SHSAT Sunset

Six SHSAT Questions

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.

RefreshNew TestYour practice tests

Question 1 of 6

2024 Test A English, question 25
Passage At Dusk

At Dusk

by Natasha Trethewey

At first I think she is calling a child,
my neighbor, leaning through her doorway
at dusk, street lamps just starting to hum
the backdrop of evening. Then I hear
the high-pitched wheedling1 we send out
to animals who know only sound, not
the meanings of our words—here here—
nor how they sometimes fall short.
In another yard, beyond my neighbor’s
sight, the cat lifts her ears, turns first
toward the voice, then back
to the constellation of fireflies flickering
near her head. It’s as if she can’t decide
whether to leap over the low hedge,
the neat row of flowers, and bound
onto the porch, into the steady circle
of light, or stay where she is: luminous
possibility—all that would keep her
away from home—flitting before her.
I listen as my neighbor’s voice trails off.
She’s given up calling for now, left me
to imagine her inside the house waiting,
perhaps in a chair in front of the TV,
or walking around, doing small tasks;
left me to wonder that I too might lift
my voice, sure of someone out there,
send it over the lines stitching here
to there, certain the sounds I make
are enough to call someone home.

“At Dusk” from NATIVE GUARD by Natasha Trethewey, published by Houghton Mifflin Company. Copyright © 2006 by Natasha Trethewey. All rights reserved.

1wheedling: speaking in a flattering manner

Question

The poet develops a theme about making connections with others mainly through the

  • Aexploration of the desires of the speaker and the neighbor.
  • Bspeaker’s observations of the sights and sounds in the neighborhood.
  • Cspeculations the speaker makes about what the neighbor does inside her house.
  • Dspeaker’s explanation of the cat’s thoughts and actions.
Show the answer

Correct answer: A

The question asks for an explanation of how the poet develops a theme about making connections with others.

A. CORRECT. The speaker first describes the neighbor calling the cat in a “high-pitched wheedling” (line 5) voice before giving up and returning indoors. The neighbor’s desire to have the cat return home prompts the speaker to wonder whether the speaker could call out and be “certain the sounds . . . / are enough to call someone home” (lines 28–29). These final lines most develop the theme of connection by conveying a desire to be able to prompt someone’s return.

B. Incorrect. Line 1, in which the speaker at first thinks the sound in the neighborhood is the neighbor “calling a child,” might be assumed to introduce a theme of making connections with others. However, other descriptions of the sights and sounds of the neighborhood, including the time of day—“at dusk, street lamps just starting to hum / the backdrop of evening” (lines 3–4) and “constellation of fireflies flickering” (line 12) near the cat—have no relationship to a theme of connection.

C. Incorrect. In lines 22–24, the speaker imagines the neighbor’s activities inside her house: “perhaps in a chair in front of the TV, / or walking around, doing small tasks.” Although the speaker does imagine the neighbor is doing these things to pass time while “waiting” (line 22) for the cat, the neighbor’s actions—and even the speaker’s imagining—are carried out alone, so they do not develop a theme of connection.

D. Incorrect. Lines 10–19 present the speaker’s observations of the cat, which “turns first / toward the voice, then back” when the neighbor calls, then appears “as if she can’t decide” whether to return to the neighbor or stay outside. Although the cat’s indecision about whether to heed the neighbor’s call might seem to develop a theme about making connections, lines 10–19 focus more on the relative appeal of the cat’s two options—returning to “the steady circle / of light” at home or pursuing the “luminous / possibility . . . flitting before her”—than on any connection between the cat and its owner or between the speaker and the neighbor.

Question analysis

This reading question asks which element of Natasha Trethewey's poem At Dusk mainly develops its theme about making connections with others. All four choices describe something that really happens in the poem, from neighborhood sights to a cat's hesitation, so students must weigh how much each part contributes to that theme.

NYS standards
  • 7R2 theme or central idea
  • 7R6 point of view and author position
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Analyzing how a theme develops is grade 7 work, but here the student must rank four genuine features of the poem by how much each builds the theme, a comparison that asks more than typical grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from the whole text
Reading level
Passage: 236 words (a poem; reading level not measured); question and choices: about grade 8, 53 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The question asks what mainly carries the theme, and every choice is a real part of the poem, so ruling choices out means ranking them, not spotting errors. The cat takes up the most lines and is the one being called home, which makes it the strongest lure, though its lines are about her choice between two places. What builds the theme is the neighbor's wish to bring the cat home, echoed by the speaker's wish to call someone home.

