it hard
- A very close wrong answer moderate
- Evidence in several places moderate
- A lot to read minor
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 11, 402 words; question and choices: about grade 12, 106 words.
- Corrected from the DOE handbook
- The DOE printed this question’s explanation after a different question; the site matches the question with its own explanation.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Every ending borrows something real from the passage: ways to begin, ranks, mental and physical benefits, or adults’ quick results. The work is deciding what the whole passage is about, the benefits of martial arts for mind and body, and then noticing which ending adds a new claim or shrinks the topic. The rank-based ending is hardest to reject because it is shaped like the key and promises help “in life,” but its focus is how easily people discover rank skills.
A very close wrong answer moderate Choosing the answer
The rank choice is built like the key, a phrase about ways or chances to train followed by what people gain; it differs in resting on the vague “skills needed to progress in rank.” (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The topic is pieced together from all five paragraphs, from the opening’s mind-and-body claim through teens, adults’ fitness and ways to learn, so a fitting ending must cover both kinds of benefit. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
A lot to read minor Understanding the question
Each choice is a two-part sentence of 21 to 26 words, and each picks up a real thread of the passage, so all four must be held against the topic. (Kintsch, 1998; Gorin & Embretson, 2006; Freedle & Kostin, 1993)
Strategy: State the passage’s topic in a few words using all five paragraphs, then test each ending: does it sum up that topic, or does it narrow it or add a new claim?
Traps
- Off the point: Adds or keeps something that does not support the paragraph's or the passage's focus, or an introduction or conclusion that misses the main point.
- 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.
The wrong answers, classified
A Too narrow (King et al., 2004)
Follows on from the last paragraph’s many ways to start, but rests the ending on vague “skills needed to progress in rank,” one thread of paragraphs 2 and 3, not the benefits overall.
C Off the point (Halliday & Hasan, 1976)
Names the passage’s “mental and physical benefits,” which fits, but ends on rising enrollment, a claim about numbers of students that the passage never discusses.
D Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Rightly says training can improve health for young people and adults, but adds that adults clearly benefit sooner, a comparison the passage never makes, and drops the mental benefits.
What was corrected from the DOE handbook, and why
- Explanation: In the DOE’s explanations appendix, the explanation printed after this question belongs to question 39 (“the sentence that would best follow and support sentence 18”) and marks C correct, and this question’s explanation (“the concluding sentence that best replaces sentence 23 and supports the topic presented in the passage”) is printed after question 39, marking B correct. Read page by page, the appendix gives this question the answer C. The site gives the question the explanation that restates it, and the answer follows that explanation: B, because it sums up the passage’s topic, the benefits of studying martial arts.
Working it out, step by step
Figure out what the question asks
This asks for a better last sentence. A good concluding sentence sums up the topic of the whole passage. Sentence 23, “People should study martial arts,” is short and plain. It doesn’t remind the reader why.
Find the passage’s topic
Sentence 5 states the topic. Martial arts can help students “enhance their mental discipline as well as their physical fitness.” Enhance means improve. Paragraph 2 covers discipline, focus and respect. Paragraph 3 covers teens and goals. Paragraph 4 covers adults and fitness. Paragraph 5 lists ways to start. So the topic is how martial arts help both mind and body.
Name the rule
A conclusion should sum up the main point. It should not shrink the point or add a brand-new claim. For example, after a report on why sleep matters, a good ending is Getting enough sleep helps both your body and your mind. A poor one is More people buy pillows now.
Check each choice
- A is wrong. It rests on vague “skills needed to progress in rank,” one small part of the passage.
- B is right. “Opportunities to practice” follows paragraph 5. “Achieving goals” and “improving themselves” sum up the benefits.
- C is wrong. Enrollment is the number of people who sign up. The passage never says it has gone up.
- D is wrong. The passage never says adults see results sooner than young people. D also leaves out the benefits to the mind.
Watch out: A is built like B and promises help “in life.” But it shrinks the topic to rank skills.
Choose the answer
B sums up what the whole passage says martial arts offer. So the answer is B, “By taking advantage of opportunities to practice martial arts, people can experience the satisfaction of achieving goals while also improving themselves.”
Why this answer and not the closest wrong one
A is the closest wrong answer. Like B, it starts with ways to begin and ends with what people gain. But its gain is vague “skills needed to progress in rank.” That is only one thread of the passage. B sums up the whole topic: reaching goals and improving yourself.
