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 C English, question 39
Passage Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”

Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”

by Melanie Canales

The author, Melanie Canales, is a first-generation Peruvian American farmer and beekeeper based in Virginia’s Shenandoah Valley, on lands of the indigenous Monacan and Manahoac tribes. Her work focuses on creating healthy relationships between people and their surrounding ecosystems.

Unburdened by the constraints of gravity, red and green peppers jut out at 45-degree angles inside the Advanced Plant Habitat (APH), a sort of space terrarium not much larger than a microwave. Four chile pepper plants stand effortlessly upright, despite the dozens of glossy fruits weighing them down. These plants have lived entirely in space; their leaves have never been chewed on by insects or rustled by a summer breeze, [and] their stems are unfamiliar with bending toward the sun’s arc across the sky. Scissors glint under the tank’s white and blue lights as astronaut Mark Vande Hei and his team snip the stems of those that are ready for harvest. The peppers whirl around their heads until the astronauts catch them and tape them against a board to photograph.

Back on Earth, the Plant Habitat-04 team of engineers and plant scientists are observing and conferring with the astronauts. Of the 26 peppers in this batch, only the 14 finest will stay on the International Space Station [ISS] for consumption. The rest will be wrapped in foil, sealed in a Ziploc bag, then frozen at a brisk −80 degrees, until they can come roaring back to Earth in the next cargo capsule to be studied later. Now, after a 137-day growth cycle, the astronauts remove the plants from the module and trash them. Project Plant Habitat-04 is complete. It’s taco night on the ISS.

Since 2014, NASA1 has experimented with growing lettuces, brassicas,2 and zinnias3 in space, an endeavor that relies on highly specialized technology over 50 years in the making. [Fall 2021’s] two successful pepper harvests . . . will provide data on the nutritional and psychological benefits of growing vegetables on-craft, as well as a crop’s ability to reliably produce long-term in microgravity. While controlled environmental agriculture is not new, the APH experiment represents an evolution in specialized growth habitats. It doesn’t aim to re-create Earth’s conditions, but to perfect each isolated variable of plant growth in the clinical environment of a spaceship.

“The Advanced Plant Habitat is the most complex plant growth system on orbit today,” says Lashelle Spencer, a plant scientist at NASA’s Kennedy Space Center. Its more than 180 sensors control and monitor temperature, humidity, and carbon dioxide. The astronauts can adjust the color and intensity of the light, and how much moisture the plants’ roots are getting. It waters itself.

It’s the day after Thanksgiving, and Spencer has been at Kennedy since 5 a.m. to facilitate the peppers’ final harvest. As part of the project team, she played a crucial role in preparing the seeds that were sent hurtling into space in June and guiding the astronauts through maintaining the plants in orbit. . . . Though astronauts can spend upwards of 100 days in space, their on-mission meals come dehydrated and pre-packaged; their vitamins and minerals are isolated in supplements, which lose nutritional value the longer they’re stored. Spencer’s goal is to create the conditions necessary for cultivating healthy plants in space, so those plants can sustain healthy astronauts on long-term missions. Astronaut food is great, she says—“especially the shrimp cocktail. But you’re missing that crunch. You’re missing that fresh pop of flavor, the green flavor that’s not there in that packaged food.”

The sensory experience of growing productive crops can also help mitigate4 the psychological effects of long-term space travel. . . . Spencer says the team cracked open the door of the APH every day to observe their vegetable companions with all the tenderness of home gardeners. When harvest day came, they batted their bounty around the ISS, taking selfies and delighting in watching the fruits pirouetting around the spacecraft. . . .

“We were thinking no heat, so that [the peppers] wouldn’t be dangerous, but maybe the astronauts need a little spice in their life,” says Paul Bosland, who along with his colleagues at the Chile Pepper Institute genetically engineered5 the NuMex Española Improved chile pepper seeds grown in Plant Habitat-04. . . .

Working with NASA, Bosland cultivated a variety that could accommodate both the nutritional needs of astronauts as well as the logistics of growing a plant in space. . . .

. . . The experiment is helping gather the data necessary to determine the nutritional content of crops grown in space, and therefore how many people they can feed, and for how long. Though much is still unknown, Spencer is certain of one thing that future astronauts will need to do: “I think in an optimal world, a scientist like me would say that they would be growing plants from day one. From the day they left to the day they came back, they would be growing them.”

From “Growing Peppers on the ISS Is Just the Start of Space Farming” by Melanie Canales from WIRED, December 21, 2021. Copyright © 2021 Condé Nast. All rights reserved.

1NASA: National Aeronautics and Space Administration

2brassicas: a large genus of herbs, such as broccoli and cabbage

3zinnias: a genus of herbs and low shrubs that have flowers at their heads

4mitigate: to make something less severe or harmful

5genetically engineered: combined parts of DNA from different plants to produce a new plant

Question

The description in paragraph 5 of Lashelle Spencer’s goal develops a central idea of the excerpt by

  • Aillustrating that certain types of packaged foods available in space lack particular flavors.
  • Bsupporting the notion that spending more than 100 days in space is detrimental to astronauts’ health.
  • Coffering an example of how the limited selection of on-mission meals becomes less appealing over time.
  • Dmaking an important point about the astronauts’ current reliance on supplements for vitamins and minerals.
Show the answer

Correct answer: D

The question asks how the description of Lashelle Spencer’s goal in paragraph 5 develops a central idea of the excerpt.

A. Incorrect. Although Spencer mentions how astronauts miss certain eating experiences like the “fresh pop” and “green flavor” not found in packaged and dehydrated food, a central idea of the excerpt is that there is a need to provide fresh, healthy foods for long missions, not that food flavor should be improved.

B. Incorrect. While the excerpt focuses on how spending more than 100 days in space affects nutrition, it does not discuss specific ways in which spending long periods of time in space is detrimental to the health of astronauts.