  1. Every choice must be checked moderate Choosing the answer

    All four choices name something that really fills the poem, so each must be weighed by how much it builds the theme of connection, not by whether it is there. (Embretson & Wetzel, 1987)

  2. Evidence in several places moderate Working it out

    The theme is built from the two ends of the poem: the neighbor calling and then waiting in lines 1–8 and 20–22, and the speaker's wish in lines 25–29 to send a voice out. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

  3. The right answer is reworded minor Choosing the answer

    The right choice speaks of “desires,” a word the poem never uses, while the wrong ones echo its sounds, the neighbor's house and the cat. (Freedle & Kostin, 1993; Kirsch & Mosenthal, 1990)

Strategy: For each choice, find the lines it refers to and ask how directly they bear on making connections with others; keep the choice whose lines do so most fully.

Traps

  • Wrong part of the text: A choice is true of another paragraph, stanza or speaker than the one asked about.
  • 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.
  • True but not the answer: A choice says something accurate about the text that does not answer this question.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    A theme is a big message about life. This poem has a theme about making connections, or reaching out to others. You need the part of the poem that mainly builds that theme.

  2. Look at what the neighbor wants

    The neighbor wants her cat to come home. She calls out at dusk with a “high-pitched wheedling” (line 5). Wheedling means sweet-talking. When she stops, the speaker pictures her “inside the house waiting” (line 22). Her wish is to reach the cat and bring her back.

  3. Look at what the speaker wants

    Her calling “left me to wonder that I too might lift / my voice” (lines 25–26). The speaker hopes the sounds “are enough to call someone home” (line 29). So the speaker wants to reach someone too. Both people wish to call someone back to them. That shared wish builds the theme of connection.

  4. Check each choice

    • A is right. The desires, or wishes, of the neighbor and the speaker carry the theme.
    • B is wrong. The humming street lamps and the fireflies set the scene. They don’t show anyone reaching out.
    • C is wrong. The guesses about the neighbor inside fill only three lines, and they show her alone.
    • D is wrong. The cat lines weigh home against the night. They don’t show one person reaching another.

    Watch out: D is tempting because the cat fills many lines. But they are about her choice, not about a connection.

  5. Choose the answer

    The poem builds its theme through what the neighbor and the speaker both want. So the answer is A.

Why this answer and not the closest wrong one

D is the closest wrong answer, since the cat takes up lines 10–19. But those lines weigh the porch light against the glowing night. The theme of connection comes from two wishes. The neighbor wants to call the cat home. The speaker wants to “call someone home” too. A names those desires.

More questions like this

The original DOE question
Question 25 as printed on page 50 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 50, question 25. Open page 50 of the handbook (PDF)
The passage “At Dusk” as printed (page 48)The passage “At Dusk” as printed on page 48 of the DOE handbook.

Question 2 of 6

2026 Practice Test A English, question 41
Passage Massachusetts: Lowell National Historical Park

Massachusetts: Lowell National Historical Park

During the first half of the 19th century, Lowell, Massachusetts, quickly transformed itself from a farm town to a bustling industrial city. In time, Lowell became a model of industry, gaining global recognition for its state-of-the-art technology, innovative canal and dam system, mill architecture, boardinghouses, churches, and ethnic neighborhoods. Young Yankee women, immigrant families, and European tourists all flocked to Lowell to find work at one of the many textile mills, or visit the industrious city that was becoming a popular tourist destination. As one Scottish traveler observed during his visit to America, “Niagara and Lowell are the two objects I will longest remember in my American journey, the one the glory of American scenery, the other of American industry.” Today, Lowell National Historical Park welcomes visitors to enjoy the sights of Lowell and learn about the history of one of America’s most significant industrial cities.

The Boston merchants who founded Lowell in 1821 and named it after Francis Cabot Lowell chose to locate the town along Massachusetts’s Merrimack River to take advantage of the kinetic energy offered by the Pawtucket waterfalls. Over six miles of canals powered the waterwheels of Lowell’s mills, whose massive five- and six-story brick buildings dominated the city’s landscape. . . . The most recognized of these buildings are the Lowell Manufacturing Company chartered in 1821, the Suffolk or Wannalancit Mill completed around the 1880s, the Boott Mill Company established in 1835, and the Boott Mill Boardinghouse that opened in 1838. By the 1850s, 40 textile mills employing over 10,000 workers stretched for about a mile along the river. . . .

