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.

Question 1 of 6

2026 Practice Test B English, question 42

Passage Letter from Brooklyn

Letter from Brooklyn

by Jacob Scheier

I can already see how this will end.
How I will grow tired of the bridge’s
steep incline, and the absent-minded tourists
wandering into the bicycle path.
The weather will turn cold.
But that all happens later.
For now it is the early edge of fall,
leaves green still while the air narrows,
is slightly crisp, almost grazing
the hair of my arm like a passing stranger,
as though the air has been forced into intimacy
by the brevity of daylight.
But when it starts darkening at 4,
this closeness, I know, will be a felt distance,
like someone drawing your attention
to their lack of intimacy.
These days I am still walking at a cathedral pace
beneath the branches bending across avenues,
brownstones like rows of lived-in chapels,
like a pop-up picture book I could have had as a child,
but didn’t. How Brooklyn makes me nostalgic
for the moment I am walking inside of.
These late afternoons filled
with a loneliness that makes me feel
distinctly myself, and an awareness
of how rare that is.

brevity: briefness
cathedral: meditative
chapels: private places of prayer or worship
nostalgic: yearning for the past

Question

The speaker’s thoughts throughout the poem develop a theme by showing that

Aalthough people may hold expectations for the future, some people long for present experiences while they are still happening.
Bthough people come from different places, most people feel drawn to the special charm a city holds.
Calthough people can make decisions about their life, there will always be some things beyond their control.
Dthough general expectations exist, people have no way of knowing what a given day will actually bring.

Show the answer

Correct answer: A

The question asks how the speaker’s thoughts throughout the poem develop a theme.

A. CORRECT. The speaker’s thoughts develop some tension because seasonal change will inevitably come: “The weather will turn cold” (line 5). However, the speaker is still able to enjoy the present experience because “that all happens later” (line 6). In lines 21–22, the speaker begins to describe experiences that create a longing for the present, even while it is still happening (“How Brooklyn makes me nostalgic / for the moment I am walking inside of”), developing a theme of the poem.

B. Incorrect. The speaker’s thoughts reveal an appreciation for the city, but this appreciation is highly personal and individual. These thoughts do not indicate that most people will feel drawn to cities.

C. Incorrect. Some things, such as seasons, are beyond human control, as the speaker concedes: “I can already see how this will end” (line 1). However, the theme of the poem is not that certain things are inevitable, but that one can live in the present moment and enjoy that experience before change occurs.

D. Incorrect. The speaker’s thoughts are not showing that people are surprised by what the days bring; the thoughts of the speaker suggest that people experience many seasons in Brooklyn and have reasonable expectations about what these days will bring.

Question analysis

This theme question asks what theme the speaker's thoughts develop across all of “Letter from Brooklyn,” from the opening line about how things will end to the closing lines about loneliness on late afternoons. Each choice is a broad statement about people in two parts, so students must check both halves against the speaker's reflections.

NYS standards: 7R2 theme or central idea
Grade level: Grade 8 reading and task
Compared with grade 7: Above grade 7 Stating a theme is a grade 7 standard, often tested with one clearly fitting choice. Here every choice is a two-part general statement about people, and students must test both halves of each against a whole poem of abstract reflection, more than typical.
Estimated difficulty: Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Thinking it demands: Depth of knowledge 3, strategic thinking · mainly analyze
What makes it hard: Reading between the lines moderate
Every choice must be checked moderate
Evidence in several places minor
Evidence: Answered from the whole text
Reading level: Passage: 217 words (a poem; reading level not measured); question and choices: about grade 9, 82 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 four themes are broad statements about people, each in two halves, and every one can borrow something from the poem: the seasons are beyond control, the city has charm, the future brings surprises. The right one matches the speaker’s double vision, knowing what is coming and longing for the present while it lasts. The strongest pull is the theme about things beyond control, whose second half fits the turning seasons and whose first half the poem never raises.

Reading between the lines moderate Working it out
The poem never states its theme; it must be built from the speaker’s forecasts in lines 1–6 and the paradox of being “nostalgic / for the moment I am walking inside of.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Every choice must be checked moderate Choosing the answer
Every choice is a two-part “although” or “though” statement about people, and three have one plausible half, so each half must be checked against the poem on its own. (Embretson & Wetzel, 1987)
Evidence in several places minor Working it out
The theme draws on the whole poem, from the opening “I can already see how this will end” to the lonely late afternoons of lines 23–26. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: Sum up in a sentence what the speaker keeps thinking about from the first line to the last, then test both halves of each choice against the poem and reject any half it does not support.

Traps

Half right: One half of a two-part choice is right and the other is not.
Too broad or too strong: A choice overstates, generalizes, or uses absolute words the text does not support.
Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.

