3 English and 3 math
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Question 1 of 6
2026 Practice Test A English, question 12Passage The Best Laid Plans of Ravens
The Best Laid Plans of Ravens
In Edgar Allan Poe’s poem “The Raven,” a raven visits a lonely man’s home and responds to the man’s pleading questions with only the word “nevermore.” The poem’s narrator interprets the word as a prediction of doom for his future. A talking, prophetic raven may seem to be the wild imaginings of the poet, but a new study published in the journal Science hints that one particular idea behind the poem might not be as far-fetched as it seems. For most of human history, people assumed that animals do not understand the passage of time in the same way people do. Some people believed that animals might remember events from the past and that instinct might drive them to make preparations in order to guarantee survival, but most people did not think that animals had the ability to plan. At Lund University in Sweden, researchers argue that ravens may be able to think ahead and even plan for the future.
It can be difficult to test an animal’s ability to plan because human observers must be certain they are not mistaking instinctual behavior for intentional planning. For example, many animals hoard food so that they will not run out later, but scientists who study animals would not call hoarding a decision to plan for the future. This action is merely instinctual. Cognitive scientists argue that in order for an animal’s behavior to qualify as preparing for the future, the animal must use specific decision-making skills to solve a problem.
To avoid mistaking instinctual behavior for evidence of decision-making, the Lund University researchers designed two experiments to test ravens’ ability to plan. Ravens belong to the corvid family, a group of birds known for their intelligence. A study in 2007 showed that corvids have the tendency to save only certain types of food, which suggests that they are planning for the future rather than acting on instinct. In order to investigate that theory, the researchers had to design experiments that would achieve results that could not be explained by an instinctual behavior of food hoarding. Therefore, the ravens were taught two behaviors that they do not normally perform in the wild.
For the first experiment, the researchers showed the birds how to use a small stone to open a box and get treats. Once the ravens learned the behavior, the researchers presented the birds with four stones. Only one stone was the right size to open the box. The birds learned to select that stone and set it aside until the researchers presented the box. The second experiment involved bartering. A researcher would trade the ravens a large treat for a bottle cap. Later, the researchers presented the ravens with a group of items, including small treats and the bottle cap. The ravens chose the bottle cap over the treats and waited for the original researcher to trade with them again so that they could get more treats. In both experiments, the ravens waited patiently for up to seventeen hours for the researcher to return.
The results of these experiments are exciting, but more evidence needs to be gathered before scientists can fully conclude that ravens can plan for the future. Some scientists argue that the ravens might be choosing the stone and bottle cap because the ravens have been trained to do so, not necessarily because the ravens are thinking ahead. Regardless, like other recent advances in animal science, these experiments show that ravens could be much smarter than first believed, and scientists now believe that ravens do actually think about their own future.
Question
The author conveys a point of view on the study of animal intelligence mainly by
- Asharing details about experiments that tested the ability of an animal to plan for the future.
- Bcomparing the results of different experiments that were designed to test animal intelligence.
- Ccritiquing experiments that aimed to demonstrate that certain animals are capable of planning for the future.
- Dexplaining how modern experiments show that previously held beliefs about animal intelligence are inaccurate.
Show the answer
Correct answer: A
The question asks how the author conveys a point of view on the study of animal intelligence.
A. CORRECT. Paragraphs 3 and 4 focus on the process and details of the experiments that scientists conducted. This detailed information from the author provides a sense of how the ravens demonstrated planning abilities beyond natural instinct. The author supports the claims from the experiments, calling the findings “exciting” and stating in the conclusion that “these experiments show that ravens could be much smarter than first believed” (paragraph 5).
B. Incorrect. Although two experiments are described in the passage, the description presents the experiments as building on each other and does not compare their results. The passage states that “these experiments show that ravens could be much smarter than first believed, and scientists now believe that ravens do actually think about their own future” (paragraph 5).
C. Incorrect. The author presents information from the experiments and the results that were gathered from them; while there is an admission that “more evidence needs to be gathered before scientists can fully conclude that ravens can plan for the future” (paragraph 5), the author does not criticize the experiments that are presented.