The city’s female workforce was significant in the history of Lowell. From the early to mid-1800s, women left the constricted lifestyle of small rural towns and rural areas for independent industrial city life. Most were young single Yankee girls, who were tired of the limited opportunities offered by their domestic work. Women found that Lowell’s mills offered monthly wages for their services and provided them room and board. Although these women gained economic independence in Lowell, the mill boardinghouse keepers constantly supervised their social activities, for which they hardly had any time, considering their daily 12- to 14-hour work schedules. At the end of the day, the factory bell signaled the “mill girls” to return to their boardinghouses. They were expected to adhere to the strict code of conduct respecting curfew and attending church.

Yankee “mill girls” continued to dominate the Lowell workforce until the 1840s, when the city began to find it difficult to compete with the growing industrial development in other New England communities. As profits fell, the mill industry cut wages. These wage cuts, deteriorating working conditions, and long workdays led the “mill girls” to protest and organize strikes. When their demands went unheard, the women left Lowell, and immigrant groups replaced them in the workforce. Despite the low wages and unhealthy work conditions, immigrants were eager to find work.

The immigrants replacing the Yankee “mill girls” during the 1840s were predominantly Irish Catholics, who traveled to America during the Great Potato Famine. Although Lowell received an influx of Irish families during this time, the Irish were a part of the city’s history from its birth, and before the “mill girls” arrived, they built Lowell’s historic canals, mills, and boardinghouses. Initially, Lowell’s Protestant community was slow to welcome Irish immigrants, but the hostility between Yankee Protestants and Irish Catholics eventually disappeared. Irish immigrants dominated the industrial scene until the Civil War, when other immigrant groups began to work in the city mills.

Like the Irish, the French-Canadians, Greeks, Poles, Portuguese, Russian Jews, and Armenians who came to work in Lowell’s mills faced long work hours, low wages, and poor living conditions in the city’s crowded tenements. By the time Lowell’s industry declined, the city had become an ethnic melting pot, where each group claimed its own distinct neighborhood, like the Irish immigrants’ “New Dublin” or “Acre,” and the French-Canadians’ “Little Canada.” The city officially began to close down its mills in the 1920s and ’30s after Lowell’s outdated mills could no longer compete against the state-of-the-art cotton mills in other communities and working conditions continued to decline as Lowell’s companies stopped reinvesting in their mills. . . . Despite a brief resurgence during World War II, the city shut down its last surviving mill by the mid-1950s.

From “Massachusetts: Lowell National Historical Park”—Public Domain/National Park Service

Yankee: native to New England
Niagara: a town in northwestern New York State well known as the location of Niagara Falls, a series of waterfalls on the Canadian border
domestic work: household duties like cooking and cleaning

Question

Which sentence best summarizes the mill girls’ experience as the dominant workforce in Lowell?

  • AThe mill girls were eager to leave their domestic duties and small towns behind, so they went to work in the mills of Lowell.
  • BOriginally, the mill girls were satisfied to work in Lowell, but as they left their jobs at the Lowell mills, immigrants arrived to fill the empty positions.
  • CYoung women left home to work in the Lowell mills, but the mill girls soon became dissatisfied with the working conditions and rigid boardinghouse rules.
  • DThe mill girls embraced city life when they came to work in Lowell’s mills, but when their protests about unfavorable working conditions went unanswered, they left.
Show the answer

Correct answer: D

The question asks for the sentence that best summarizes the mill girls’ time as the dominant workforce in Lowell.

A. Incorrect. While the passage explains that mill girls were initially eager to leave the domestic duties of life in rural areas, the summary sentence does not address the details about the mill girls’ time working in the mills or the changes that led the mill girls to leave the industry.

B. Incorrect. Mill girls initially found satisfaction in the mill work and lifestyle, and when they did leave, immigrants filled the empty jobs. This summary sentence, however, does not address the details about the mill girls’ time as the primary workforce in Lowell or the circumstances that led them to leave their jobs in the mid-1800s.

C. Incorrect. Mill girls did leave home to work in the Lowell mills, and they did grow dissatisfied over time, but this summary sentence does not include details about the mill girls’ actions to improve the working conditions.