C. Incorrect. Although paragraph 5 states that astronauts “can spend upwards of 100 days in space,” the excerpt does not develop a central idea that existing meals in space become less appealing over time.

D. CORRECT. The paragraph explains that astronauts currently rely on supplements for vitamins and minerals, which lose their nutritional value over time. Spencer’s goal for growing plants in space is to “sustain healthy astronauts,” supporting a central idea that astronauts need more nutritionally valuable food to sustain them while in space for long periods of time.

Question analysis

Lashelle Spencer’s goal for growing plants in space is described in paragraph 5 of the WIRED excerpt, and this central-idea question asks how that description develops a central idea of the whole excerpt. Students must connect a single sentence about a scientist’s aim to the article’s larger point, and every choice draws on details from that same paragraph.

NYS standards
  • 7R2 theme or central idea
  • 7R5 structure and genre features
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 students trace how a central idea develops, usually through a plainly stated example. Here the goal’s connection to the central idea runs through the sentences around it, and the choices are abstract restatements, which 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 10, 890 words; question and choices: about grade 12, 75 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Every choice draws on paragraph 5, and none mentions growing plants, which leaves students looking for the goal without finding it. The flavor quotation that follows the goal is the most memorable detail and the easiest wrong pick. The key works only through context: the goal answers the problem the previous sentence sets out, crews depending on supplements that weaken in storage, which is why it serves the article’s case for fresh food on long missions.

  1. Reading between the lines moderate Working it out

    Spencer’s goal names healthy plants and healthy astronauts but no supplements; its link to the key runs through the sentence before it, where vitamins sit in supplements that “lose nutritional value the longer they’re stored.” (Graesser, Singer & Trabasso, 1994; Kintsch, 1998)

  2. Every choice must be checked moderate Choosing the answer

    No choice restates the goal of growing plants itself, so none can be matched at a glance; each must be tested for whether it ties the goal to the excerpt’s concern with nutrition on long missions. (Embretson & Wetzel, 1987)

  3. How, not what minor Working it out

    The question asks how the description develops a central idea, its role in the article, so knowing what Spencer wants is only the first step toward the answer. (Anderson & Krathwohl, 2001)

  4. Evidence in several places minor Working it out

    The central idea must come from the whole excerpt: paragraph 3’s “nutritional and psychological benefits,” paragraph 8’s “nutritional needs of astronauts” and paragraph 9’s “nutritional content of crops.” (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

Strategy: State a central idea of the whole excerpt in your own words, reread Spencer’s goal with the sentences around it in paragraph 5, and pick the option that connects the goal to that central idea.

Traps

  • Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
  • Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
  • Reads too much in: A reasonable-sounding conclusion that goes further than the text allows.

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 central idea is a main point the whole article keeps coming back to. This question asks how Spencer’s goal, in paragraph 5, helps build one of those main points. So first, find the goal. Then connect it to the big idea.

  2. Find the goal and the sentence before

    Paragraph 5 says: “Spencer’s goal is to create the conditions necessary for cultivating healthy plants in space, so those plants can sustain healthy astronauts on long-term missions.” Cultivating means growing. The sentence just before it shows why she has this goal. Astronauts’ “vitamins and minerals are isolated in supplements, which lose nutritional value the longer they’re stored.”

  3. Connect the goal to the big idea

    Today astronauts get vitamins from pills, called supplements. Those pills lose their health value as they sit. Spencer wants fresh plants grown in space to keep astronauts healthy instead. So her goal points to a problem: relying on weak pills. The article returns to food and health again and again. Paragraph 8 mentions “the nutritional needs of astronauts.” Nutritional means having to do with healthy food.

  4. Check each choice

    • A is wrong. The “fresh pop of flavor” line comes after the goal. It is about taste, a side point.
    • B is wrong. The article never says long trips in space harm astronauts’ health.
    • C is wrong. It is the stored supplements that lose value over time, not meals that get less tasty.
    • D is right. The goal answers a problem: astronauts depend on supplements that weaken in storage. That ties to the article’s idea that astronauts need healthy fresh food on long trips.

    Watch out: Spencer’s flavor quote is the most memorable line nearby, so A pulls hard. But her goal is about health, not taste.

  5. Choose the answer

    Spencer wants healthy plants because pills are not enough. So the answer is D, “making an important point about the astronauts’ current reliance on supplements for vitamins and minerals.” Reliance means depending on something.

Why this answer and not the closest wrong one

A is the closest wrong answer. Spencer really does miss the crunch and flavor of fresh food. But her goal is to “sustain healthy astronauts,” which is about health. Health is the big idea the article keeps returning to. D connects the goal to that idea through the supplements that lose value.

The original DOE question
Question 39 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 C English, page 57, question 39.
The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed (pages 50–51)The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed on page 50 of the DOE handbook.The passage “Excerpt from “Growing Peppers on the ISS Is Just the Start of Space Farming”” as printed on page 51 of the DOE handbook.

Question 2 of 6

2026 Practice Test D English, question 40
Passage Martial Arts for the Mind and Body

Martial Arts for the Mind and Body

(1) The martial arts blend a series of physical movements with strategic mental discipline so that practitioners can defend themselves, physically defeat an opponent, or both. (2) Historians are unsure of exactly when and where martial arts were first used. (3) Martial arts have been practiced by several different societies for many centuries. (4) Martial arts such as karate, kung fu, tae kwon do, and judo are still taught and practiced as methods of self-defense, but they offer students more than that. (5) The study of martial arts can provide students with a way to enhance their mental discipline as well as their physical fitness.