D. Incorrect. While the author does discuss some previously held beliefs about animal intelligence in paragraph 1, the focus of the passage is that experiments indicate that there is reason to question these beliefs, since “these experiments show that ravens could be much smarter than first believed” (paragraph 5). The previously held beliefs are not considered inaccurate by the discussion in the passage because only one example—the raven—is provided. The passage does not state that beliefs about animal intelligence as a whole are inaccurate.
Question analysis
This author’s point-of-view question asks how the writer of “The Best Laid Plans of Ravens” mainly conveys a view of research into animal intelligence. Students must look at the article as a whole and decide how it presents that view. The choices describe ways of writing in abstract terms, which makes them easy to blur together.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Grade 7 point-of-view questions usually ask what an author thinks. This one asks how the author mainly conveys a view across the whole article, and the choices name methods that sound alike, closer to grade 8 work on how authors handle differing views.
- 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
- Reading between the lines moderate
- Every choice must be checked minor
- Evidence
- Answered from the whole text
- Reading level
- Passage: about grade 11, 599 words; question and choices: about grade 13, 74 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 sounds too plain to carry a point of view, which is exactly what makes this question hard. Students expect a view to be argued, so they reach for the choice that says the experiments prove old beliefs wrong, an overstatement of the author’s hedged “could be,” or for criticism, which belongs to other scientists. The article persuades by reporting the experiments in detail and calling them exciting.
How, not what major Working it out
The question asks how the view comes across, not what it is, and the answer is a method: the author lets the detailed account of the experiments in paragraphs 3–4 carry a favorable view. (Anderson & Krathwohl, 2001)
Reading between the lines moderate Working it out
The author never states an opinion outright; the view must be pieced together from words such as “exciting” and “could be much smarter than first believed” in paragraph 5. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Every choice must be checked minor Choosing the answer
The choices name ways of writing in abstract terms, sharing, comparing, critiquing and explaining, so each must be held against what the whole article actually does. (Embretson & Wetzel, 1987)
Strategy: Settle first on how the author regards the raven research, then check each choice against what the article actually does from beginning to end, not against a single paragraph.
Traps
- Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
- Wrong tone or attitude: Misjudges the tone, attitude or point of view, such as reading admiration as criticism, or taking a character's or subject's feelings for the author's.
- 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 Twists what the text says (King et al., 2004)
Notices that two experiments are described and assumes they are set side by side, but the article reports the stone test and the bartering test in turn without comparing results.
C Wrong tone or attitude (Graesser, Singer & Trabasso, 1994)
Takes the doubt that “some scientists” raise about training for the author’s own criticism, though the author calls the results “exciting” and moves past the objection.
D Too broad or too strong (King et al., 2004)
Builds on the point that ravens may be smarter than believed but overstates it: the author hedges with “could be,” discusses only ravens, and never calls older beliefs wrong.
Working it out, step by step
Figure out what the question asks
This asks about the author’s point of view, what the author thinks about studying animal intelligence. It also asks how the author mainly shows that view. Think about the whole article, not one paragraph.
Find the author’s view
In paragraph 5, the author says the results “are exciting.” The author also says the experiments “show that ravens could be much smarter than first believed.” So the author is interested in this research and hopeful about it.
See how the article is built
Most of the article explains the experiments. Paragraph 3 tells why the researchers planned two of them. Paragraph 4 gives the details step by step: the stone, the box, the bottle cap, the trades and the long wait. The author lets these details show why the research matters. Then the author calls the results exciting.
Check each choice
- A fits. The author shares details of experiments that tested whether an animal can plan.
- B does not fit. The two experiments are told one after the other. Their results are never compared.
- C does not fit. The doubt comes from “some scientists,” not the author. The author answers it with “Regardless.”
- D does not fit. It goes too far. The author says ravens “could be” smarter, which means maybe. The article never calls old beliefs wrong.
Watch out: D is tempting because paragraph 1 describes old beliefs. But “could be” is not the same as “are.”