D. CORRECT. This sentence summary best captures the mill girls’ experience as outlined in paragraphs 3 and 4. The sentence concisely summarizes both the women’s initial excitement about the opportunity to live independently (“Women found that Lowell’s mills offered monthly wages for their services and provided them room and board” [paragraph 3]) and their eventual inability to secure better working conditions (“When their demands went unheard, the women left Lowell, and immigrant groups replaced them in the workforce” [paragraph 4]).

Question analysis

This summary question asks which sentence best sums up the experience of the Yankee mill girls during the years they were Lowell's main workforce. Students must pull together the account spread over paragraphs 3 and 4, and every choice is a two-part sentence that sounds accurate, so each must be checked for what it includes, what it leaves out and what it gets slightly wrong.

NYS standards
  • 7R2 theme or central idea
  • 7R3 plot elements and ideas
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Summarizing part of a text is a grade 7 standard, usually tested with one clearly complete choice. Here all four summaries are long, two-part and largely accurate, so ranking them by completeness and precision asks more than typical grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from several paragraphs or stanzas
Reading level
Passage: about grade 15, 764 words; question and choices: about grade 11, 116 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

This is a completeness question: every summary is built from true pieces of paragraphs 3 and 4, and the right one is the only one that runs from arrival to departure with the cause in between. Students who stop at dissatisfaction feel they have the whole arc, because the turn against working conditions is the story's middle. Writing a one-line summary first, with a beginning, a turning point and an end, makes the gaps in the others easy to see.

  1. Every choice must be checked moderate Choosing the answer

    All four summaries are two-part sentences of 24 to 27 words that sound accurate, so each has to be checked for what it leaves out: the arrival, the wage cuts and protests, or the departure. (Embretson & Wetzel, 1987)

  2. A very close wrong answer moderate Choosing the answer

    The dissatisfaction summary shares the key's shape, women coming to the mills and then turning against their working conditions; it differs only in the ending, where the key has unanswered protests and the women leaving. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  3. Evidence in several places minor Working it out

    The mill girls' story runs from paragraph 3, on why they came and how they lived, to paragraph 4, on wage cuts, strikes and their departure in the 1840s. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: Write your own one-sentence summary of paragraphs 3 and 4 before reading the choices, then compare each choice with it claim by claim, including its words about timing and cause.

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.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    This question asks for the best summary. A summary retells the main events in a few words. It covers the beginning, the middle and the end. Here you sum up the mill girls’ time as Lowell’s main workforce. Their story is in paragraphs 3 and 4.

  2. Find the beginning of their story

    Paragraph 3 says the women came for “independent industrial city life.” They found that the mills “offered monthly wages for their services and provided them room and board.” Room and board means a place to live and meals. So at first, they were glad to come. Their days were long, though, and the rules were strict.

  3. Find the middle and the end

    Paragraph 4 gives the turning point. In the 1840s, profits fell and the mills cut wages. “These wage cuts, deteriorating working conditions, and long workdays” led the women to protest and strike. Deteriorating means getting worse. Then comes the end: “When their demands went unheard, the women left Lowell.”

  4. Check each choice

    • A is wrong. It tells only why they came. It stops before their years at work and their leaving.
    • B is wrong. It has the start and the end. But it skips the middle: the wage cuts and protests that made them leave.
    • C is wrong. It has the start and the unhappy middle, but no protests and no leaving. Also, “soon” is off, since the trouble came years later, in the 1840s.
    • D is right. It covers all three parts: they embraced city life, protested bad conditions, and left when no one listened. Embraced means happily welcomed.

    Watch out: C feels complete because it ends with the women unhappy. But their story doesn’t end there. They protested, and then they left.

  5. Choose the answer

    Only one summary runs from the mill girls’ arrival to their leaving, with the cause in between. So the answer is D.

Why this answer and not the closest wrong one

C is the closest wrong answer. Like D, it starts with the women coming to the mills and then growing unhappy. But it stops there. It leaves out the protests and the women leaving Lowell, which is how their time as the main workforce ended. D tells the whole story.

More questions like this

The original DOE question
Question 41 as shown on the DOE’s digital test, page 56 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test A English, page 56, question 41.
The passage “Massachusetts: Lowell National Historical Park” as printed (page 50)The passage “Massachusetts: Lowell National Historical Park” as printed on page 50 of the DOE handbook.

Question 3 of 6

2024 Test B English, question 1

Question

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.

NYS standards
  • 7L1 grammar and usage conventions
  • 7L3a precise and concise language
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.
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.

  1. 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)

  2. 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)

  3. 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

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    You need to 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.