The wrong answers, classified

B Too broad or too strong (King et al., 2004)
Reveals partial knowledge Expected pull: moderate
Turns one speaker’s love of Brooklyn into a claim that “most people” feel drawn to a city’s charm, though no other person’s view appears in the poem.
C Half right (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Reveals partial knowledge Expected pull: strong
Accepts the half about things beyond control, since the weather will turn cold regardless, but the poem says nothing about people making decisions about their lives.
D Twists what the text says (King et al., 2004)
Reveals partial knowledge Expected pull: weak
Turns the coming season into an unknown, though the speaker opens with “I can already see how this will end” and knows exactly what the weather will bring.

How the questions are analyzed, and the research behind it

Working it out, step by step

Figure out what the question asks
This question asks for the theme of the whole poem. A theme is a big message about life. Each choice has two halves, joined by although or though. Both halves must fit the poem. If one half doesn’t, the choice is wrong.
Trace the speaker’s thoughts
The poem opens by looking ahead: “I can already see how this will end.” The speaker expects to tire of the bridge, and “The weather will turn cold.” Then the speaker turns to now: “But that all happens later.” Most of the poem enjoys the fall walk. Lines 21–22 sum it up: “How Brooklyn makes me nostalgic / for the moment I am walking inside of.”
Put it in your own words
Nostalgic means longing for the past. Yet the speaker longs for the present, while it is still going on. So the speaker does two things at once. The speaker expects what the future will bring. And the speaker treasures, or deeply values, the present. That is the theme.
Check each choice
- A is right. First half: the speaker expects cold weather and boredom. Second half: the speaker longs for the walk while it is still going on.
- B is wrong. Only one person speaks in the poem. Nothing says most people feel drawn to cities.
- C is wrong. The weather is beyond anyone’s control, so its second half fits. But the poem never talks about people making decisions about their lives.
- D is wrong. The speaker knows what is coming. The future isn’t a mystery here.
Watch out: C is tempting because the speaker can’t stop the cold. But test both halves. Its first half, about making decisions, isn’t in the poem.
Choose the answer
So the answer is A: “although people may hold expectations for the future, some people long for present experiences while they are still happening.”

Why this answer and not the closest wrong one

C is the closest wrong answer, because the seasons are beyond the speaker’s control. But the poem never mentions people making decisions about their lives. A matches both halves: the speaker expects what is coming, and longs for the present while it lasts.

More questions like this

The original DOE question

Question 42 as shown on the DOE’s digital test, page 57 of its printable version. — As printed in the DOE’s printable version of 2026 Practice Test B English, page 57, question 42.

The passage “Letter from Brooklyn” as printed (page 50)

The passage “Letter from Brooklyn” as printed on page 50 of the DOE handbook.

Question 2 of 6

2024 Test B English, question 48

Passage Snowy Mountains

Snowy Mountains

by John Gould Fletcher

Higher and still more high,
Palaces made for cloud,
Above the dingy city-roofs
Blue-white like angels with broad wings,
Pillars of the sky at rest
The mountains from the great plateau
Uprise.

But the world heeds them not;
They have been here now for too long a time.
The world makes war on them,
Tunnels their granite cliffs,
Splits down their shining sides,
Plasters their cliffs with soap-advertisements,
Destroys the lonely fragments of their peace.

Vaster and still more vast,
Peak after peak, pile after pile,
Wilderness still untamed,
To which the future is as was the past,
Barrier spread by Gods,
Sunning their shining foreheads,
Barrier broken down by those who do not need
The joy of time-resisting storm-worn stone,
The mountains swing along
The south horizon of the sky;
Welcoming with wide floors of blue-green ice
The mists that dance and drive before the sun.

“Snowy Mountains” by John Gould Fletcher—Public Domain

Question

How do the details in the third stanza (lines 15–26) most contribute to the development of a theme of the poem?

Aby reflecting nature’s capacity to resist change
Bby showing that nature is capable of influencing human will
Cby exposing how a lack of awareness leads to nature’s ruin
Dby explaining why people must respect nature

Show the answer

Correct answer: A

The question asks how the details in the third stanza most contribute to the development of a theme of the poem.

A. CORRECT. In the third stanza, phrases such as “Wilderness still untamed” (line 17), “time-resisting storm-worn stone” (line 22), and “The mountains swing along” (line 23) convey the message that in spite of the destruction described in the second stanza, the mountains manage to maintain their wild magnificence.

B. Incorrect. While the phrase “Barrier broken down” (line 21) conveys the idea that people can have some effect on the natural landscape, it does not convey how nature affects people.

C. Incorrect. The phrase “those who do not need” (line 21) implies a choice to damage nature and not a lack of awareness or understanding.

D. Incorrect. The third stanza is not a call to humanity to respect the mountains but a description of the untamed, welcoming mountains and the joy they provide for those who appreciate them.

Question analysis

Students trace how the details of the third and final stanza of “Snowy Mountains,” lines 15–26, most contribute to developing a theme of the poem. Because the stanza is a single sentence that runs from line 15 to the poem’s last word, students must keep its whole movement in mind before deciding what it adds.