Choose the answer
The author shows a view mostly through details of the experiments. So the answer is A.
Why this answer and not the closest wrong one
D is the closest wrong choice. The author does think ravens may be smarter than people believed. But the author is careful and says they “could be.” D says experiments prove old beliefs wrong, which is too strong. What the author mostly does is share the experiments’ details. That is A.
More questions like this
The original DOE question
The passage “The Best Laid Plans of Ravens” as printed (page 12)
Question 2 of 6
2024 Test A English, question 49Passage Excerpt from The Highest Tide
Excerpt from The Highest Tide
by Jim Lynch
The narrator’s summer job is collecting marine specimens in Puget Sound, Washington. In this excerpt, he is looking for specimens in the mudflats before daybreak. Mudflats, or flats, are coastal landforms created when sediment and silt from tides are deposited as the tides recede.
I rounded the oyster beds, to the far side. . . . It was low tide by then, and I saw the water hesitating at its apex, neither leaving nor returning, patiently waiting for the gravitational gears to shift. Dozens of anxious clams started squirting in unison like they did whenever vibrating grains of sand warned them predators were approaching. I stopped and waited with them, to actually see the moment when the tide started returning with its invisible buffet of plankton for the clams, oysters, mussels and other filter feeders. It was right then, ankle deep in the Sound, feet numbing, eyes relaxed, that I saw the nudibranch.1
In all my time on the flats I’d never seen one before. I’d read about them, sure. I’d handled them at aquariums but never in the wild, and I’d never even seen a photo of one this stunning. It was just three inches long but with dozens of fluorescent, orange-tipped hornlike plumes jutting from the back of its see-through body that appeared to be lit from within.
Nudibranchs are often called the butterflies of the sea, but even that understates their dazzle. Almost everything else in the northern Pacific is dressed to blend with pale surroundings. Nudibranchs don’t bother, in part because they taste so lousy they don’t need camouflage to survive. But also, I decided right then, because their beauty is so startling it earns them a free pass, the same way everyday life brakes for peacocks, parade floats. . . .
The dark mudflats loomed like wet, flattened dunes stretching deep into Skookumchuck Bay in front of our house. From a distance, they looked too barren to support sea life. Up close, they still did, unless you knew where to find the hearty clams, worms and tiny creatures that flourish in mud. . . . I’m not sure why I decided to take a look. It was still an hour before sunrise, and I knew exactly what the bars2 looked like in the moonlight, but for some reason, I couldn’t resist.
I heard it long before I saw it. It was an exhale, a release of sorts, and I instantly wondered if a whale was stranded again. We had a young minke3 stuck out there two summers prior, and it made similar noises until the tide rose high enough for rescuers to help free it. . . . I looked for a hulking silhouette but couldn’t find one. I waited, but there were no more sounds. Still, I went toward what I thought I’d heard, avoiding stepping into the mud until I had to. I knew the flats well enough to know I could get stuck just about anywhere. The general rule was you didn’t venture out past the shells and gravel with an incoming tide. I sank up to my knees twice, and numbing water filled my boots.
. . . I kept stepping toward the one sound I’d heard, a growing part of me hoping I’d find nothing at all. When I stopped to rest and yank up my socks, my headlamp crossed it. My first thought? A giant octopus.
Puget Sound has some of the biggest octopi in the world. They often balloon to a hundred pounds. Even the great Jacques Cousteau4 himself came to study them. But when I saw the long tubular shape of its upper body and the tangle of tentacles below it, I knew it was more than an octopus. I came closer, within fifty feet, close enough to see its large cylindrical siphon5 quiver. I couldn’t tell if it was making any sounds at that point, because it was impossible to hear anything over the blood in my ears. . . .