  2. 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.

  3. 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.

  4. 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 1 as printed on page 159 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 159, question 1. Open page 159 of the handbook (PDF)

Question 4 of 6

2018 Test A Math, question 30

Question

Today, Tien’s age is 14\frac{1}{4} of Jordan’s age. In 2 years, Tien’s age will be 13\frac{1}{3} 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 (TT) and Jordan’s age (JJ) today:

T=14JT=\frac{1}{4}J

Two years from now, Tien’s age will be T+2T+2, and Jordan’s age will be J+2J+2.

Set up an equation about the relationship between Tien’s age and Jordan’s age in two years:

T+2=13(J+2)T+2=\frac{1}{3}(J+2)

Solve the above equation for TT:

T=13(J+2)−2T=\frac{1}{3}(J+2)-2

Now set the two equations equal to each other and solve for JJ:

14J=13(J+2)−2\frac{1}{4}J=\frac{1}{3}(J+2)-2

14J=13J−43\frac{1}{4}J=\frac{1}{3}J-\frac{4}{3}

−112J=−43-\frac{1}{12}J=-\frac{4}{3}

J=−43(−121)J=-\frac{4}{3}\left(-\frac{12}{1}\right)

J=16J=16

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
  • 8.EE.8c systems in real-world problems
  • 8.EE.7b linear equations with rational coefficients
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.
What makes it hard
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.

  1. 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)

  2. 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

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Distributive property
a×(b+c)=a×b+a×ca \times (b + c) = a \times b + a \times c
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.

  1. Sort out what you know

    Today, Tien’s age is 14\frac{1}{4} 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 13\frac{1}{3} of Jordan’s. So Jordan will be 3 times as old as Tien. You need Jordan’s age today.

  2. 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:

    PersonTodayIn 2 years
    Tienttt+2t + 2
    Jordan4t4t4t+24t + 2

    Watch out: Jordan gets 2 years older too. Do not forget to add 2 to his age.

  3. Write an equation for later

    In 2 years, Jordan’s age will be 3 times Tien’s age. Write that as an equation:

    4t+2=3×(t+2)4t + 2 = 3 \times (t + 2)

    Use the distributive property on the right side. Multiply both t and 2 by 3:

    4t+2=3t+64t + 2 = 3t + 6

  4. Solve for Tien’s age

    Take 3t away from both sides. Doing the same thing to both sides keeps them equal:

    t+2=6t + 2 = 6

    Now take 2 away from both sides:

    t=4t = 4

    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.

  5. Find Jordan’s age

    Jordan is 4 times as old as Tien:

    4×4=164 \times 4 = 16

    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 87 as printed on page 87 of the DOE handbook.
As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 87, question 87. Open page 87 of the handbook (PDF)

Question 5 of 6

2018 Test A Math, question 21

Question

In a sample of 10 cards, 4 are red and 6 are blue. If 2 cards are selected at random from the sample, one at a time without replacement, what is the probability that both cards are not blue?

  • A215\frac{2}{15}
  • B425\frac{4}{25}
  • C310\frac{3}{10}
  • D13\frac{1}{3}
Show the answer

Correct answer: A

The probability that both cards are not blue is the same as the probability that both cards are red. There are 4 red cards out of the 10, so the probability of the first card being red is

410\frac{4}{10}

Now there are 9 cards left, and 3 of those are red, so the probability of the second card being red is

39\frac{3}{9}

Multiply the two probabilities to find the probability that both cards are red (not blue):

(410)(39)=1290=215\left (\frac{4}{10} \right )\left ( \frac{3}{9} \right )=\frac{12}{90}=\frac{2}{15}

Question analysis

This probability question draws 2 cards, one at a time and without replacement, from 10 cards: 4 red and 6 blue. Students find the chance that neither card drawn is blue. The second draw has one fewer card, and the word not changes which color to count.

NYS standards
  • 7.SP.8a compound event as fraction of outcomes
  • 7.SP.8b sample spaces for compound events
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 compound probability is usually found with a list or tree of equally likely outcomes. Dependent draws without replacement, plus a negative phrasing to translate, go beyond that typical work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
3 steps
Reading level
Question and choices: about grade 5, 39 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 ideas stack here: restating not blue as red, and changing the second draw's numbers after a card is removed. Students who know to multiply but forget the removal reach a listed choice, and so do students who compute both blue. Writing the second fraction explicitly as 3 red out of 9 cards, before multiplying, is what separates right from nearly right.