More questions like this
The original DOE question
The passage “Martial Arts for the Mind and Body” as printed (page 52)
Question 2 of 6
2026 Practice Test B English, question 22Passage Excerpt from In Search of the Unknown
Excerpt from In Search of the Unknown
by Robert W. Chambers
It was at that time the policy of the trustees and officers of the Zoological Gardens neither to employ collectors nor to send out expeditions in search of specimens. The society decided to depend upon voluntary contributions, and I was always busy, part of the day, in dictating answers to correspondents who wrote offering their services as hunters of big game, collectors of all sorts of fauna, trappers, snarers, and also to those who offered specimens for sale, usually at exorbitant rates.
To the proprietors of . . . mangy lynxes, moth-eaten coyotes, and dancing bears I returned courteous but uncompromising refusals—of course, first submitting all such letters, together with my replies, to Professor Farrago.
One day towards the end of May, however, just as I was leaving Bronx Park to return to town, Professor Lesard, of the reptilian department, called out to me that Professor Farrago wanted to see me a moment; so I . . . retraced my steps to the temporary, wooden building occupied by Professor Farrago, general superintendent of the Zoological Gardens. The professor, who was sitting at his desk before a pile of letters and replies submitted for approval by me, pushed his glasses down and looked over them at me with a whimsical smile that suggested amusement, impatience, annoyance, and perhaps a faint trace of apology.
“Now, here’s a letter,” he said, with a deliberate gesture towards a sheet of paper impaled on a file—“a letter that I suppose you remember.” He disengaged the sheet of paper and handed it to me.
“Oh yes,” I replied, with a shrug; “of course the man is mistaken—or—”
“Or what?” demanded Professor Farrago, tranquilly, wiping his glasses.
“—Or a liar,” I replied.
After a silence he leaned back in his chair and bade me read the letter to him again, and I did so with a contemptuous tolerance for the writer, who must have been either a very innocent victim or a very stupid swindler. I said as much to Professor Farrago, but, to my surprise, he appeared to waver.
“I suppose,” he said, with his near-sighted, embarrassed smile, “that nine hundred and ninety-nine men in a thousand would throw that letter aside and condemn the writer as a liar or a fool?”
“In my opinion,” said I, “he’s one or the other.”
“He isn’t—in mine,” said the professor, placidly.
“What!” I exclaimed. “Here is a man living all alone on a strip of rock and sand between the wilderness and the sea, who wants you to send somebody to take charge of a bird that doesn’t exist!”
“How do you know,” asked Professor Farrago, “that the bird in question does not exist?”
“It is generally accepted,” I replied, sarcastically, “that the great auk has been extinct for years. Therefore I may be pardoned for doubting that our correspondent possesses a pair of them alive.”
“Oh, you young fellows,” said the professor, smiling wearily, “you embark on a theory for destinations that don’t exist.”
He leaned back in his chair, his amused eyes searching space for the imagery that made him smile.
“Like swimming squirrels, you navigate with the help of Heaven and a stiff breeze, but you never land where you hope to—do you?”
Rather red in the face, I said: “Don’t you believe the great auk to be extinct?”
“Audubon saw the great auk.”
“Who has seen a single specimen since?”
“Nobody—except our correspondent here,” he replied, laughing.
I laughed, too, considering the interview at an end, but the professor went on, coolly:
“Whatever it is that our correspondent has—and I am daring to believe that it is the great auk itself—I want you to secure it for the society.”
When my astonishment subsided my first conscious sentiment was one of pity. Clearly, Professor Farrago was on the verge of dotage—ah, what a loss to the world!
I believe now that Professor Farrago perfectly interpreted my thoughts, but he betrayed neither resentment nor impatience. I drew a chair up beside his desk—there was nothing to do but to obey, and this fool’s errand was none of my conceiving.
Together we made out a list of articles necessary for me and itemized the expenses I might incur, and I set a date for my return, allowing no margin for a successful termination to the expedition.
“Never mind that,” said the professor. “What I want you to do is to get those birds here safely. Now, how many men will you take?”
“None,” I replied, bluntly; “it’s a useless expense, unless there is something to bring back. If there is I’ll wire you, you may be sure.”
“Very well,” said Professor Farrago, good-humoredly, “you shall have all the assistance you may require. Can you leave to-night?”
The old gentleman was certainly prompt. I nodded, half-sulkily, aware of his amusement.
“So,” I said, picking up my hat, “I am to start north to find a place called Black Harbor, where there is a man named Halyard who possesses, among other household utensils, two extinct great auks—”
We were both laughing by this time. I asked him why on earth he credited the assertion of a man he had never before heard of.
“I suppose,” he replied, with the same half-apologetic, half-humorous smile, “it is instinct. I feel, somehow, that this man Halyard has got an auk—perhaps two. I can’t get away from the idea that we are on the eve of acquiring the rarest of living creatures. It’s odd for a scientist to talk as I do; doubtless you’re shocked—admit it, now!”