The creature’s body came to a triangular point above narrow fins that lay flat on the mud like wings, but it was hard to be sure exactly where it all began or ended, or how long its tentacles truly were, because I was afraid to pry my eyes off its jumble of arms for more than half a second. I didn’t know whether I was within reach, and its arms were as big around as my ankle and lined with suckers the size of half-dollars. If they even twitched I would have run. So, I was looking at it and not looking at it while my heart spangled my vision. I saw fragments, pieces, and tried to fuse them in my mind but couldn’t be certain of the whole. I knew what it had to be, but I wouldn’t allow myself to even think the two words. Then I gradually realized the dark shiny disc in the middle of the rubbery mass was too perfectly round to be mud or a reflection.
It was too late to smother my scream. Its eye was the size of a hubcap.6
From THE HIGHEST TIDE by Jim Lynch. Copyright © 2005 by Jim Lynch. Used by permission of Bloomsbury USA. All rights reserved.
1nudibranch: type of sea slug
2bars: sandbars
3minke: species of small whale
4Jacques Cousteau: renowned French oceanographer
5siphon: tube-like organ that is used for drawing in or removing fluids
6hubcap: removable cap over the end of a wheel axle
Question
Read these sentences from paragraph 8.
So, I was looking at it and not looking at it while my heart spangled my vision. I saw fragments, pieces, and tried to fuse them in my mind but couldn’t be certain of the whole.
The sensory language “spangled my vision,” “I saw fragments, pieces,” and “tried to fuse them in my mind” conveys the narrator’s
- Aextreme excitement about making a great discovery.
- Breluctant acceptance that he needs to leave the mudflats.
- Cterrified confusion about the creature in the mudflats.
- Dsudden concern about his personal safety.
Show the answer
Correct answer: C
The question asks what the sensory language in the sentences from paragraph 8 conveys about the narrator.
A. Incorrect. While the narrator does not leave the mudflats and is curious about what has been found, the main emotions described in paragraph 8 are fear and confusion as the narrator tries to comprehend the size of the animal.
B. Incorrect. The language focuses on the narrator’s inability to organize what he sees into useful thoughts and conclusions, and while the narrator feels fear in paragraph 8—“I was afraid” and “I would have run”—the narrator refuses to leave the mudflats out of curiosity.
C. CORRECT. The phrase “spangled my vision” illustrates that the narrator cannot fully recognize what has appeared on the mudflats. The sight is so amazing, the narrator is trying to “fuse” together “fragments” and “pieces” because seeing the creature has created so much emotion in the narrator that he feels confused.
D. Incorrect. While the narrator is feeling some fear, as expressed in paragraph 8, the phrases actually indicate that the narrator’s amazement causes him to struggle to take in the view of the creature before him.
Question analysis
This question about sensory language asks what three phrases, including “spangled my vision,” convey about the narrator as he stares at a huge creature in the mud in an excerpt from The Highest Tide. Students must interpret unusual imagery and choose among emotions that all seem possible at such a startling moment.
- Grade level
- Grade 8 reading and task
- Compared with grade 7
- Above grade 7 Interpreting sensory language for a character's state of mind is grade 7 work, but spangled is an unusual verb, and the paragraph partly supports several of the emotions offered, so the choice must be matched precisely to the quoted phrases.
- 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 analyze
- What makes it hard
- Figurative or literary language major
- A very close wrong answer moderate
- Hard words minor
- Evidence
- Answered from one paragraph or stanza
- Reading level
- Passage: about grade 6, 902 words; question and choices: about grade 7, 92 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 quoted phrases are about perception, not feeling: the narrator sees fragments and cannot assemble them, while his heart pounds hard enough to blur his sight. The fear is clear from the surrounding sentences, where he is afraid to look away and ready to run, and that context makes the choice about personal safety very tempting. The answer must cover both the terror and the confusion, and the word “spangled” can mislead readers into hearing excitement.
Figurative or literary language major Understanding the question
The phrases describe seeing in pieces, “looking at it and not looking at it”, a heart that “spangled” his vision, “fragments” he cannot “fuse”, and the emotion has to be read from that broken sight. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
A very close wrong answer moderate Choosing the answer
The right choice and the one about concern for his safety both name fear; they part on what the quoted phrases show, a mind unable to piece the creature together or a worry about its reach. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Hard words minor Understanding the question
“Spangled”, to scatter with glittering spots, is a rare word, and its sparkle can suggest delight, which opens a reading of excitement to students who miss the fear around it. (Perfetti, 2007; Freedle & Kostin, 1993)
Strategy: Ask what the three quoted phrases together say about how the narrator is seeing and thinking at this moment, then choose the emotion that accounts for all three, not just one.