(6) Discipline, focus, and respect are important qualities for everyone to have. (7) However, for most people these qualities are not innate; they must be learned and practiced. (8) The study of martial arts can provide an opportunity to develop these skills. (9) Students are rewarded for their dedication by passing tests and advancing to higher ranks or levels. (10) For example, in a typical tae kwon do class, students learn discipline by diligently practicing moves, improve focus by listening carefully, and demonstrate respect by bowing to the instructor and following directions.

(11) For teenagers, martial arts classes provide a safe and structured environment for gaining physical skills, building confidence, and enjoying a sense of community. (12) A lot of teens go through hard situations as they try to do well in school and in life. (13) A martial arts class can provide teens with a physical outlet for stress while also challenging them mentally. (14) Participating in a martial arts program also helps children and teens focus on self-improvement rather than on competition. (15) Progressing through levels of achievement involves mastering more physically demanding techniques. (16) It requires students to take responsibility and be accountable for achieving set goals. (17) Students gain confidence and experience companionship with other students who are progressing through the ranks.

(18) Adults who practice martial arts can experience many of the same benefits that younger people do, but perhaps the greatest of these is health and fitness. (19) Adult martial arts students often see changes in their body within weeks of beginning a program.

(20) For people interested in studying a martial art, there are many ways to learn and practice. (21) In addition to private studios, community recreation centers often offer low-cost or free martial arts classes. (22) There are even online videos that introduce students to the basic concepts. (23) People should study martial arts.

Question

Which concluding sentence should replace sentence 23 to best support the topic presented in the passage?

  • AWith so many ways to begin studying martial arts, people can easily discover how the skills needed to progress in rank may help them in life.
  • BBy taking advantage of opportunities to practice martial arts, people can experience the satisfaction of achieving goals while also improving themselves.
  • CBecause people are eager to reap the mental and physical benefits of studying martial arts, enrollment in martial arts courses has increased.
  • DWhile taking martial arts classes can improve health for both young people and adults, the effects are clearly more immediate for adults.
Show the answer

Correct answer: B

The question asks for the concluding sentence that best replaces sentence 23 and supports the topic presented in the passage.

A. Incorrect. The phrase “the skills needed to progress in rank” is vague, and progressing in rank is not related to the overall topic of the passage, which is the benefits of studying martial arts. The topic of the passage is not the “many ways to begin studying martial arts” or how “people can easily discover” the benefits of martial arts.

B. CORRECT. This option is correct because it best supports the topic of the passage—the benefits of studying martial arts—by stating two reasons why people should study martial arts: to “experience the satisfaction of achieving goals while also improving themselves.”

C. Incorrect. Some readers may choose this option because it refers to the benefits of martial arts, but the word “because” and the detail that “enrollment in martial arts courses has increased” make this sentence unrelated to the overall topic of the passage, which is about the benefits of studying martial arts, not the number of people who participate.

D. Incorrect. Although the benefits of studying martial arts are described for both teens (in the third paragraph) and adults (in the fourth paragraph), the topic of the passage is the overall benefits of studying martial arts, which include mental discipline (discussed in the first, second, and third paragraphs) in addition to health benefits. Furthermore, the passage does not compare the health effects of studying martial arts across age groups.

Question analysis

This conclusion question asks which sentence should replace sentence 23, the bare closing line “People should study martial arts,” to best support the topic of the passage. Students must keep all five paragraphs in view, from mental discipline to fitness to ways of getting started, because every choice sounds like a reasonable final line when read on its own.

NYS standards
  • 7W2e concluding informative writing
Grade level
Grade 8 reading and task
Compared with grade 7
Above grade 7 Grade 7 writers choose conclusions that follow from a passage’s topic. This passage covers mental and physical benefits for different ages, and each long choice picks up a real thread, so judging the best fit takes more than typical grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
Evidence
Answered from the whole text
Reading level
Passage: about grade 11, 402 words; question and choices: about grade 12, 106 words.
Corrected from the DOE handbook
  • The DOE printed this question’s explanation after a different question; the site matches the question with its own explanation.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Every ending borrows something real from the passage: ways to begin, ranks, mental and physical benefits, or adults’ quick results. The work is deciding what the whole passage is about, the benefits of martial arts for mind and body, and then noticing which ending adds a new claim or shrinks the topic. The rank-based ending is hardest to reject because it is shaped like the key and promises help “in life,” but its focus is how easily people discover rank skills.

  1. A very close wrong answer moderate Choosing the answer

    The rank choice is built like the key, a phrase about ways or chances to train followed by what people gain; it differs in resting on the vague “skills needed to progress in rank.” (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  2. Evidence in several places moderate Working it out

    The topic is pieced together from all five paragraphs, from the opening’s mind-and-body claim through teens, adults’ fitness and ways to learn, so a fitting ending must cover both kinds of benefit. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

  3. A lot to read minor Understanding the question

    Each choice is a two-part sentence of 21 to 26 words, and each picks up a real thread of the passage, so all four must be held against the topic. (Kintsch, 1998; Gorin & Embretson, 2006; Freedle & Kostin, 1993)

Strategy: State the passage’s topic in a few words using all five paragraphs, then test each ending: does it sum up that topic, or does it narrow it or add a new claim?

Traps

  • Off the point: Adds or keeps something that does not support the paragraph's or the passage's focus, or an introduction or conclusion that misses the main point.
  • Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: In the DOE’s explanations appendix, the explanation printed after this question belongs to question 39 (“the sentence that would best follow and support sentence 18”) and marks C correct, and this question’s explanation (“the concluding sentence that best replaces sentence 23 and supports the topic presented in the passage”) is printed after question 39, marking B correct. Read page by page, the appendix gives this question the answer C. The site gives the question the explanation that restates it, and the answer follows that explanation: B, because it sums up the passage’s topic, the benefits of studying martial arts.

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    This asks for a better last sentence. A good concluding sentence sums up the topic of the whole passage. Sentence 23, “People should study martial arts,” is short and plain. It doesn’t remind the reader why.