But I was not shocked; on the contrary, I was conscious that the same strange hope that Professor Farrago cherished was beginning, in spite of me, to stir my pulses, too.
“If he has—” I began, then stopped.
The professor and I looked hard at each other in silence.
“Go on,” he said, encouragingly.
But I had nothing more to say, for the prospect of beholding with my own eyes a living specimen of the great auk produced a series of conflicting emotions within me which rendered speech profanely superfluous.
From IN SEARCH OF THE UNKNOWN by Robert W. Chambers—Public Domain
Audubon: John James Audubon, an ornithologist and artist who created scientific illustrations of birds
dotage: a loss of reasoning brought about by old age
Question
How does the author develop the contrast between the narrator’s point of view and the professor’s point of view?
- Aby providing both the narrator’s and professor’s thoughts on how age and experience influence each other’s reasoning
- Bby using the conversation between the narrator and the professor to emphasize their reactions to the letter
- Cby describing the professor’s persistent efforts to change the narrator’s mind about the letter
- Dby including dialogue that explains why the professor is the supervisor and the narrator is his subordinate
Show the answer
Correct answer: B
The question asks how the author develops the contrast between the narrator’s point of view and the professor’s point of view.
A. Incorrect. The excerpt does not describe the narrator’s thoughts about how age and experience influence the professor’s reasoning in enough detail to fully contrast them against the thoughts about the narrator that the professor expresses in paragraphs 15–17. The narrator’s idea that the professor might be “on the verge of dotage” (paragraph 24) is meant in a humorous way.
B. CORRECT. The primary conflict of the excerpt revolves around the narrator’s disagreement with the professor about whether the letter about the great auks could be true. As the two men converse, their contrasting attitudes toward the letter become clear: the narrator dismisses the possibility of great auks out of hand (“ ‘of course the man is mistaken’ ” [paragraph 5]; “ ‘here is a man . . . who wants you to send somebody to take charge of a bird that doesn’t exist!’ ” [paragraph 12]), while the professor calmly admits that although “ ‘nine hundred and ninety-nine men in a thousand would throw that letter aside and condemn the writer’ ” (paragraph 9), he himself believes that the writer could be telling the truth (“ ‘How do you know,’ asked Professor Farrago, ‘that the bird in question does not exist?’ ” [paragraph 13]).
C. Incorrect. The professor explains why he disagrees with the narrator (paragraphs 19–21), but he does not make persistent efforts to convince the narrator to change his mind about the letter. Instead he states that the narrator will go on an expedition to retrieve “ ‘whatever it is that our correspondent has’ ” (paragraph 23), thereby requiring the narrator to go collect the great auks whether the narrator believes in them or not.
D. Incorrect. The point of the dialogue is not to explain the subordinate-supervisor relationship between the narrator and the professor but rather to contrast what each character believes about the contents of the letter.
Question analysis
This point-of-view question asks how Robert W. Chambers develops the contrast between the narrator’s outlook and Professor Farrago’s in the excerpt from In Search of the Unknown. Students must step back from single lines and judge the author’s method across the whole excerpt. The choices describe techniques in general terms, and several connect to real moments in the story.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Analyzing how an author contrasts two characters’ points of view is the grade 7 standard itself, but here students must judge the main method across the whole excerpt, and each choice names an abstract method that touches something in the text.
- 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
- How, not what major
- A very close wrong answer moderate
- Evidence in several places moderate
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 9, 1066 words; question and choices: about grade 11, 84 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 right choice is plain enough to seem too obvious, so students look for something more specific. The excerpt offers a candidate: the professor teases “you young fellows,” and the narrator decides the old man is near “dotage,” which makes age look like the method. Those remarks are passing jokes, while the men’s opposite reactions to Halyard’s letter run through the whole conversation. The question rewards judging what carries the contrast from start to end rather than what is most striking.
How, not what major Working it out
The question asks for the author’s method across the whole excerpt, and every choice names an abstract technique, so students must step back from single lines to see that the dialogue carries the contrast. (Anderson & Krathwohl, 2001)
A very close wrong answer moderate Choosing the answer
The choice about age and experience and the right one both describe the two men’s opposed views as they come out in the excerpt; they part on the subject, their ages or the letter. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Evidence in several places moderate Working it out
The contrast builds from the narrator’s “of course the man is mistaken” in paragraph 5 to the professor’s appeal to “instinct” in paragraph 33, so no single passage shows the method. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)
Strategy: For each choice, find where the excerpt does what the choice describes, and ask whether that method carries the contrast through the whole excerpt or appears only once or twice.
Traps
- Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
- Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
- Wrong purpose or structure: Names a purpose, structure or effect that the part does not serve, or describes what a part says when the question asks what it does.