NYS standards: 7R2 theme or central idea
7R1 textual evidence and inferences
Grade level: Grade 8 reading and task
Compared with grade 7: Above grade 7 Grade 7 theme questions usually rest on a few clear details. Here students must hold a twelve-line stanza of inverted, piled-up phrases in mind and pick among four reasonable lessons about nature, a heavier load closer to grade 8.
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: Complex sentences moderate
Figurative or literary language moderate
Evidence in several places moderate
Evidence: Answered from one paragraph or stanza
Reading level: Passage: 161 words (a poem; reading level not measured); question and choices: about grade 7, 55 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 final stanza holds both endurance and damage, and the stem’s “most” asks which of the two its details build. Students who fix on the broken barrier choose ruin, a reading the second stanza seems to confirm, while those who tally the stanza’s details find untamed wilderness, time-resisting stone and mountains swinging at ease. Because the stanza is one long, inverted sentence, that tally is slow, which is what makes the question hard.

Complex sentences moderate Understanding the question
Lines 15–26 are one sentence in which phrase after phrase, from “Vaster and still more vast” to “storm-worn stone,” comes before its subject, “The mountains,” in line 23. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Figurative or literary language moderate Understanding the question
The message of endurance is carried by personification: the peaks have “shining foreheads,” are “spread by Gods,” and “swing along” the horizon welcoming the mists. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Evidence in several places moderate Working it out
The theme has to be assembled from details scattered over twelve lines, “Wilderness still untamed,” “the future is as was the past,” “time-resisting,” and weighed against the single line of damage. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: Read lines 15–26 as one long sentence, find its main subject and verb, and sum up its message in a phrase; then check each choice against the whole stanza, not a single line.

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.
Outside knowledge: A choice is plausible in the real world but not supported by this text.
Reversed relationship: Cause and effect, or the order of events, turned around.

The wrong answers, classified

B Reversed relationship (King et al., 2004)
Reveals partial knowledge Expected pull: weak
Turns the influence around: in this stanza people break down the barrier while the peaks endure, and nothing shows the mountains shaping what people want.
C Too narrow (King et al., 2004)
Reveals partial knowledge Expected pull: strong
Builds on line 21’s “Barrier broken down,” the stanza’s one line of damage, and lets it stand for twelve lines that mostly celebrate the mountains as wild and lasting.
D Outside knowledge (King et al., 2004; Recht & Leslie, 1988)
Reveals a misconception Expected pull: moderate
States the lesson a nature poem is expected to teach, that people must respect nature, but the stanza describes the mountains and never tells readers what to do.

How the questions are analyzed, and the research behind it

Working it out, step by step

Figure out what the question asks
This asks about theme, the big message of the poem. You need to see what the details of the third stanza, lines 15 to 26, add to that message. The word “most” matters. Pick the idea that most of the details support, not just one line.
Gather the details in lines 15 to 26
The peaks grow “Vaster and still more vast” (line 15). They are a “Wilderness still untamed” (line 17). For them, the future is “as was the past” (line 18). Their stone is “time-resisting” (line 22). In the last four lines, “The mountains swing along” the sky and welcome the mists. Only line 21 shows damage: the barrier is “broken down.”
Find what the details share
Untamed means still wild, not controlled by people. If the future is the same as the past, the mountains are not changing. Time-resisting means they hold out against the years. And at the end of the stanza, they are still moving along at ease. Nearly every detail shows the same thing. The mountains last and stay wild, which is nature’s power to resist change.
Check each choice
- A fits. Wild, unchanging, time-resisting mountains show nature holding out against change.
- B does not fit. It turns things around. In this stanza, people affect the mountains. Nothing shows the mountains changing what people want.
- C does not fit. Line 21 shows damage, but it is one line out of twelve. The stanza does not end in ruin either: the mountains still swing along and welcome the mists.
- D does not fit. These lines paint a picture of the peaks. They give readers no orders and no reasons to behave a certain way.
Choose the answer
Most of the third stanza shows mountains that stay wild and lasting. So the answer is A.

Why this answer and not the closest wrong one

C is the closest trap, because line 21 does show the barrier “broken down,” and the second stanza is full of harm. But this question is about the third stanza, and it asks what the details most add. Most of the other lines there show mountains that are vast, wild and lasting. That builds A, not ruin.

More questions like this

The original DOE question

Question 48 as printed on page 192 of the DOE handbook. — As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 192, question 48. Open page 192 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).

The passage “Snowy Mountains” as printed (page 142)

The passage “Snowy Mountains” as printed on page 142 of the DOE handbook.

Question 3 of 6

2024 Test B English, question 20

Passage Excerpt from “How Exercise Could Help You Learn a New Language”

Excerpt from “How Exercise Could Help You Learn a New Language”

by Gretchen Reynolds

Many scientists suspect that exercise alters the biology of the brain in ways that make it more malleable and receptive to new information, a process that scientists refer to as plasticity.