  2. Find the passage’s topic

    Sentence 5 states the topic. Martial arts can help students “enhance their mental discipline as well as their physical fitness.” Enhance means improve. Paragraph 2 covers discipline, focus and respect. Paragraph 3 covers teens and goals. Paragraph 4 covers adults and fitness. Paragraph 5 lists ways to start. So the topic is how martial arts help both mind and body.

  3. Name the rule

    A conclusion should sum up the main point. It should not shrink the point or add a brand-new claim. For example, after a report on why sleep matters, a good ending is Getting enough sleep helps both your body and your mind. A poor one is More people buy pillows now.

  4. Check each choice

    • A is wrong. It rests on vague “skills needed to progress in rank,” one small part of the passage.
    • B is right. “Opportunities to practice” follows paragraph 5. “Achieving goals” and “improving themselves” sum up the benefits.
    • C is wrong. Enrollment is the number of people who sign up. The passage never says it has gone up.
    • D is wrong. The passage never says adults see results sooner than young people. D also leaves out the benefits to the mind.

    Watch out: A is built like B and promises help “in life.” But it shrinks the topic to rank skills.

  5. Choose the answer

    B sums up what the whole passage says martial arts offer. So the answer is B, “By taking advantage of opportunities to practice martial arts, people can experience the satisfaction of achieving goals while also improving themselves.”

Why this answer and not the closest wrong one

A is the closest wrong answer. Like B, it starts with ways to begin and ends with what people gain. But its gain is vague “skills needed to progress in rank.” That is only one thread of the passage. B sums up the whole topic: reaching goals and improving yourself.

The original DOE question
Question 40 as shown on the DOE’s digital test, page 58 of its printable version.
As printed in the DOE’s printable version of 2026 Practice Test D English, page 58, question 40. This is the DOE’s version, before the corrections listed in the analysis.
The passage “Martial Arts for the Mind and Body” as printed (page 52)The passage “Martial Arts for the Mind and Body” as printed on page 52 of the DOE handbook.

Question 3 of 6

2024 Test B English, question 56
Passage Excerpt from “The Past and the Future of the Earth’s Oldest Trees”

Excerpt from “The Past and the Future of the Earth’s Oldest Trees”

by Alex Ross

About forty-five hundred years ago, not long after the completion of the Great Pyramid at Giza, a seed of Pinus longaeva, the Great Basin bristlecone pine, landed on a steep slope in what are now known as the White Mountains, in eastern California. The seed may have travelled there on a gust of wind, its flight aided by a winglike attachment to the nut. Or it could have been planted by a bird known as the Clark’s nutcracker, which likes to hide pine seeds in caches; nutcrackers have phenomenal spatial1 memory and can recall thousands of such caches. This seed, however, lay undisturbed. On a moist day in fall, or in the wake of melting snows in spring, a seedling appeared above ground—a stubby one-inch stem with a tuft of bright-green shoots.

Most seedlings die within a year; the mortality rate is more than ninety-nine percent. The survivors are sometimes seen growing in the shadow of a fallen tree. The landscape of the Ancient Bristlecone Pine Forest, as this area of the White Mountains is called, is littered with fragments of dead trees—trunks, limbs, roots, and smaller chunks. Pinus longaeva grows exclusively in subalpine regions of the Great Basin, which stretches from the eastern slopes of the Sierra Nevada to the Wasatch Range, in Utah. Conditions are generally too arid for the dead wood to rot; instead, it erodes, sanded down like rock. The remnants may harbor nutrients and fungi that help new trees grow. Bristlecones rise from the bones of their ancestors—a city within a cemetery.

Coast redwoods and giant sequoias, California’s gargantuan world-record-holding trees, can grow fifty feet or more in their first twenty years. Bristlecones rise agonizingly slowly. After four or five years, the seedling on the steep slope would have been just a few inches higher, sprouting needles in place of the embryonic shoots. The needles are a deep green, tough, resinous, and closely bunched in groups of five. On a mature tree, they live for fifty years or more. Decades may have passed before the tree was human height, and decades more before it resembled a conventional pine. Bristlecone saplings grow straight up, with relatively sparse foliage, looking like undernourished Christmas trees. After a few hundred years—by which time the Old Kingdom of Egypt had fallen—it was probably forty or fifty feet in height.

Many tree species live for hundreds of years. A smaller but not inconsiderable number, including the sequoias and certain yews, oaks, cypresses, and junipers, survive for thousands. Once a bristlecone has established itself in the unforgiving conditions of the White Mountains, it can last almost indefinitely. The trees tend to grow some distance from one another, so fires almost never destroy an entire stand. Because only a few other plant species can handle the dry, cold climate, the bristlecones face little competition. Unlike most plants, they tolerate dolomite soil, which is composed of a chalky type of limestone that is heavily alkaline and low in nutrients. As for insect threats, bristlecone wood is so dense that mountain-pine beetles and other pests can rarely burrow their way into it.

Empires rose and fell; wars raged; . . . and the tree from 2500 B.C. continued its implacable slow-motion existence, adding about two-hundredths of an inch to the diameter of its trunk each year. Minute changes in the tree-ring record make bristlecones an exceptionally useful source of data about changing conditions on Earth. When rains are heavier than normal, the rings widen. When volcanic eruptions cause global cooling, frost rings make the anomaly2 visible. . . .

As the millennia go by, bristlecones become contorted and wraithlike.3 The main stem, or leader, dies back. Entire branches, even the trunk itself, become fossils. At first glance, the tree may look dead. Such is the case of the forty-five-hundred-year-old tree that clings to life near the tourist path that now runs through the Ancient Bristlecone Pine Forest. Spears of dead wood jut into the air. The trunk is a marbled hulk stripped of bark, like driftwood thrown from a vanished ocean. A ribbon of live bark runs up one side, funneling water and nutrients to clumps of green needles high above. All told, the tree is an unprepossessing specimen; most people march past it without giving it a second glance. . . .