Traps
- True but not the answer: A choice says something accurate about the text that does not answer this question.
- Wrong tone or attitude: Misjudges the tone, attitude or point of view, such as reading admiration as criticism, or taking a character's or subject's feelings for the author's.
The wrong answers, classified
A Wrong tone or attitude (Graesser, Singer & Trabasso, 1994)
Reads the pounding heart and glittering vision as the thrill of a great find, missing that he is afraid to take his eyes off the creature and cannot make sense of it.
B Twists what the text says (King et al., 2004)
Turns “If they even twitched I would have run”, a possibility, into an accepted need to leave, though the narrator stays and the phrases describe how he sees.
D True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Matches the fear in paragraph 8, where he wonders whether he is within reach, but the quoted phrases describe broken seeing and puzzling, and his fear has been building, not sudden.
Working it out, step by step
Know what the question asks
Sensory language describes what a character sees, hears or feels. This asks what feeling the three quoted phrases show. Your answer must explain all three phrases, not just one.
Explain the hard words
To spangle means to cover with glittering spots. His heart pounds so hard that his sight seems to sparkle and blur. Fragments are small broken pieces. To fuse means to join together.
Put the phrases together
He sees only “fragments, pieces.” He tries “to fuse them in my mind” but “couldn’t be certain of the whole.” So he is confused, unable to tell what the creature really is. The sentences around them show he is also terrified. He is “afraid to pry my eyes off” its arms, and his heart is racing.
Check each choice
- C fits: “terrified confusion” covers both his fear and his broken, puzzled seeing.
- A is wrong because “spangled” may sound happy, but he is frightened, not thrilled.
- B is wrong because he never decides to leave, and he would run only if the arms moved.
- D is wrong because the phrases show confused seeing, and his fear has been growing since paragraph 6.
Watch out: D is close, since he is afraid. But it leaves out the confusion the phrases show.
Choose the answer
The phrases show a frightened narrator who cannot piece together what he sees. So the answer is C.
Why this answer and not the closest wrong one
D comes closest, because the narrator truly fears for his safety. But the quoted phrases are about how he sees: in pieces he can’t join. That is confusion. C names both the fear and the confusion, so it fits all three phrases.
More questions like this
The original DOE question
The passage “Excerpt from The Highest Tide” as printed (pages 64–65)
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
2024 Test B Math, question 44Question
Which inequality is equivalent to ?
- A
- B
- C
- D
Show the answer
Correct answer: D
Distribute the coefficient −2 on the right-hand side:
Subtract from both sides:
Add 10 to both sides:
Divide both sides by 5:
This is equivalent to
Question analysis
Students choose the simplest equivalent form of a linear inequality that has x on both sides and a negative number multiplied into parentheses. It tests distributing, combining like terms and solving inequalities. Sign errors in the distribution, and reading the direction of the final inequality, are where most mistakes happen.
- NYS standards
- Grade level
- Grade 8 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 inequalities have the form px + q < r. This one has x on both sides and a negative factor to distribute across a subtraction, steps that belong to grade 8 equation work, so it is harder than typical grade 7 practice.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 1, recall and reproduction · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- A very close wrong answer moderate
- Many steps minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 16+, 10 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Every move is standard algebra, but the inequality is built so that small slips change the answer completely. The −2 has to reach both terms in the parentheses, and once the boundary −2 is found its direction still has to be read correctly, since the variable ends up on the right as −2 < x. Rewriting that as x > −2, or substituting x = 0 into the original, catches the trap.