The wrong answers, classified
A Too narrow (King et al., 2004)
Notices the jab at “you young fellows” and the narrator’s thought of “dotage,” but two passing remarks about age are not how the author builds the contrast across the excerpt.
C Twists what the text says (King et al., 2004)
Overstates the professor’s role, since he asks a few calm questions and then simply assigns the trip, never working to win the narrator over.
D Wrong purpose or structure (Anderson & Krathwohl, 2001)
Knows that the professor is the superior, but no line of dialogue explains how either man got his position; the talk is about the letter, not their ranks.
Working it out, step by step
Figure out what the question asks
This asks about the author’s method. How does the author show that the two men see things differently? Look at how the whole excerpt is built, not just one line.
Notice how the excerpt is told
Most of the excerpt is a conversation. The two men talk back and forth about the letter. Each answer shows how one man reacts to it. So their reactions to the letter are where the contrast shows up. A contrast is a clear difference between two things.
Find the two reactions
The narrator says “of course the man is mistaken” (paragraph 5). He laughs at the idea of “a bird that doesn’t exist!” (paragraph 12). The professor stays open. In paragraph 13 he asks how the narrator can be sure “that the bird in question does not exist.” In paragraph 23, he is “daring to believe” it is the great auk.
Check each choice
- A does not fit. Age comes up only twice: “you young fellows” and the narrator’s thought about “dotage.” Two short remarks do not build the contrast.
- B fits. The talk about the letter shows their opposite reactions.
- C does not fit. The professor asks a few calm questions and then simply sends the narrator. He does not keep trying to change his mind.
- D does not fit. No line explains how either man got his job.
Watch out: A is tempting because those remarks about age are real. But they are passing moments, not the author’s main method.
Choose the answer
The author builds the contrast through the two men’s talk about the letter. So the answer is B, “by using the conversation between the narrator and the professor to emphasize their reactions to the letter.”
Why this answer and not the closest wrong one
A is the closest wrong choice. The professor does tease “you young fellows,” and the narrator does think of “dotage.” But those are two quick remarks. From paragraph 5 to paragraph 33, the two men keep reacting to the letter in opposite ways. That steady back-and-forth builds the contrast, so B fits.
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
2026 Practice Test B English, question 33Passage Using Fire to Keep a Prairie Healthy
Using Fire to Keep a Prairie Healthy
Inside the 40,000-acre Joseph H. Williams Tallgrass Prairie Preserve in northern Oklahoma, herds of bison roam on the scenic land that is home to hundreds of different species of plants and animals. While one of the greatest threats to the prairie is wildfire, the use of controlled fires is actually an effective way to protect this idyllic landscape.
Fires that are started by lightning or other natural circumstances are inevitable, and the results can be disastrous. However, hundreds of years ago the American Indian people who inhabited the Great Plains area between Minnesota and Texas realized that these fires could also be helpful. The bison in the area seemed to prefer grazing on tender new grass on the recently burned land rather than on grass in the unburned areas. The American Indian people began to deliberately burn areas of land for bison to graze on, which enticed the herds away from the people’s crops.
Today conservationists at the Tallgrass Prairie Preserve and farmers in the Great Plains continue to use controlled burns for land management. Intentionally burning a portion of land can dramatically improve the quality of the vegetation that regrows there. The fires burn away weedy undergrowth and help limit the overcrowding of shrubs and trees in the burn area, creating less competition for water and nutrients. Additionally, the process of burning excess plant matter adds nitrogen, an essential element for plant growth, to the soil.
One common target of controlled burns at the preserve and the surrounding area is the invasive red cedar tree. A single red cedar tree can consume up to 40 gallons of water per day, taking this vital resource away from other plant life. These tall trees also cast shade that prevents sunlight from reaching the plants beneath them. The fast-growing red cedar trees tend to crowd out prairie grasses, the primary food source for wild and domestic animals that make the prairie their home. An imbalance in one component of the prairie’s ecosystem affects the entire web of life. Controlled burns help maintain this ecosystem’s delicate balance.
Of course, these controlled fires are intended to burn only a portion of an area. A total burn, which is a risk with an uncontrolled wildfire, would destroy all wildlife as well as the crops farmers plant for income. The key to using controlled fires is knowing which areas of land to burn and when. Conservation experts at the preserve employ the “patch-burn” approach, meaning they rotate which portion of land is burned each year. They study the land to find out which areas would most benefit from being burned, and then they arrange about a dozen burns over one-third of the land. This patch burning contains the fire within a specific area and allows animals in the burn area to safely relocate. The following year, conservationists will burn a different section of the preserve, while the land burned the previous year regrows healthier than before.