. . . No two super-elderly trees look alike, to the point where they have acquired the characteristics of individuals. Trees are prone to anthropomorphism; we project our dreams and our anxieties onto them. Bristlecones have been called elders, sentinels, sages. The possibility that climate change will cause their extinction has inspired a spate4 of alarmed news stories, although tree scientists tend to discount the idea that the bristlecones are in immediate danger. They have survived any number of catastrophes in the past; they may survive humanity.

From “The Past and the Future of the Earth’s Oldest Trees” by Alex Ross from THE NEW YORKER, January 20, 2020. Copyright © 2020 by Condé Nast. All rights reserved.

1spatial: relating to physical space

2anomaly: oddity

3wraithlike: ghostly

4spate: sudden abundance

Question

What is the best summary of the bristlecone pine’s life cycle?

  • AThe bristlecone pine takes root as a stubby seedling in the mountains. Over time, it grows slowly in a hostile environment with alkaline soil that ensures little competition from other trees.
  • BThe bristlecone pine grows up slowly from the fragments of its dead ancestors. Over time, it begins to become contorted in appearance but continues to funnel water and nutrients to its stem.
  • CThe bristlecone pine grows slowly in an environment hostile to other trees. Over time, its trunk and some branches fossilize, but it funnels water and nutrients to other parts that are still alive.
  • DThe bristlecone pine grows only in one location in the mountains. Over time, it develops sparse foliage that fossilizes slowly, but the trunk and branches stay alive, as revealed by ribbons of live bark.
Show the answer

Correct answer: C

The question asks for the best summary of the bristlecone pine’s life cycle.

A. Incorrect. Though the summary in this option covers key points in the life cycle, it focuses on minor details (“stubby seedling” and “alkaline soil”) while leaving out major details of the life cycle (for example, the fact that parts of the trees become fossilized over time).

B. Incorrect. This option addresses the unique quality of the pine growing from “fragments of its dead ancestors”; however, it does not address the fossilization phase, which is a major part of the life cycle. In addition, this option incorrectly states that the tree continues to funnel nutrients to its stem.

C. CORRECT. The option describes the key phases of the pine’s life cycle without focusing on minor details. The organization of the summary is chronological, and the information presented is accurate.

D. Incorrect. The option focuses more on the location and the appearance of the pine than on the phases of the pine’s life cycle. The option also describes the pine’s appearance inaccurately: it says that the foliage fossilizes and the trunk and branches stay alive, but paragraph 6 says that “entire branches, even the trunk itself, become fossils.” It provides little information about the main phases of the pine’s life cycle.

Question analysis

This summary question asks students to choose the best summary of the life cycle of the Great Basin bristlecone pine, as described across Alex Ross’s excerpt about the Earth’s oldest trees. Each choice is two sentences long and sounds accurate, and the differences lie in which stages of the tree’s long life each one includes and how faithfully it reports them.

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 a process is regular grade 7 work, but this life cycle unfolds across six paragraphs of dense description, and each choice is a two-sentence summary with accurate-sounding details, so spotting small omissions and errors takes more than typical care.
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: about grade 8, 851 words; question and choices: about grade 9, 141 words.
Corrected from the DOE handbook
  • An inaccurate statement 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

A good summary of this life cycle has to reach old age, when the trunk and branches turn to fossil while a strip of bark keeps the tree alive, and it has to get that stage right. One wrong choice never gets past youth, another reaches old age but keeps the wrong part alive, and a third mixes up which parts fossilize. Recalling paragraph 6 exactly, with every choice two sentences long, is what makes the question slow.

  1. Every choice must be checked major Choosing the answer

    Each two-sentence summary sounds accurate, and its flaw is an omission or a wrong detail, such as nutrients sent to a stem that dies back or foliage that fossilizes, so every clause must be checked. (Embretson & Wetzel, 1987)

  2. Evidence in several places moderate Working it out

    The life cycle runs across six paragraphs: the seedling in paragraph 1, the dead ancestors in 2, slow growth in 3, harsh conditions in 4, and fossilized wood with a live ribbon of bark in 6. (Kirsch & Mosenthal, 1990; Gorin & Embretson, 2006)

  3. A very close wrong answer moderate Choosing the answer

    The ancestors-and-stem summary has the key’s shape, slow growth, then decline, then water and nutrients still funneled; it differs in where they go, the stem, which paragraph 6 says “dies back.” (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

Strategy: Before reading the choices, list the stages of the tree’s life from seed to old age with one detail each, then check every sentence of each summary against the passage.

Traps

  • Too narrow: A single detail offered as the central idea or a summary, or a summary that keeps minor details and leaves out an essential part.
  • Twists what the text says: Uses the text's topic and ideas but changes what it says: who did it, how much, when, or why.
  • Half right: One half of a two-part choice is right and the other is not.

The wrong answers, classified

What was corrected from the DOE handbook, and why

  • Explanation: The handbook says Option D “contains an accurate description of the pine’s appearance.” It does not: Option D says the foliage fossilizes and the trunk and branches stay alive, but paragraph 6 says that “entire branches, even the trunk itself, become fossils,” as the correct answer, Option C, also says. The site now says that the option describes the pine’s appearance inaccurately.

How the questions are analyzed, and the research behind it

Working it out, step by step

  1. Figure out what the question asks

    This asks for the best summary of the bristlecone’s life cycle. A life cycle is the stages of a living thing’s life, from its start to old age. A good summary covers the main stages in order and gets each one right.