  1. Something you must already know moderate Working it out

    Multiplying the first draw's chance by the second draw's, with the second adjusted for the card already taken, is a rule the test assumes and does not give. (Anderson & Krathwohl, 2001)

  2. A very close wrong answer moderate Choosing the answer

    2/15 and 4/25 are about 0.13 and 0.16, too close to tell apart by estimate; only the second draw's fraction, 3 red of 9 cards rather than 4 of 10, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  3. Turning words into math minor Understanding the question

    "Both cards are not blue" has to be restated as both cards red, and the bold not also invites computing the chance that both are blue. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

  4. An answer in an unexpected form minor Choosing the answer

    The product comes out as 12/90, and it has to be reduced to lowest terms before it matches any of the listed fractions. (Enright, Morley & Sheehan, 2002)

Strategy: Restate not blue as red, then multiply the chance of red on the first draw by the chance of red on the second, with one card fewer.

Traps

  • Without replacement: In a second pick there is one fewer item, which changes the probability.
  • Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Probability
P=favorabletotalP = \frac{\text{favorable}}{\text{total}}
P is the probability, the chance that something happens. Favorable is the number of ways to get what you want, here a red card. Total is the number of all possible picks, here all the cards you can pick from. It works when every pick is equally likely.
Two events in a row
P(A and B)=P(A)×P(B after A)P(\text{A and B}) = P(\text{A}) \times P(\text{B after A})
A is the first event and B is the second. P( ) means the probability of what is inside. The chance that both happen is the first chance times the second. For the second chance, count only what is left after the first event.

  1. Sort out the question

    There are 10 cards: 4 red and 6 blue. You pick 2 cards “one at a time without replacement”. That means the first card is not put back. “Both cards are not blue” means both are red, since red is the only other color. You need the probability, or chance, of that.

  2. Find the chance the first card is red

    4 of the 10 cards are red. Each card is equally likely to be picked. Use the probability formula.

    P(red first)=410P(\text{red first}) = \frac{4}{10}

  3. Find the chance the second card is red

    One red card is gone now, and it is not put back. So 9 cards are left, and 3 of them are red.

    P(red second)=39P(\text{red second}) = \frac{3}{9}

    Watch out: using 4/10 again acts as if the card went back. That gives 4/25, choice B.

  4. Multiply the two chances

    Both cards must be red. So multiply the first chance by the second. To multiply fractions, multiply the tops, then multiply the bottoms.

    410×39=4×310×9=1290\frac{4}{10} \times \frac{3}{9} = \frac{4 \times 3}{10 \times 9} = \frac{12}{90}

  5. Simplify the fraction

    None of the choices is 12/90, so simplify it. Divide the top and the bottom by 6, the biggest number that goes into both.

    12÷690÷6=215\frac{12 \div 6}{90 \div 6} = \frac{2}{15}

    Watch out: the chance that both are blue is 610×59=13\frac{6}{10} \times \frac{5}{9} = \frac{1}{3}, choice D. The question says not blue. So the answer is A, 215\frac{2}{15}.

Check your answer

Count the ways. There are 10×9=9010 \times 9 = 90 ways to pick two cards in order. Red then red has 4×3=124 \times 3 = 12 ways. That gives 12/90, or 2/15. The answer is small, which makes sense, because there are fewer red cards than blue ones.

More questions like this

The original DOE question
Question 78 as printed on page 85 of the DOE handbook.
As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 85, question 78. Open page 85 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).

Question 6 of 6

2024 Test B Math, question 57

Question

If x and y are both negative integers with x<yx<y, which expression has the least value?

  • Ax2yx^{2}y
  • Bxy2xy^{2}
  • C−x2y-x^{2}y
  • D−xy2-xy^{2}
Show the answer

Correct answer: A

Since x and y are both negative integers, both x2x^{2} and y2y^{2} are positive.

Therefore, both x2yx^{2}y and xy2xy^{2} are negative, and both −x2y-x^{2}y and −xy2-xy^{2} are positive.

Because x<yx<y and both x and y are negative, |y|<|x||y|<|x| and y2<x2y^{2}<x^{2}. So |y2|<|x2||y^{2}|<|x^{2}|.

Since |y|<|x||y|<|x| and x and y are integers, |xy2|<|x2y||xy^{2}|<|x^{2}y|.

So x2y<xy2x^{2}y<xy^{2}.