But many questions have remained unanswered about movement and learning, including whether exercise is most beneficial before, during or after instruction and how much and what types of exercise might be best.

So for a new study, which was published recently in PLOS One, researchers in China and Italy decided to home in on language learning and the adult brain.

Language learning is interesting. As young children, almost all of us picked up our first language easily. We didn’t have to be formally taught; we simply absorbed words and concepts.

But by early adulthood, the brain generally begins to lose some of its innate language capability. It displays less plasticity in areas of the brain related to language. As a result, for most of us, it becomes harder to learn a second language after childhood.

To see what effects exercise might have on this process, the researchers first recruited 40 college-age Chinese men and women who were trying to learn English. The students had some facility with this second language but were far from proficient.

The researchers then divided the students into two groups. Those in one group would continue to learn English as they had before, primarily while seated in rote vocabulary-memorization sessions.

The others would supplement these sessions with exercise.

Specifically, the students would ride exercise bikes at a gentle pace (about 60 percent of their maximum aerobic capacity) beginning 20 minutes before the start of the lessons and continuing throughout the 15 minutes or so of instruction.

Both groups learned their new vocabulary by watching words projected onto large screens, together with comparable pictures, such as “apple” and a Red Delicious. They were shown 40 words per session, with the sequence repeated several times.

Afterward, the students all rested briefly and then completed a vocabulary quiz, using computer keys to note as quickly as possible whether a word was with its correct picture. They also responded to sentences using the new words, marking whether the sentences were accurate or, in the case of “The apple is a dentist,” nonsensical. Most linguists¹ feel that understanding sentences shows greater mastery of a new language than does simple vocabulary improvement.

The students completed eight vocabulary sessions over the course of two months.

And at the end of each lesson, the students who had ridden bikes performed better on the subsequent vocabulary tests than did the students who sat still.

They also became more proficient at recognizing proper sentences than the sedentary students, although that difference did not emerge until after several weeks of instruction.

Perhaps most interesting, the gains in vocabulary and comprehension lingered longest for the cyclists. When the researchers asked the students to return to the lab for a final round of testing a month after the lessons—without practicing in the meantime—the cyclists remembered words and understood them in sentences more accurately than did the students who had not moved.

“The results suggest that physical activity during learning improves that learning,” says Simone Sulpizio, a professor of psychology and linguistics at the University Vita-Salute San Raffaele in Milan, Italy, and a study co-author.

These improvements extend beyond simply aiding in memorization, she added. The exercise also deepened language learners’ grasp of how to use their newly acquired words.

This study involved college students performing relatively light exercise, though, and cannot tell us whether other people completing other types of exercise would achieve the same results.

It also offers no clues about what is occurring inside the brain that might be contributing to the benefits of the exercise. But many past studies have shown that exercise prompts the release of multiple neurochemicals in the brain that increase the number of new brain cells and the connections between neurons, Dr. Sulpizio says. These effects improve the brain’s plasticity and augment the ability to learn.

From a real-world standpoint, the study’s implications might seem at first to be impractical. Few classrooms are equipped with stationary bicycles. But specialized equipment is probably unnecessary, Dr. Sulpizio says.

“We are not suggesting that schools or teachers buy lots of bicycles,” she says. “A simpler take-home message may be that instruction should be flanked by physical activity.”

¹linguists: scientists who study language

Question

Read these sentences from paragraph 17.

These improvements extend beyond simply aiding in memorization, she added. The exercise also deepened language learners’ grasp of how to use their newly acquired words.

Which sentence from the excerpt best explains why Sulpizio feels confident in the conclusion stated in these sentences?

A“They were shown 40 words per session, with the sequence repeated several times.” (paragraph 10)
B“They also responded to sentences using the new words, marking whether the sentences were accurate or, in the case of ‘The apple is a dentist,’ nonsensical.” (paragraph 11)
C“And at the end of each lesson, the students who had ridden bikes performed better on the subsequent vocabulary tests than did the students who sat still.” (paragraph 13)
D“They also became more proficient at recognizing proper sentences than the sedentary students, although that difference did not emerge until after several weeks of instruction.” (paragraph 14)

Show the answer

Correct answer: D

The question asks which sentence from the excerpt best supports Sulpizio’s assertion in paragraph 17 that exercise went beyond helping with memorization to deepen the language learners’ ability to use new vocabulary.

A. Incorrect. This sentence merely describes what the language-learning sessions were like, without making any claims about how the exercise affected the subjects’ understanding of how to use new words.

B. Incorrect. While this sentence does address the fact that learners were required to think about how the new words should be used rather than just memorizing the words, it does not discuss results such as how the exercise affected their ability to do this.

C. Incorrect. This sentence establishes only that exercise helped with the memorization of new words, not that exercise deepened learners’ grasp of how to use the new words.

D. CORRECT. The fact that learners who exercised were better at identifying when the new words were used correctly in sentences directly supports Sulpizio’s assertion that the exercise deepened their grasp of how to use the new words.