Researchers have tracked and studied the variety of plant species and animals that live on the preserve, and their studies show that the patch-burn approach has restored biodiversity to the area by promoting the growth of species that were at risk of being crowded out. The patch-burn system is so successful that the conservationists at the preserve provide training to prairie farmers about conducting controlled burns on their own land. Burning land to make it healthy may seem counterintuitive, but strategic controlled fires have helped the prairie sustain life for hundreds of years and, with careful management, will continue to do so.
Question
Read this sentence from paragraph 6.
Burning land to make it healthy may seem counterintuitive, but strategic controlled fires have helped the prairie sustain life for hundreds of years and, with careful management, will continue to do so.
The words “counterintuitive” and “strategic” in the sentence convey the idea that
- Athe safest methods are sometimes the least effective at solving complex challenges.
- Bthorough investigation of uncommon methodologies can lead to beneficial results.
- Cdetailed planning can ensure that a potentially destructive action has a positive impact.
- Dplans that entail a certain amount of risk almost always result in success.
Show the answer
Correct answer: C
The question asks which idea the words “counterintuitive” and “strategic” convey in the last sentence in paragraph 6 in the passage.
A. Incorrect. Though the author states in paragraph 6 that conservationists have used safe and “strategic” methods, those methods have not been ineffective, since “the patch-burn system is so successful that the conservationists at the preserve provide training to prairie farmers about conducting controlled burns on their own land” (paragraph 6). Therefore, the words “counterintuitive” and “strategic” in the last sentence of paragraph 6 do not convey the idea that the safest methods are sometimes the least effective at solving complex challenges.
B. Incorrect. Although the author points out in paragraph 6 that researchers’ studies have shown “that the patch-burn approach has restored biodiversity to the area by promoting the growth of species that were at risk of being crowded out,” the author does not suggest that the methodologies conservationists used to conduct the patch burns are uncommon, since the methods were used by “the American Indian people [who] began to deliberately burn areas of land for bison to graze on” (paragraph 2). Therefore, the words “counterintuitive” and “strategic” in the last sentence of paragraph 6 do not convey the idea that thorough investigation of uncommon methodologies can lead to beneficial results.
C. CORRECT. In paragraph 1, the author states that “one of the greatest threats to the prairie is wildfire,” so the idea of conducting controlled burns suggests risk and runs “counter,” or contrary, to people’s common expectations, or “intuition,” about the dangers of fires. Thus, the words “counterintuitive” and “strategic” in the last sentence of paragraph 6 convey the idea that detailed planning can ensure that a potentially destructive action has a positive impact.
D. Incorrect. The author states in paragraph 6 that “the patch-burn system is so successful that the conservationists at the preserve provide training to prairie farmers.” This statement supports the idea of the action being “strategic” in order to achieve success. However, the statement does not suggest that because the process is “counterintuitive,” or unexpected, it involves a certain amount of risk to achieve that success. Therefore, the words “counterintuitive” and “strategic” in the last sentence of paragraph 6 do not convey the idea that plans that entail a certain amount of risk almost always result in success.
Question analysis
This vocabulary question takes the last sentence of the prairie article, which says burning land to make it healthy may seem counterintuitive, and asks what the words “counterintuitive” and “strategic” convey together. Students need the meaning of a hard word built from a prefix, then must match the pair to a general statement, and the choices are worded abstractly.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 A typical grade 7 vocabulary question asks what one word means in context. This one pairs a hard word, “counterintuitive,” with “strategic” and asks for the idea they express together, with four abstract general statements to weigh.
- 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 understand
- What makes it hard
- A very close wrong answer moderate
- Hard words moderate
- Combines ideas minor
- Evidence
- Answered from one sentence or line
- Reading level
- Passage: about grade 11, 598 words; question and choices: about grade 11, 97 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
Students first need the meaning of “counterintuitive,” then must see what it says here: that burning land to heal it seems backward because fire destroys. “Strategic” supplies the other half, careful planning. The most tempting wrong answer gets the planning right but misreads the first word as “uncommon,” and others turn the pair into a rule about risk or a warning about safe methods. The question rewards translating each word before reading the abstract choices.
A very close wrong answer moderate Choosing the answer
The choice about “thorough investigation of uncommon methodologies” follows the key’s pattern, planning that leads to a good result, and differs only in calling the method uncommon instead of potentially destructive. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Hard words moderate Understanding the question
“Counterintuitive,” contrary to what one would expect, is an uncommon word, and the choices add “methodologies” and “entail,” so the options are as hard to read as the sentence. (Perfetti, 2007; Freedle & Kostin, 1993)
Combines ideas minor Working it out
The two words point different ways, one to burning that seems harmful and one to careful planning, and the answer must join both into a single general statement. (Embretson, 1998; Daniel & Embretson, 2010)
Strategy: Break “counterintuitive” into its parts, counter and intuitive, decide what each of the two words says about burning land, then find the statement that joins both meanings without adding claims of its own.