  2. List the stages from the excerpt

    1. Young: the seedling grows “agonizingly slowly” (paragraph 3).
    2. Settled: it lives where few plants “can handle the dry, cold climate” (paragraph 4).
    3. Old: “The main stem, or leader, dies back,” and “Entire branches, even the trunk itself, become fossils” (paragraph 6).
    4. Still alive: “A ribbon of live bark runs up one side, funneling water and nutrients to clumps of green needles high above” (paragraph 6).
  3. Explain the hard words

    Hostile means unfriendly or harsh. To fossilize here means to turn into hard, dead wood, almost like stone. To funnel is to carry something along a narrow path. Contorted means twisted out of shape. Nutrients are the things a plant needs to grow. Foliage means leaves, which for a pine are its needles.

  4. Check each choice

    • A does not fit. It stops while the tree is young. It never reaches old age, when parts of the tree turn to fossil.
    • B does not fit. The main stem “dies back,” so water is not sent to the stem. B also leaves out the fossil stage.
    • C fits. It gives slow growth in a harsh place, then a fossilized trunk and branches, with water still carried to the living parts.
    • D does not fit. Paragraph 2 says bristlecones grow in high areas across the Great Basin, a region that stretches into Utah. That is not one location. D also mixes up the parts: the trunk and branches turn to fossil, not the foliage.
  5. Choose the answer

    Only one summary reaches old age and gets every stage right. So the answer is C.

Why this answer and not the closest wrong one

B looks the most like the right answer. Like C, it moves from young growth to old age and has water and nutrients still flowing. But it sends them to the stem, and paragraph 6 says the stem “dies back.” C sends them to the parts still alive, which matches the ribbon of live bark.

The original DOE question
Question 56 as printed on page 196 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 196, question 56. Open page 196 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). This is the DOE’s version, before the corrections listed in the analysis.
The passage “Excerpt from “The Past and the Future of the Earth’s Oldest Trees”” as printed (pages 193–194)The passage “Excerpt from “The Past and the Future of the Earth’s Oldest Trees”” as printed on page 193 of the DOE handbook.The passage “Excerpt from “The Past and the Future of the Earth’s Oldest Trees”” as printed on page 194 of the DOE handbook.

Question 4 of 6

2024 Test B Math, question 44

Question

Which inequality is equivalent to 6x−20<5x−2(5−3x)6x-20<5x-2(5-3x)?

  • Ax<16x<16
  • Bx<52x<\frac{5}{2}
  • Cx<−2x<-2
  • Dx>−2x>-2
Show the answer

Correct answer: D

6x−20<5x−2(5−3x)6x-20<5x-2(5-3x)

Distribute the coefficient −2 on the right-hand side:

6x−20<5x+(−2)(5)+(−2)(−3x)6x-20<5x+(-2)(5)+(-2)(-3x)

6x−20<5x−10+6x6x-20<5x-10+6x

Subtract 6x6x from both sides:

−20<5x−10-20<5x-10

Add 10 to both sides:

−10<5x-10<5x

Divide both sides by 5:

−2<x-2<x

This is equivalent to

x>−2x>-2

Question analysis

Students choose the simplest equivalent form of a linear inequality that has x on both sides and a negative number multiplied into parentheses. It tests distributing, combining like terms and solving inequalities. Sign errors in the distribution, and reading the direction of the final inequality, are where most mistakes happen.

NYS standards
  • 7.EE.4b two-step inequalities
  • 8.EE.7b linear equations with rational coefficients
  • 7.EE.1 linear expressions with rational coefficients
Grade level
Grade 8 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 inequalities have the form px + q < r. This one has x on both sides and a negative factor to distribute across a subtraction, steps that belong to grade 8 equation work, so it is harder than typical grade 7 practice.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Solution
4 steps
Reading level
Question and choices: about grade 16+, 10 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Every move is standard algebra, but the inequality is built so that small slips change the answer completely. The −2 has to reach both terms in the parentheses, and once the boundary −2 is found its direction still has to be read correctly, since the variable ends up on the right as −2 < x. Rewriting that as x > −2, or substituting x = 0 into the original, catches the trap.

  1. Error-prone arithmetic moderate Working it out

    Distributing −2 over (5 − 3x) gives −10 + 6x, two sign decisions in one move, and the x terms then sit on both sides of the inequality. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

  2. A very close wrong answer moderate Choosing the answer

    x < −2 and x > −2 share the boundary and differ only in direction, which depends on reading −2 < x correctly or flipping the sign when dividing by a negative. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

  3. Many steps minor Working it out

    Four moves follow one another, distributing, collecting 5x + 6x, moving the x terms and dividing by 5, and a slip at any of them changes the result. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)

Strategy: Distribute the −2 to both terms in the parentheses, combine the x terms on the right, then gather the x terms on the side that keeps their coefficient positive.

Traps

  • Order of operations: Working left to right, or distributing a minus sign wrongly, gives a choice.
  • Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
  • A faulty procedure: A systematic but wrong procedure: adding fractions straight across, applying an exponent to each term of a sum, dropping a sign when moving a term.

The wrong answers, classified

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(b + c) = a \times b + a \times c
a is the number outside the parentheses. b and c are the terms inside. Multiply a by each one. A minus sign inside counts as a negative term, so 5 − 3x is 5 + (−3x). A negative times a negative is positive.
Keeping an inequality true
if a<b, then a+c<b+c\text{if } a < b \text{, then } a + c < b + c
a and b are the two sides, and c is any number. Adding or subtracting the same number on both sides keeps the inequality true. Dividing both sides by a positive number also keeps it true. Only multiplying or dividing by a negative number flips the sign.
  1. Sort out the question

    An inequality compares two sides with a sign like <, which means is less than. To solve it, you get x alone on one side.

    You need the short inequality that has the same answers as the long one.

  2. Distribute the −2

    Multiply −2 by both terms inside the parentheses, 5 and −3x.