Question analysis

This textual evidence question quotes Simone Sulpizio’s conclusion that exercise did more than help learners memorize new English words. Students choose the sentence from the article that best explains why she can be confident of it. All four choices come from the article’s account of the study, so students must match evidence to the exact claim rather than to its general topic.

NYS standards: 7R1 textual evidence and inferences
7R8 evaluating arguments and claims
Grade level: Grade 8 reading and task
Compared with grade 7: Above grade 7 Grade 7 evidence questions usually match a quotation to a stated claim. This claim has two parts, gains beyond memorizing and a better grasp of usage, and two quotations touch it closely, a sharper test than typical grade 7 work.
Estimated difficulty: Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Thinking it demands: Depth of knowledge 3, strategic thinking · mainly evaluate
What makes it hard: A very close wrong answer major
Reading between the lines moderate
Evidence in several places minor
Evidence: Answered from several paragraphs or stanzas
Reading level: Passage: about grade 11, 764 words; question and choices: about grade 11, 142 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

Sulpizio’s claim has two parts, gains beyond memorizing and a better grasp of using words, and two of the quotations each touch one part. The vocabulary result is real evidence that exercise helped, but of the very memorizing she says the gains went beyond, and the sentence-task description mentions using words but reports no result. Only a result about sentences proves the claim, so the question rewards asking of each line what it shows, not what it is about.

A very close wrong answer major Choosing the answer
The vocabulary-test result in paragraph 13 and the sentence result in paragraph 14 are worded alike, cyclists outperforming students who sat still; only the skill measured, memorizing words or using them, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Reading between the lines moderate Working it out
Students must map the claim’s two halves onto the study’s two measures: vocabulary tests show memorization, and recognizing proper sentences shows the “grasp of how to use” new words. (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)
Evidence in several places minor Working it out
The four quotations come from paragraphs 10, 11, 13 and 14, and each must be weighed against a claim made later, in paragraph 17. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: Pin down what the quoted claim says the exercise achieved, then test each sentence by asking whether it reports a result that proves that specific achievement.

Traps

Supports only part of the claim: In a question about evidence: a line that backs one half of the claim but not the other, or a related point rather than the claim itself.
True but not the answer: A choice says something accurate about the text that does not answer this question.

The wrong answers, classified

A True but not the answer (King et al., 2004; Embretson & Wetzel, 1987)
Reveals a surface strategy Expected pull: weak
Picks a sentence about how the lessons were run, 40 words repeated several times, accurate but silent on what the exercise did for the learners.
B Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Reveals partial knowledge Expected pull: moderate
Matches the claim’s focus on using words to the sentence-judging task, but this line only describes the task and reports no result showing that exercise helped.
C Supports only part of the claim (King et al., 2004; Thissen, Steinberg & Fitzpatrick, 1989)
Reveals partial knowledge Expected pull: strong
Picks a real finding in favor of the cyclists, but better vocabulary-test scores show only the memorizing that Sulpizio says the gains went beyond.

How the questions are analyzed, and the research behind it

Working it out, step by step

Figure out what the question asks
Sulpizio says the exercise did more than help students memorize words. It “deepened language learners’ grasp of how to use their newly acquired words.” A grasp is an understanding. You need the sentence that best proves this claim. Proof should be a result, not just a description.
Break the claim into two parts
- Part 1: the gains went “beyond simply aiding in memorization.” Memorization is learning words by heart.
- Part 2: the cyclists got better at using the words.
So the proof must show the bike riders did better with words in sentences. A test that only checks memory won’t prove it.
Check each choice
- A (paragraph 10) tells how many words were shown. It gives no result.
- B (paragraph 11) describes the sentence task. But it doesn’t say who did better.
- C (paragraph 13) is a result. But it is about “vocabulary tests,” which check memory. That is the part she says the gains went beyond.
- D (paragraph 14) says the cyclists “became more proficient at recognizing proper sentences than the sedentary students.” Proficient means skilled. Sedentary means sitting still. That is a result about using words.
Pick the answer
Watch out: C is very tempting. It shows that exercise helped. But it proves the wrong kind of help. Only one choice shows the cyclists did better at using words in sentences. So the answer is D.

Why this answer and not the closest wrong one

C is the closest wrong answer. Both C and D say the bike riders beat the students who sat still. The difference is the skill that was tested. C’s vocabulary tests show memory. D’s sentence test shows the learners knew how to use the words, which is exactly Sulpizio’s claim.

More questions like this

The original DOE question

Question 20 as printed on page 174 of the DOE handbook. — As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 174, question 20. Open page 174 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).

The passage “Excerpt from “How Exercise Could Help You Learn a New Language”” as printed (pages 171–172)

The passage “Excerpt from “How Exercise Could Help You Learn a New Language”” as printed on page 171 of the DOE handbook.

The passage “Excerpt from “How Exercise Could Help You Learn a New Language”” as printed on page 172 of the DOE handbook.