Traps
- Half right: One half of a two-part choice is right and the other is not.
- Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
- 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 Twists what the text says (King et al., 2004)
Reads “counterintuitive” as a hint that the safe choice fails, but the sentence praises carefully managed fire and never says safer methods are less effective.
B Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Matches “strategic” to thorough investigation, since the experts “study the land,” but takes “counterintuitive” to mean uncommon, though the passage traces burning back hundreds of years.
D Too broad or too strong (King et al., 2004)
Hears risk in “counterintuitive” and success in “strategic” but turns them into a rule that risky plans “almost always” succeed, far more than one sentence about the prairie claims.
Working it out, step by step
Figure out what the question asks
This question asks about two words in the last sentence: “counterintuitive” and “strategic.” You need the idea the two words give together. So first figure out what each word means here.
Break down “counterintuitive”
Counter means against. Intuitive means what you would naturally expect. So counterintuitive means the opposite of what you would expect. The sentence says “Burning land to make it healthy may seem counterintuitive.” Fire usually destroys things. So burning land to help it seems backward. Paragraph 1 even calls wildfire “one of the greatest threats to the prairie.”
Figure out “strategic”
Strategic means carefully planned to reach a goal. Paragraph 5 shows that planning. The experts “study the land to find out which areas would most benefit from being burned.” Then they burn only part of the land each year. Put the two words together. Fire seems harmful, but careful planning makes it helpful.
Check each choice
- A is wrong. The sentence doesn’t say safe methods fail. It praises a method that works.
- B is wrong. It treats counterintuitive as if it meant uncommon. But burning isn’t new. Paragraph 2 says people did it “hundreds of years ago.”
- C is right. Strategic matches detailed planning. Counterintuitive matches an action that could destroy, fire, which turns out to help.
- D is wrong. “Almost always” is far too strong. The sentence is about prairie fires, not all risky plans.
Watch out: B gets strategic right, since the experts study the land. But counterintuitive doesn’t mean uncommon. It means against what you would expect.
Choose the answer
Fire seems destructive, but a careful plan makes it helpful. So the answer is C: “detailed planning can ensure that a potentially destructive action has a positive impact.”
Why this answer and not the closest wrong one
B is the closest wrong answer, because its first part, careful study, fits strategic. But its second part calls the method uncommon, and people have burned the prairie for hundreds of years. C fits both words: careful planning, and an action that seems harmful but helps.
More questions like this
The original DOE question
The passage “Using Fire to Keep a Prairie Healthy” as printed (page 41)
Question 4 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 5 of 6
2026 Practice Test C Math, question 15Question
A grocery store sells 1-gallon containers of milk for $3.99. The store also sells orange juice in a 6-pack of 5.5-fluid-ounce bottles for $1.79. Suppose the store wants to sell its orange juice in gallon containers instead. To the nearest dollar, how much more would a gallon of orange juice cost than a gallon of milk?
Enter your answer in the space.
Fill-in question: work out the answer and type it as a number.
Show the answer
Correct answer: 3
To determine the cost of a gallon of orange juice, begin by finding the total number of ounces in the 6-pack of bottles:
So, 33 oz of orange juice costs $1.79.
There are 128 oz in 1 gallon. Set up a proportion using the $1.79 cost per 33 oz of orange juice and the unknown cost (x) per 1 gallon of orange juice:
Cross multiply to solve for x in the proportion:
So, the orange juice costs $6.94 per gallon, and the milk costs $3.99 per gallon.
Subtract the cost per gallon of milk from the cost per gallon of orange juice.
Round the difference to the nearest dollar.
$2.95 rounds to $3.
Question analysis
A store sells milk by the gallon for $3.99 and orange juice in six-packs of 5.5-fluid-ounce bottles for $1.79. Students work out what a gallon of the juice would cost at the same price per ounce and how much more that is than the milk, to the nearest dollar. The ounces in a gallon must be known, and several steps involve decimals.
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Unit prices are grade 6 and 7 work, but this chains five steps with decimals and needs a fact the question does not give, the number of fluid ounces in a gallon. Typing a rounded difference, with no choices, adds risk.
- 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
- Something you must already know moderate
- Many steps moderate
- Error-prone arithmetic minor
- An answer in an unexpected form minor
- Solution
- 5 steps
- Reading level
- Question and choices: about grade 5, 60 words.
- Corrected from the DOE handbook
- A rounded value in the explanation is now marked as approximate (≈ instead of =).