Error-prone arithmetic moderate Working it out
Distributing −2 over (5 − 3x) gives −10 + 6x, two sign decisions in one move, and the x terms then sit on both sides of the inequality. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
A very close wrong answer moderate Choosing the answer
x < −2 and x > −2 share the boundary and differ only in direction, which depends on reading −2 < x correctly or flipping the sign when dividing by a negative. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Many steps minor Working it out
Four moves follow one another, distributing, collecting 5x + 6x, moving the x terms and dividing by 5, and a slip at any of them changes the result. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Strategy: Distribute the −2 to both terms in the parentheses, combine the x terms on the right, then gather the x terms on the side that keeps their coefficient positive.
Traps
- Order of operations: Working left to right, or distributing a minus sign wrongly, gives a choice.
- Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
- A faulty procedure: A systematic but wrong procedure: adding fractions straight across, applying an exponent to each term of a sum, dropping a sign when moving a term.
The wrong answers, classified
A A faulty procedure (Brown & Burton, 1978; Tatsuoka, 1983)
Treats 5 − 3x as 2, combining a number with an x term, so the right side becomes 5x − 4 and the solution x < 16.
B Order of operations (Brown & Burton, 1978)
Multiplies the −2 by the 5 but not by the −3x, writing 5x − 10 − 3x, which leads to 4x < 10 and x < 5/2.
C Negatives and direction (Brown & Burton, 1978)
Finds the boundary −2 but points the inequality the wrong way, by misreading −2 < x or by not flipping the sign after dividing by −5.
Worked solution, step by step
Formulas used
- Distributive property
- a is the number outside the parentheses. b and c are the terms inside. Multiply a by each one. A minus sign inside counts as a negative term, so 5 − 3x is 5 + (−3x). A negative times a negative is positive.
- Keeping an inequality true
- a and b are the two sides, and c is any number. Adding or subtracting the same number on both sides keeps the inequality true. Dividing both sides by a positive number also keeps it true. Only multiplying or dividing by a negative number flips the sign.
Sort out the question
An inequality compares two sides with a sign like <, which means is less than. To solve it, you get x alone on one side.
You need the short inequality that has the same answers as the long one.
Distribute the −2
Multiply −2 by both terms inside the parentheses, 5 and −3x.
A negative times a negative is positive, so the second part is +6x. Watch out: If the −2 multiplies only the 5, you end up with , choice B.
Combine the x terms
The right side is now 5x − 10 + 6x. Put the x terms together: 5x + 6x = 11x.
Gather the x terms on one side
Subtract 6x from both sides. That leaves the x terms on the right, where they stay positive.
Get x by itself
Add 10 to both sides. Then divide both sides by 5.
You divided by a positive 5, so the sign does not flip.
Read it with x first
says −2 is less than x. That is the same as saying x is greater than −2, just as 3 < 5 means 5 > 3.
Watch out: , choice C, has the same number but points the wrong way.
So the answer is D, .
Check your answer
Test x = 0, which is greater than −2. The left side is . The right side is . And −20 < −10 is true. Now test x = −3. The left side is −38 and the right side is −43. That is false, as it should be.
More questions like this
The original DOE question
Question 5 of 6
2018 Test B Math, question 53Question
At North High School, a survey asked two questions, Question A and Question B. For each question, students could answer either “yes” or “no.” Of the 800 students who responded to the survey, 720 answered “yes” to Question A, and 640 answered “yes” to Question B. What is the least possible number of these students who could have answered “yes” to both questions?
- A80
- B160
- C560
- D640
Show the answer
Correct answer: C
None of the 80 students (800 − 720) who answered “no” to Question A could have answered “yes” to both questions.
Therefore, the least possible number of students who could have answered “yes” to both questions can be found by subtracting the 80 who answered “no” to Question A from the 640 who answered “yes” to Question B or 640 − 80 = 560.
Question analysis
In a survey of 800 students at North High School, 720 said yes to the first question and 640 said yes to the second. Students must find the smallest possible number who said yes to both. It tests reasoning about overlapping groups, and asking for the least possible overlap rather than an exact count makes it unusual.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 students work with Venn diagrams and two-way tables when all counts are given. Finding the smallest possible overlap requires reasoning about extremes rather than computing, which is rare in grade 7 and new to most students.