Question 4 of 6

2018 Test A Math, question 30

Question

Today, Tien’s age is $\frac{1}{4}$ of Jordan’s age. In 2 years, Tien’s age will be $\frac{1}{3}$ 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 ( $T$ ) and Jordan’s age ( $J$ ) today:

$T=\frac{1}{4}J$

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

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

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

Solve the above equation for $T$ :

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

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

$\frac{1}{4}J=\frac{1}{3}(J+2)-2$

$\frac{1}{4}J=\frac{1}{3}J-\frac{4}{3}$

$-\frac{1}{12}J=-\frac{4}{3}$

$J=-\frac{4}{3}\left(-\frac{12}{1}\right)$

$J=16$

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.
Thinking it demands: Depth of knowledge 2, skills and concepts · mainly apply
What makes it hard: Turning words into math major
Error-prone arithmetic moderate
Solution: 4 steps
Reading level: Question and choices: about grade 1, 31 words.
Students, last 30 days: Not enough answers yet to show (it takes 10).

Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The difficulty is in the setup: two fractional relationships at two different times, with both people aging. Once the equations are right, the algebra is short, but it ends with two ages and only one is asked for. Testing the choices against both conditions is a reliable alternative that avoids the algebra entirely.

Turning words into math major Understanding the question
The second sentence must become T + 2 = (J + 2)/3; writing J/3, or forgetting that Jordan also ages two years, breaks the equation. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Error-prone arithmetic moderate Working it out
Substituting J/4 for T leaves J/4 + 2 = (J + 2)/3, an equation with fractions on both sides that must be cleared, usually by multiplying by 12. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

Strategy: Let Jordan's age be J, write Tien's age as J/4, and set J/4 + 2 equal to one third of (J + 2); or test each choice against both conditions.

Traps

Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.

The wrong answers, classified

A Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Reveals partial knowledge Expected pull: strong
Solves the equations correctly but reports Tien's age today, 4, which is one fourth of Jordan's 16, instead of Jordan's age.
B Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Reveals a slip Expected pull: weak
Gives Tien's age two years from now, 4 + 2 = 6, answering for the wrong person and the wrong time.
C Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Reveals a surface strategy Expected pull: moderate
Picks 12 because it is a multiple of both 4 and 3, but then Tien would be 3 and later 5, not a third of 14.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Distributive property: $a \times (b + c) = a \times b + a \times c$; 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.

Sort out what you know
Today, Tien’s age is $\frac{1}{4}$ 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 $\frac{1}{3}$ of Jordan’s. So Jordan will be 3 times as old as Tien. You need Jordan’s age today.
Name the ages with a letter
Let t stand for Tien’s age today. Jordan is 4 times as old, so his age is 4t, which means 4 times t. Add 2 years to each age:
Person Today In 2 years
Tien $t$ $t + 2$
Jordan $4t$ $4t + 2$
Watch out: Jordan gets 2 years older too. Do not forget to add 2 to his age.
Write an equation for later
In 2 years, Jordan’s age will be 3 times Tien’s age. Write that as an equation:
$4t + 2 = 3 \times (t + 2)$
Use the distributive property on the right side. Multiply both t and 2 by 3:
$4t + 2 = 3t + 6$
Solve for Tien’s age
Take 3t away from both sides. Doing the same thing to both sides keeps them equal:
$t + 2 = 6$
Now take 2 away from both sides:
$t = 4$
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.
Find Jordan’s age
Jordan is 4 times as old as Tien:
$4 \times 4 = 16$
So the answer is D, 16 years old.

Person	Today	In 2 years
Tien	$t$	$t + 2$
Jordan	$4t$	$4t + 2$

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 B Math, question 46

Question

In a sample of 50 cars at a local dealership, there are 12 red cars and 10 cars with backup cameras. Of the 12 red cars, 4 have backup cameras. If a car is selected at random from the given sample, what is the probability that both of the following are true: the car is not red and does not have a backup camera?

A $\frac{3}{5}$
B $\frac{16}{25}$
C $\frac{19}{25}$
D $\frac{4}{5}$

Show the answer

Correct answer: B

Create a chart using the given information and use subtraction to figure out how many cars are not red and do not have a back-up camera:

	Red	Not Red	TOTAL
Back-up Camera	4	6 (10-4)	10
No back-up Camera		32 (38-6)
TOTAL	12	38 (50-12)	50

The probability of selecting a car that meets both conditions from the total of 50 cars at the dealership is $\frac{32}{50}=\frac{16}{25}$ .

Question analysis

In a sample of 50 cars, 12 are red, 10 have backup cameras, and 4 of the red cars have cameras. Students find the probability that a randomly chosen car is neither red nor equipped with a camera. It tests compound probability with overlapping groups, and the overlap between red cars and camera cars is what makes it tricky.