    −2(5−3x)=(−2)×5+(−2)×(−3x)=−10+6x-2(5 - 3x) = (-2) \times 5 + (-2) \times (-3x) = -10 + 6x

    A negative times a negative is positive, so the second part is +6x. Watch out: If the −2 multiplies only the 5, you end up with x<52x < \frac{5}{2}, choice B.

  3. Combine the x terms

    The right side is now 5x − 10 + 6x. Put the x terms together: 5x + 6x = 11x.

    6x−20<11x−106x - 20 < 11x - 10

  4. Gather the x terms on one side

    Subtract 6x from both sides. That leaves the x terms on the right, where they stay positive.

    6x−20−6x<11x−10−6x6x - 20 - 6x < 11x - 10 - 6x

    −20<5x−10-20 < 5x - 10

  5. Get x by itself

    Add 10 to both sides. Then divide both sides by 5.

    −10<5x-10 < 5x

    −2<x-2 < x

    You divided by a positive 5, so the sign does not flip.

  6. Read it with x first

    −2<x-2 < x says −2 is less than x. That is the same as saying x is greater than −2, just as 3 < 5 means 5 > 3.

    x>−2x > -2

    Watch out: x<−2x < -2, choice C, has the same number but points the wrong way.

    So the answer is D, x>−2x > -2.

Check your answer

Test x = 0, which is greater than −2. The left side is 6(0)−20=−206(0) - 20 = -20. The right side is 5(0)−2(5−0)=−105(0) - 2(5 - 0) = -10. And −20 < −10 is true. Now test x = −3. The left side is −38 and the right side is −43. That is false, as it should be.

The original DOE question
Question 101 as printed on page 211 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 211, question 101. Open page 211 of the handbook (PDF)

Question 5 of 6

2024 Test B Math, question 14

Question

Karen reads at the rate of 60 pages per day. Martina reads 25% more pages per day than Karen. If the two students begin 1,500-page reading assignments on the same day, how many days sooner will Martina complete the assignment than Karen?

  • A4
  • B5
  • C7
  • D15
Show the answer

Correct answer: B

First, determine the rate at which Martina reads, in pages per day, using the rate at which Karen reads, 60 pages per day.

60+60∙25100=60+60\bullet\frac{25}{100}=

60+60∙0.25=60+60\bullet 0.25=

60+15=7560+15=75

Next, determine the number of days it will take each person to complete the 1,500-page reading assignment.

Karen: 1,500 pagesk days=60 pages1 day\frac{1{,}500\text{ pages}}{k\text{ days}}=\frac{60\text{ pages}}{1\text{ day}}

60k=1,50060k=1{,}500

(60÷60)k=1,500÷60(60\div 60)k=1{,}500\div 60

k=25 daysk=25\text{ days}

Martina: 1,500 pagesm days=75 pages1 day\frac{1{,}500\text{ pages}}{m\text{ days}}=\frac{75\text{ pages}}{1\text{ day}}

75m=1,50075m=1{,}500

(75÷75)m=1,500÷75(75\div 75)m=1{,}500\div 75

m=20 daysm=20\text{ days}

Finally, determine the difference between the two numbers of days.

25−20=525-20=5

So Martina will complete the assignment 5 days sooner than Karen.

Question analysis

A reading-rate word problem: Karen reads 60 pages a day, and Martina reads 25% more pages a day. Both start a 1,500-page assignment on the same day, and students find how many days sooner Martina finishes. It combines a percent increase with rates and times, and asks for a difference in days.

NYS standards
  • 7.RP.3 multistep ratio and percent problems
  • 6.RP.3b unit rate problems
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
Above grade 7 Grade 7 percent problems usually stop after one increase or decrease. This one turns the percent into a new rate, finds two finishing times and compares them, four steps that go beyond a typical grade 7 task.
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 6, 40 words.
Students, last 30 days
Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Each step is easy on its own; the difficulty is in carrying the chain to the end. Three of the choices are numbers a student meets or makes along the way: the extra pages per day, a quotient of two rates, or a rate built on 25 pages instead of 25%. Writing both finishing times down before subtracting keeps the target, a number of days, in view.

  1. Many steps moderate Working it out

    Four operations chain together: 25% of 60, Martina's 75 pages, the two finishing times 1,500 ÷ 60 and 1,500 ÷ 75, and finally their difference. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)

  2. Combines ideas moderate Working it out

    A percent increase in a daily rate has to be turned into a change in days, and 25% more pages a day does not mean 25% fewer days. (Embretson, 1998; Daniel & Embretson, 2010)

  3. Turning words into math minor Understanding the question

    “25% more pages per day than Karen” makes Martina's rate 1.25 × 60, and “how many days sooner” asks for a difference of two times, not of two rates. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

Strategy: Increase 60 by 25% to get Martina's daily pages, divide 1,500 by each girl's daily rate to get her number of days, then subtract the two numbers of days.

Traps

  • Stops one step early: A choice is a number from partway through the solution.
  • 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.
  • Numbers taken from the question: Combines the numbers in the question without a model of the situation, or is simply a number that appears in the question.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Percent increase
new=old+p100×old\text{new} = \text{old} + \frac{p}{100} \times \text{old}
Old is the starting amount, and p is the percent it grows by. First find p percent of the old amount. That is the extra. Then add the extra to the old amount to get the new amount.
Time from a rate
days=total pages÷pages per day\text{days} = \text{total pages} \div \text{pages per day}
Total pages is the whole assignment. Pages per day is how fast someone reads. Dividing tells how many days of reading fit into the whole job.
  1. Sort out what you know

    Karen reads 60 pages per day. Martina reads 25% more pages per day than Karen. Each girl must read 1,500 pages. You need how many days sooner Martina finishes. That is the difference between their numbers of days.