−xy2=|xy2| and −x2y=|x2y|-xy^{2}=|xy^{2}|\text{ and }-x^{2}y=|x^{2}y|

Therefore, x2y<xy2<−xy2<−x2yx^{2}y<xy^{2}<-xy^{2}<-x^{2}y.

Question analysis

Two negative integers x and y, with x less than y, appear in four expressions built from squares and minus signs. Students find the expression with the least value. It tests multiplying negative numbers and comparing their sizes, and the difficulty is tracking how each minus sign and each square changes both the sign and the size of the result.

NYS standards
  • 7.NS.2a rational number multiplication
  • 6.NS.7d absolute value versus order
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 students multiply negative numbers, but this asks them to compare four variable expressions for any pair of negative integers. Deciding how the squares compare when x is less than y goes beyond typical grade 7 sign practice.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Solution
3 steps
Reading level
Question and choices: about grade 8, 20 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 facts settle the question: squares of negatives are positive, and the more negative number has the larger square. Students who track the minus signs carelessly think a leading minus makes an expression negative, and students who assume the larger y has the larger square choose the wrong negative expression. Substituting x = −3 and y = −2 gives −18, −12, 18 and 12, which orders all four at once.

  1. Variables instead of numbers moderate Understanding the question

    No values are given, only that x and y are negative integers with x < y, so students must reason about signs or invent a pair such as −3 and −2. (Koedinger & Nathan, 2004; Enright, Morley & Sheehan, 2002)

  2. A very close wrong answer moderate Choosing the answer

    x²y and xy² use the same letters with the exponent moved; both are negative, and only comparing x² with y² separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  3. Every choice must be checked minor Choosing the answer

    All four expressions have to be placed in order, because the minus signs in front of the last two turn those expressions positive. (Embretson & Wetzel, 1987)

Strategy: Pick two negative integers with x less than y, such as −3 and −2, evaluate all four expressions, and confirm the order with a second pair.

Traps

  • Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
  • Misunderstands the concept: A wrong belief about a concept: that percents can be added, that area grows like length, that averages can be averaged, that a bigger denominator means a bigger fraction.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Signs in multiplication
(−a)×(−b)=a×b(-a) \times (-b) = a \times b
a and b are positive numbers, so −a and −b are negative. A negative times a negative is positive. A negative times a positive is negative. So a product is positive when it has an even number of negative factors.
Squaring a number
x2=x×xx^2 = x \times x
x is any number. x² (x squared) means x times itself. The square of a number other than 0 is always positive, because two negatives or two positives multiply to a positive.

  1. Sort out the question

    x and y are negative integers, such as −3 and −2. Since x < y, x is to the left of y on the number line. So x is more negative, farther from 0.

    You need the expression with the least value. That is the most negative one.

  2. Find the sign of each expression

    Squares are positive, so x2x^2 and y2y^2 are positive.

    • x2yx^2 y is a positive times a negative, so it is negative.
    • xy2x y^2 is a negative times a positive, so it is negative.
    • −x2y-x^2 y and −xy2-x y^2 are the opposites of these, so they are positive.

    So the least value must be A or B. Watch out: The minus sign in front of C and D does not make them negative. It turns a negative into a positive.

  3. Compare A and B with numbers

    Try x = −3 and y = −2, since −3 < −2.

    x2y=(−3)2×(−2)=9×(−2)=−18x^2 y = (-3)^2 \times (-2) = 9 \times (-2) = -18

    xy2=(−3)×(−2)2=(−3)×4=−12x y^2 = (-3) \times (-2)^2 = (-3) \times 4 = -12

    Since −18 < −12, A is smaller.

  4. See why it always works

    Both expressions contain x × y, which is positive. x2y=(xy)×xx^2 y = (xy) \times x and xy2=(xy)×yx y^2 = (xy) \times y. Multiplying the same positive number by the more negative x gives the more negative result.

    Watch out: y is bigger than x, but y2y^2 is smaller than x2x^2: 4 is less than 9. Thinking y² is bigger leads to choice B.

    So the answer is A, x2yx^2 y.

Check your answer

Try another pair, x = −5 and y = −1. Then A is 25×(−1)=−2525 \times (-1) = -25, B is (−5)×1=−5(-5) \times 1 = -5, C is 25 and D is 5. A is still the least.

More questions like this

The original DOE question
Question 114 as printed on page 215 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 215, question 114. Open page 215 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).

Sample #19035