- 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
- No obvious method major
- Turning words into math moderate
- A very close wrong answer minor
- Solution
- 2 steps
- Reading level
- Question and choices: about grade 8, 60 words.
- Corrected from the DOE handbook
- A repeated phrase and a stray comma in the explanation were removed.
- 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
Most students have never been asked for a smallest overlap, so they fall back on a picture of nested groups and give the largest one. The key move is to push the two yes groups apart as far as possible: only the 80 students who said no to Question A can absorb some of Question B's yes answers. Once that is seen, the arithmetic is one subtraction, so the question rewards reasoning far more than computation.
No obvious method major Working it out
Nothing in the wording points to the method: the smallest overlap appears only when all 80 students who said no to Question A are imagined saying yes to Question B. (Schoenfeld, 1985)
Turning words into math moderate Understanding the question
"The least possible number of these students who could have answered “yes” to both questions" asks for an extreme case, which has to be turned into an arrangement of the 800 students. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
A very close wrong answer minor Choosing the answer
640 is only 80 above the right 560, so a rough sense of size cannot choose between them; only asking whether the overlap is the least or the greatest separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Strategy: Add the two yes counts and compare the sum with the number of students; any amount above the total must come from students counted in both groups.
Traps
- NOT, LEAST or EXCEPT: The question asks for the exception, the least, or what is not true.
- Stops one step early: A choice is a number from partway through the solution.
- 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 Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds the 80 students who said no to Question A, 800 − 720, and stops before subtracting them from the 640 who said yes to Question B.
B Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Finds the 160 students who said no to Question B, 800 − 640, which bears on the count but is not the overlap asked about.
D Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Assumes everyone who said yes to Question B also said yes to Question A, giving the greatest possible overlap instead of the least.
What was corrected from the DOE handbook, and why
- Explanation: The handbook prints “(800 − 720)” twice in its first sentence, after “80 students” and again after “Question A,” and puts a comma between subject and verb in “the least possible number of students who could have answered “yes” to both questions, can be found.” The site keeps the first “(800 − 720)” and drops the comma.
Worked solution, step by step
Formulas used
- Least overlap of two groups
- a is the size of the first group and b is the size of the second. t is the total number of people. If a + b is more than t, some people must be in both groups. The extra amount is the smallest number that can be in both.
Sort out what you know
There were 800 students. Of them, 720 said yes to Question A and 640 said yes to Question B. You need the least number who could have said yes to both. The overlap is the group in both yes groups. You want the smallest overlap.
Find who said no to A
Students who said no to Question A cannot be in the overlap.
So 80 students said no to Question A.
Watch out: 80 is not the answer. It is only a step, and it is choice A.
Keep the overlap small
To make the overlap as small as you can, put as many B yes answers outside it as possible. The only students outside it are the 80 who said no to A. So pretend all 80 of them said yes to B.
Count the rest of the yes group
The other yes answers to B must come from students who also said yes to A.
So at least 560 students said yes to both.
Watch out: 640 is the most that could say yes to both, not the least. That is choice D.
Give the answer
The fewest students who could say yes to both questions is 560. So the answer is C, 560.
Check your answer
Use the overlap formula: . There are 1,360 yes answers but only 800 students, so 560 students must be counted twice. You can also check the groups. 560 said yes to both, 160 to A only and 80 to B only. That makes .
More questions like this
The original DOE question
Question 6 of 6
2026 Practice Test B Math, question 24Question
A chemical decays in such a way that the amount left at the end of each week is 20% less than the amount at the beginning of that same week. What percentage of the original amount is left after two weeks?
- A40%
- B60%
- C64%
- D80%
Show the answer
Correct answer: C
Let x be the original amount of the chemical. It loses 20% after each week, which means 80% of the chemical remains at the end of each week. End of first week:
At the end of the second week, 80% of the amount left at the end of the first week remains.
End of second week: or 64%
Question analysis
A chemical loses 20% of the amount present at the start of each week, and students find what percentage of the original amount is left after two weeks. It tests applying a percent decrease more than once. The question turns on which amount each week's loss is measured against.