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 usually uses a ready-made table or tree. Here students must build the two-way table from words, handle an overlap, and use a "not this and not that" condition, several steps beyond typical 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: Much to keep track of major
Many steps moderate
A very close wrong answer moderate
Complex sentences minor
Solution: 4 steps
Reading level: Question and choices: about grade 6, 63 words.
Corrected from the DOE handbook: A grammar slip in the explanation was corrected.
Students, last 30 days: Not enough answers yet to show (it takes 10).

Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

This is an overlap problem dressed as probability: the hard part is counting the cars that avoid both features, not the division by 50. A two-way table makes it routine, but students working in their heads often keep only one of the two conditions. The question rewards placing the 4 red cars with cameras in the table before doing any subtraction.

Much to keep track of major Working it out
Three overlapping counts, 12 red, 10 with cameras and 4 that are both, must be sorted into four groups before the wanted one, neither red nor with a camera, can be found. (Sweller, 1988; Carpenter, Just & Shell, 1990)
Many steps moderate Working it out
Find the non-red cars with cameras, 10 − 4 = 6, and the non-red cars, 50 − 12 = 38, subtract to get 32, then simplify 32/50. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
A very close wrong answer moderate Choosing the answer
19/25, or 38/50, has the same denominator as the right 16/25 and sits just above it; only removing the 6 non-red cars that have cameras from the 38 separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Complex sentences minor Understanding the question
The last sentence stacks "both of the following are true", a colon and two negatives, "not red" and "does not have"; untangling it is reading work, not extra math. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)

Strategy: Draw a two-way table with red and not red across, camera and no camera down, fill in the given counts, and complete the missing cells by subtraction.

Traps

Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
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)
Reveals partial knowledge Expected pull: weak
Finds the 6 non-red cars with cameras and divides by the 10 camera cars, 6/10 = 3/5, a different probability from the one asked.
C Misreads the question (Hegarty, Mayer & Monk, 1995)
Reveals partial knowledge Expected pull: strong
Uses only the 38 cars that are not red, 38/50, and ignores the second condition that the car also lacks a backup camera.
D Misreads the question (Hegarty, Mayer & Monk, 1995)
Reveals partial knowledge Expected pull: moderate
Counts only the 40 cars without backup cameras, 40/50, dropping the requirement that the car must not be red as well.

What was corrected from the DOE handbook, and why

Explanation: The handbook says “a car that meet both conditions”; the site says “a car that meets both conditions.”

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Probability: $P = \frac{\text{number you want}}{\text{total number}}$; P is the probability, the chance that something happens. The top counts the results you want. The bottom counts every possible result. Use it when each result is equally likely, like picking one at random.

Sort out what you know
There are 50 cars. Of these, 12 are red and 10 have backup cameras. Of the red cars, 4 have cameras. You pick one car at random. You need the chance that “both of the following are true”: the car is not red, and it has no camera.
Set up a two-way table
A two-way table sorts each car by two things at once: its color and its camera. Put in the numbers you know.
Red Not red Total
Camera 4 ? 10
No camera ?
Total 12 ? 50
Fill in the missing numbers
Not red with a camera: $10 - 4 = 6$ cars.
All cars that are not red: $50 - 12 = 38$ cars.
Not red with no camera: $38 - 6 = 32$ cars.
Watch out: the 38 cars that are not red include 6 with cameras. Using 38 gives $\frac{38}{50} = \frac{19}{25}$ , choice C. Using all 40 cars with no camera gives $\frac{40}{50} = \frac{4}{5}$ , choice D.
Write the probability
Use the probability formula. There are 32 cars you want out of 50 cars in all.
$P = \frac{32}{50}$
Divide the top and bottom by 2.
$\frac{32}{50} = \frac{16}{25}$
So the answer is B, $\frac{16}{25}$ .

	Red	Not red	Total
Camera	4	?	10
No camera		?
Total	12	?	50

Check your answer

Finish the table. Red cars with no camera: $12 - 4 = 8$ . Now add the four inside boxes: $4 + 6 + 8 + 32 = 50$ . That is every car, so the numbers fit. Also, the cars with no camera are $8 + 32 = 40$ , and $50 - 10 = 40$ too.

More questions like this

The original DOE question

Question 103 as printed on page 162 of the DOE handbook. — As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 162, question 103. Open page 162 of the handbook (PDF) This is the DOE’s version, before the corrections listed in the analysis.

Question 6 of 6

2024 Test A Math, question 6

Question

Mr. Jones has 550 goats, which is 10% more than Mr. King has. How many more goats does Mr. Jones have than Mr. King?

A50
B55
C495
D500

Show the answer

Correct answer: A

First, set up a proportion to determine x, the number of goats Mr. King has.

$\frac{\text{King}}{\text{Jones}} = \frac{x}{550}$

$\frac{x}{550} = \frac{100\%}{100\% + 10\%}$

Then solve the proportion for x.