- 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 calculation is long, and its key fact is missing from the page. Students who know the 128 fluid ounces still face a division by 33 that does not come out evenly, which tempts them to round the price per ounce to 5 cents and lose about 50 cents a gallon. Keeping the exact quotient to the end, or scaling 33 ounces up by about 3.9, keeps the difference near $2.95, which rounds to 3.
Something you must already know moderate Working it out
The question never says that a gallon holds 128 fluid ounces, yet the whole comparison depends on it; the 6-pack holds only 6 × 5.5 = 33 ounces. (Anderson & Krathwohl, 2001)
Many steps moderate Working it out
Five moves follow one another: the ounces in a pack, the scale-up to 128 ounces, the division by 33, the subtraction of $3.99 and the rounding to a whole dollar. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Error-prone arithmetic minor Working it out
1.79 × 128 = 229.12 and 229.12 ÷ 33 are long decimal calculations without a calculator, and a slip in either moves the price of a gallon. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
An answer in an unexpected form minor Choosing the answer
The rounded difference is typed with no choices, so an unrounded $2.95, or a figure rounded too soon, looks just as finished as the whole-dollar answer. (Enright, Morley & Sheehan, 2002)
Strategy: Find the ounces in one six-pack, scale its price up to the 128 fluid ounces in a gallon, subtract the milk's price, and round only at the end.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- Rounds too early: Rounds a value partway through, or rounds the wrong way, so the final answer drifts from the exact one.
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
The wrong answers, classified
7 Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds the juice's cost per gallon, about $6.94, rounds it to $7, and enters that without subtracting the $3.99 price of the milk.
2 Rounds too early (King et al., 2004)
Rounds the price per ounce, 1.79 ÷ 33 ≈ 0.054, to $0.05, so a gallon costs $6.40 and the difference, $2.41, rounds to 2.
2.95 Misreads the question (Hegarty, Mayer & Monk, 1995)
Works out the difference of $2.95 correctly but enters it as it stands, though the question asks for it to the nearest dollar.
What was corrected from the DOE handbook, and why
- Explanation: The DOE’s explanation goes from 33x = $229.12 to “x = $6.94”. But 229.12 ÷ 33 = 6.9430…, so $6.94 is the cost per gallon rounded to the cent. The site writes x ≈ $6.94. Nothing else changes: $6.94 − $3.99 = $2.95, which rounds to $3, and the unrounded cost gives the same answer.
Worked solution, step by step
Formulas used
- Fluid ounces in a gallon
- A gallon holds 128 fluid ounces. This is a fact you must know, because the question does not give it. A fluid ounce measures an amount of liquid. Multiply gallons by 128 to change them into fluid ounces.
- Cross-multiplying a proportion
- A proportion says two ratios are equal. Here each ratio is ounces over dollars. a and c are the tops, and b and d are the bottoms. Multiply each top by the other bottom, and the two products are equal. That turns the proportion into an equation.
Sort out the question
Milk costs $3.99 for 1 gallon. Orange juice comes in a 6-pack of 5.5-fluid-ounce bottles for $1.79. You need how much more a gallon of juice would cost than a gallon of milk. Round to the nearest dollar.
The question doesn’t say how big a gallon is. You must know this fact: 1 gallon is 128 fluid ounces.
Find the ounces in a 6-pack
Each of the 6 bottles holds 5.5 fluid ounces:
So $1.79 buys 33 fluid ounces of juice.
Set up a proportion
Let x be the cost in dollars of a gallon, 128 fluid ounces, of juice. The price per ounce stays the same. So ounces over dollars is the same for the pack and the gallon:
Cross-multiply:
Find the cost of a gallon
Divide both sides by 33:
The sign ≈ means about equal. The exact value is 6.943…, so a gallon of juice costs about $6.94.
Watch out: don’t round too early. One ounce costs about $0.054. Rounding that to $0.05 makes a gallon $6.40, and your answer becomes 2.
Subtract the milk’s price
Find how much more the juice costs:
A gallon of juice costs $2.95 more than a gallon of milk.
Watch out: entering 7, the juice’s price, forgets to subtract the milk.
Round and enter it
The question asks for the nearest dollar. $2.95 is between $2 and $3. Its cents, 95, are 50 or more, so it rounds up to $3. Do not enter 2.95.
Type only the number in the box. So you would enter 3.
Check your answer
Estimate. 128 ounces is almost 4 packs, since . Four packs cost dollars, so a gallon costs a bit less than that. Milk costs about $4. About $7 minus $4 is $3, which matches.
More questions like this
The original DOE question
Question 6 of 6
2024 Test B Math, question 52Question
Five numbered balls are placed in two boxes as shown in the figure above. Davina picks one ball at random from Box B and places it in Box A. Then Yusuf picks one ball from Box A without looking. What is the probability that Yusuf will pick a ball with an odd number?