- NYS standards
- 7.RP.3 multistep ratio and percent problems
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 A typical grade 7 percent task applies one increase or decrease to one amount. This one applies a weekly decrease twice in a row, an early form of exponential decay that goes beyond 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 apply
- What makes it hard
- A very close wrong answer major
- Turning words into math moderate
- Variables instead of numbers minor
- Solution
- 2 steps
- Reading level
- Question and choices: about grade 8, 40 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 equal decreases in a row feel like one decrease of twice the size, and that is the trap: 20% and 20% suggest 40% gone. The stem states the rule, each loss measured from that week’s start, in one quick phrase. Working week by week from 100 shows the second loss is 16, not 20, which separates the answer from the choice four points away, while stopping after one week or reporting the loss costs the point more simply.
A very close wrong answer major Choosing the answer
The choices 60% and 64% sit four percentage points apart, so a rough estimate cannot choose between them; only seeing that the second 20% is taken from 80, not 100, does. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Turning words into math moderate Understanding the question
The phrase “the amount at the beginning of that same week” sets each week’s base, so the second week’s 20% is measured from what was left after the first week. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Variables instead of numbers minor Understanding the question
No starting amount is given, so students must pick one, such as 100 grams, or work with a percent of a percent, 0.8 × 0.8. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)
Strategy: Use a starting amount of 100 so that percents become units, find what remains after the first week, then apply the same 20% loss to that remainder.
Traps
- Percent of the wrong amount: Finding the whole from a part, or a percent change measured from the wrong starting amount.
- Stops one step early: A choice is a number from partway through the solution.
- 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)
Adds the weekly losses, 20% + 20% = 40%, and gives that figure, which describes the amount lost rather than the percentage still left.
B Percent of the wrong amount (Parker & Leinhardt, 1995)
Subtracts 20% of the original amount twice, 100 − 20 − 20 = 60, though the second week’s 20% comes from the 80% left, not the starting amount.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Finds that 80% remains after the first week and stops, never taking the second week’s 20% from that remainder.
Worked solution, step by step
Formulas used
- Percent of an amount
- p is the percent, and amount is the whole you take the percent of. Percent means out of 100, so 20% is 20/100. Multiply to find the part. Be sure the amount is the right whole. Here, each week uses the amount at the start of that week.
- Percent left after a loss
- The whole amount is 100%. If 20% goes away, the rest stays. So 80% of each week’s starting amount is left at the end of that week. Keeping 80% is the same as multiplying by 0.8.
Sort out the question
Each week the chemical loses 20% of what it has. The key words are “the amount at the beginning of that same week.” So each week’s 20% comes from that week’s starting amount. No amount is given. You need the percent of the original amount that is left after two weeks.
Pick an easy starting amount
Pretend the chemical starts at 100 grams. With 100, the number of grams left is the same as the percent left. Any starting amount gives the same percent, so choose the easiest one.
Work out the first week
Use the percent formula. The first week starts with 100 grams:
The chemical loses 20 grams, so grams are left. That is 80% after one week.
Watch out: 80% is only the first week. Stopping here gives choice D.
Work out the second week
The second week starts with 80 grams, not 100. So take 20% of 80:
This time the chemical loses only 16 grams, so grams are left.
Watch out: taking away 20 grams again uses the original amount. That gives 60%, choice B. Choice A, 40%, adds the two losses. But the question asks what is left, and only 36% was lost.
Read the answer as a percent
Week Start (grams) Loss (grams) Left (grams) 1 100 20 80 2 80 16 64 Another way: each week keeps 80%, or 0.8, of its start. Two weeks gives , which is 64%.
64 grams out of the original 100 grams is 64%. So the answer is C, 64%.
Check your answer
Think about the size of the second loss. The second week starts with less, so it loses less than 20 grams. That means more than 60% is left. It does lose something, so less than 80% is left. Of the four choices, only 64% is between 60% and 80%.
More questions like this
The original DOE question