  2. Find Martina’s pages per day

    25% more means Karen’s 60 pages plus 25% of 60.

    new=old+p100×old\text{new} = \text{old} + \frac{p}{100} \times \text{old}

    60+25100×60=60+15=7560 + \frac{25}{100} \times 60 = 60 + 15 = 75

    Martina reads 75 pages per day. Watch out: 15 is extra pages, not days. Stopping here gives 15, choice D. Adding 25 pages instead of 25% gives 85 pages and leads to 7, choice C.

  3. Find each girl’s number of days

    Divide the whole assignment by each girl’s pages per day.

    days=total pages÷pages per day\text{days} = \text{total pages} \div \text{pages per day}

    Karen: 1,500÷60=25\text{Karen: } 1{,}500 \div 60 = 25

    Martina: 1,500÷75=20\text{Martina: } 1{,}500 \div 75 = 20

    Karen needs 25 days, and Martina needs 20 days.

  4. Subtract the days

    “How many days sooner” asks for the difference.

    25−20=525 - 20 = 5

    Martina finishes 5 days sooner. Watch out: dividing 60 by 15 mixes two rates and gives 4, choice A.

    So the answer is B, 5.

Check your answer

Multiply back. Karen: 25×60=1,50025 \times 60 = 1{,}500 pages. Martina: 20×75=1,50020 \times 75 = 1{,}500 pages. Both read all 1,500 pages, and 25 days is 5 days more than 20 days.

The original DOE question
Question 71 as printed on page 202 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 202, question 71. Open page 202 of the handbook (PDF)

Question 6 of 6

2024 Test B Math, question 17

Question

A bowl contains 12 green candies, 4 yellow candies, and some red candies. The probability of choosing a green candy at random is twice as great as the probability of choosing a red candy at random. What is the probability of choosing a yellow candy at random?

  • A211\frac{2}{11}
  • B29\frac{2}{9}
  • C14\frac{1}{4}
  • D311\frac{3}{11}
Show the answer

Correct answer: A

The probability of choosing a green candy is twice as great as the probability of choosing a red candy. There are 12 green candies. Let r = the number of red candies.

12=2r12=2r

r=6r=6

So there are 6 red candies. 12 green candies + 4 yellow candies + 6 red candies = 22 total candies.

There are 4 yellow candies out of a total of 22 candies. So the probability of choosing a yellow candy is

422=211\frac{4}{22}=\frac{2}{11}.

Question analysis

A probability question about a bowl of 12 green candies, 4 yellow candies and an unknown number of red ones. A green candy is twice as likely to be picked as a red one, and students find the chance of picking a yellow candy. The missing red count has to be worked out before any probability can be found.

NYS standards
Grade level
Grade 6 content, by NYS standard
Compared with grade 7
Above grade 7 Simple probability is grade 6 content in New York, and grade 7 problems usually give every count. Working backward from a comparison of two probabilities to a missing count, then forward to a third probability, is more than typical grade 7 work.
Estimated difficulty
Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
What makes it hard
Solution
3 steps
Reading level
Question and choices: about grade 7, 49 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 withholds the red count, and everything depends on recovering it from the comparison of probabilities. Students who cannot make that step tend to leave red out altogether, while those who find 6 red candies can still slip at the end by using the wrong total or the wrong color. Writing all three counts and the total of 22 before forming any fraction prevents both endings.

  1. Turning words into math moderate Understanding the question

    “Twice as great as the probability of choosing a red candy” must become 12 = 2 × the red count, which works only because both probabilities share one total. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

  2. Combines ideas moderate Working it out

    An unknown count has to be found from a ratio before any probability can be written, joining proportional reasoning with probability as a part over the total. (Embretson, 1998; Daniel & Embretson, 2010)

Strategy: Turn twice as likely into a statement about numbers of candies to find the red count, add all three colors for the total, then put the yellow count over that total and simplify.

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.
  • Numbers taken from the question: Combines the numbers in the question without a model of the situation, or is simply a number that appears in the question.

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Probability
P=number of the kind you wanttotal numberP = \frac{\text{number of the kind you want}}{\text{total number}}
P is the probability, the chance that something happens. The top is how many candies are the kind you want. The bottom is how many candies there are in all. Each candy is just as likely to be picked, so this fraction gives the chance.
  1. Sort out what you know

    The bowl has 12 green candies, 4 yellow candies and some red candies. You are not told how many are red. Let r be the number of red candies.

    The chance of picking green is twice the chance of picking red. You need the probability (the chance) of picking yellow.

  2. Compare green and red

    Write each chance with the probability formula.

    P=number of the kind you wanttotal numberP = \frac{\text{number of the kind you want}}{\text{total number}}

    Green and red have the same bottom number, the total number of candies. So if the chance of green is twice the chance of red, there are twice as many green candies as red ones.

    12=2×r12 = 2 \times r

  3. Find the red candies and the total

    r=12÷2=6r = 12 \div 2 = 6

    There are 6 red candies. Now add up all the candies.

    12+4+6=2212 + 4 + 6 = 22

    There are 22 candies in all. Watch out: do not leave out the red candies just because their number was not given. Using 16 as the total gives 1/4, choice C.

  4. Find the chance of yellow

    There are 4 yellow candies out of 22.

    P=422=211P = \frac{4}{22} = \frac{2}{11}

    Divide the top and the bottom by 2 to simplify. Watch out: the question asks for yellow, not red. 6/22 = 3/11 is the chance of red, choice D. The bottom must be all 22 candies. Using 18 gives 2/9, choice B.

    So the answer is A, 211\frac{2}{11}.

Check your answer

Check the clue. The chance of green is 1222\frac{12}{22}, and the chance of red is 622\frac{6}{22}. Twelve is twice 6, so green is twice as likely. Also, the three chances add up to 1: 1222+422+622=2222=1\frac{12}{22} + \frac{4}{22} + \frac{6}{22} = \frac{22}{22} = 1.

The original DOE question
Question 74 as printed on page 203 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 203, question 74. Open page 203 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 #114929