$\frac{x}{550} = \frac{100\%}{100\% + 10\%}$

$550(100\%) = x(100\% + 10\%)$

$550(100\%) = x(110\%)$

$550(1) = x(1.10)$

$550 = 1.10x$

$550 \div 1.10 = (1.10 \div 1.10)x$

$500 = x$

Finally, determine the difference between the number of goats Mr. Jones has, 550, and the number of goats Mr. King has, 500.

$550 - 500 = 50$

Mr. Jones has 50 more goats than Mr. King.

Question analysis

A percent word problem: Mr. Jones has 550 goats, which is 10% more than Mr. King has, and students find how many more goats Mr. Jones has. It asks students to work with a percent increase when only the larger amount is known. The tricky part is deciding which amount the 10% is taken of.

NYS standards: 7.RP.3 multistep ratio and percent problems
6.RP.3c percent as a rate per 100
Grade level: Grade 7 content, by NYS standard
Compared with grade 7: Above grade 7 Grade 7 students usually find a percent increase from a known original amount. This runs the task backward: the increased amount is given, and the original must be recovered before the difference can be found, a step many do not expect.
Estimated difficulty: Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Thinking it demands: Depth of knowledge 2, skills and concepts · mainly apply
What makes it hard: Turning words into math major
A very close wrong answer moderate
Solution: 2 steps
Reading level: Question and choices: about grade 1, 22 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 arithmetic is one division and one subtraction, so the question is really about the base of a percent. The sentence gives the bigger number and calls it 10% more, and the reflex is to take 10% of the number on the page. That shortcut lands on a listed choice five goats from the answer. Students who find King's herd first, 550 ÷ 1.1, still have to remember that the question wants the difference, not the herd.

Turning words into math major Understanding the question
The clause "which is 10% more than" makes King's unknown herd the base of the 10%, so 550 is 110% of his number rather than the amount the 10% is taken of. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
A very close wrong answer moderate Choosing the answer
The choices 50 and 55 are only 5 goats apart, and both are 10% of a herd; only taking the percent of King's 500 rather than of 550 separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

Strategy: Mr. Jones's 550 is 110% of Mr. King's number, so divide 550 by 1.10 to find Mr. King's goats, then subtract that from 550.

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.

The wrong answers, classified

B Percent of the wrong amount (Parker & Leinhardt, 1995)
Reveals a misconception Expected pull: strong
Takes 10% of 550, measuring the increase from Jones's herd instead of from King's smaller herd, which is the amount the 10% is based on.
C Percent of the wrong amount (Parker & Leinhardt, 1995)
Reveals a misconception Expected pull: weak
Takes 10% off 550 to get King's herd, 550 − 55 = 495, using the wrong base, then gives that herd instead of the difference.
D Stops one step early (King et al., 2004; Gierl et al., 2017)
Reveals partial knowledge Expected pull: moderate
Finds King's herd correctly, 550 ÷ 1.1 = 500, then stops there instead of subtracting it from 550 to get how many more.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Percent increase: $\text{new} = \text{original} \times \left(1 + \frac{p}{100}\right)$; The original is the amount you start from, the one the percent is taken of. p is the percent of increase. The new amount is all of the original, which is 100%, plus p% more. For 10% more, you multiply by 1.10.

Sort out the question
Mr. Jones has 550 goats. That is “10% more than Mr. King has”. You need how many more goats Mr. Jones has than Mr. King. That is the difference between the two herds, not the size of a herd.
Decide what the 10% is of
The words “10% more than Mr. King” mean the 10% is a part of Mr. King’s herd. So Mr. King’s herd is the original. Mr. Jones has all of Mr. King’s goats, 100%, plus 10% more. That is 110% of Mr. King’s herd. Watch out: do not take 10% of 550. That gives 55, choice B. It uses the wrong herd. Taking those 55 away from 550 gives 495, choice C, which is also wrong.
Find Mr. King’s herd
Call Mr. King’s number of goats K. Use the percent increase formula with p = 10. The new amount is 550.
$\text{new} = \text{original} \times \left(1 + \frac{p}{100}\right)$
$550 = K \times 1.10$
$K = 550 \div 1.10 = 500$
Mr. King has 500 goats. Watch out: 500 is Mr. King’s herd, choice D. It is not the difference.
Find the difference
$550 - 500 = 50$
Mr. Jones has 50 more goats than Mr. King. So the answer is A, 50.

Check your answer

Check the 10%. 10% of 500 is $0.10 \times 500 = 50$ , and $500 + 50 = 550$ , Mr. Jones’s herd. So 550 really is 10% more than 500. If King had 495, then 10% more would be about 545, not 550.

More questions like this

The original DOE question

Question 63 as printed on page 77 of the DOE handbook. — As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 77, question 63. Open page 77 of the handbook (PDF)

Sample #211108

Six SHSAT Questions

3 English and 3 math

Question analysis

Working it out, step by step

Question analysis

Working it out, step by step

Question analysis

Working it out, step by step

Question analysis

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Question analysis

Worked solution, step by step

Question analysis

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