- A
- B
- C
- D
Show the answer
Correct answer: A
The probability of Davina picking an odd-numbered ball from Box B is . If Davina places an odd-numbered ball in Box A, then the probability of Yusuf picking an odd-numbered ball from Box A is . The probability of both of these events happening is the product of the two probabilities.
Question analysis
Two boxes hold five numbered balls, and Davina moves one ball at random from Box B into Box A before Yusuf draws one from Box A. Students find the probability that Yusuf's ball shows an odd number. It tests two-stage probability, and the tricky part is that the second draw depends on which ball was moved.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 compound probability lists outcomes for independent stages such as coins or spinners. Here the first random move changes what is in the second box, so students must follow two linked stages, a dependence typical grade 7 work does not include.
- 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
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 4, 57 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 chance events are hidden in what reads like a question about a single draw. Every listed wrong answer is a reasonable single-stage answer, either one of the two factors on its own or a count of odd balls across both boxes. Listing the nine equally likely pairs, Davina's ball and then Yusuf's, shows that only two of them end with an odd ball and makes the structure visible without any formula.
No obvious method major Working it out
The stem asks one question about Yusuf's draw, but the answer depends on Davina's earlier random pick; the key is that Box A starts with only even balls, so Yusuf can draw odd only by drawing the ball she moved. (Schoenfeld, 1985)
Something you must already know minor Working it out
Multiplying the chances of the two stages, 2/3 for an odd ball moving and 1/3 for Yusuf then drawing it, is a rule students must bring themselves. (Anderson & Krathwohl, 2001)
Reading a figure, table or graph minor Understanding the question
The numbers appear only in the figure, Box A holding 2 and 6 and Box B holding 3, 4 and 5, so the odd balls have to be spotted there. (Lesh, Post & Behr, 1987; Kirsch & Mosenthal, 1990)
Strategy: List every equally likely pair of a ball moved by Davina and a ball picked by Yusuf, and count the pairs that end with an odd ball.
Traps
- Stops one step early: A choice is a number from partway through the solution.
- Numbers taken from the question: Combines the numbers in the question without a model of the situation, or is simply a number that appears in the question.
The wrong answers, classified
B Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds Yusuf's chance of drawing the odd ball once one is in Box A, 1 out of 3, leaving out the chance that Davina moves an odd ball at all.
C Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Counts the odd balls in the figure, 3 and 5, over all five balls, 2/5, ignoring that Yusuf draws only from Box A.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Gives the chance that Davina moves an odd ball, 2 out of 3, the first stage only, without multiplying by Yusuf's 1/3 chance of drawing it.
Worked solution, step by step
Formulas used
- Probability
- P is the probability, the chance that something happens. It is a number from 0 to 1. The top counts the results you want. The bottom counts all the results that can happen. It works when every result is equally likely.
- Chance of events in a row
- A and B are two events that happen one after the other. P(A) is the chance of the first. P(B after A) is the chance of the second, counting only what is left after the first. You multiply because the second must also happen inside the share of times the first did.
Read the figure
Box A holds balls numbered 2 and 6. Box B holds balls numbered 3, 4 and 5.
An odd number does not divide evenly by 2. So the only odd balls are 3 and 5, and both start in Box B. Box A starts with no odd balls at all.
Spot the two chance events
Two things happen by chance, one after the other:
- Davina picks one of the 3 balls in Box B and moves it to Box A.
- Then Yusuf picks one of the 3 balls now in Box A.
Yusuf gets an odd ball only if both go right. Davina must move an odd ball. Then Yusuf must pick that very ball.
The question asks only about Yusuf. But his chance depends on Davina’s pick, which comes first.
Find the chance for Davina’s pick
Box B has 3 balls, and 2 of them, the 3 and the 5, are odd.
If she moves the 4 instead, Box A holds only even balls. Then Yusuf can’t get an odd ball at all.
Find the chance for Yusuf’s pick
Say Davina moved an odd ball. Box A now holds 3 balls: the 2, the 6 and that one odd ball.
Watch out: alone is choice B. It forgets that Davina might move the 4.
Multiply the two chances
Both events must happen, so use the rule for events in a row.
Watch out: alone, choice D, stops after Davina’s pick. , choice C, counts 2 odd balls out of all 5. But Yusuf picks only from Box A.
So the answer is A, .
Check your answer
List all 9 equally likely outcomes. Davina can move 3, 4 or 5. Then Yusuf picks one of 3 balls.
| Ball moved | Box A then | Odd picks |
|---|---|---|
| 3 | 2, 6, 3 | 1 |
| 4 | 2, 6, 4 | 0 |
| 5 | 2, 6, 5 | 1 |
That is 2 odd picks out of 9, or .
More questions like this
The original DOE question
