Quiz: How would you do on the 2023 Digital PSAT?

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Your PSAT score is more than a prediction of your ACT or SAT score; it can also qualify you for a National Merit Scholarship. Take this quiz to find out how you might score on the different sections of the Digital PSAT.

Question 1: Math

If 36 + 3(4x − 9) = c(2x + 1) + 25 has no solution and c is a constant, what is the value of c ?

A. -3
B. 3
C. 6
D. 12

C: If a linear equation has no solution, the variables cancel out, leaving two numbers that are not equal to each other. Start by simplifying the left side of the equation:

36 + 3(4x – 9) = c(2x + 1) + 25

36 + 12x – 27 = c(2x + 1) + 25

The variable term on the left is 12x. Because the variable terms must cancel, the right side of the equation must also have a 12x, so it must be that c = 6

Question 2: Math

You may use a calculator for this question.

An amusement park is building a scale model of an airplane for a 3D ride. The real airplane measures 220 feet, 6 inches from nose to tail.

The amusement park plans to make the ride 36 feet, 9 inches long. If the wingspan of the real plane is 176.5 feet, how long in inches should the wingspan on the ride be?

(1 foot = 12 inches)

A. 7 feet, 3 inches
B. 29 feet, 5 inches
C. 35 feet, 2 inches
D. 45 feet, 11 inches

Pay careful attention to the units. You need to convert all of the dimensions to inches, then set up and solve a proportion. There 12 inches in 1 foot, so the real plane’s length is (220 x 12) + 6 = 2,640 + 6 = 2,646 inches; the length of the wingspan on the real plane is 176.5 x 12 = 2,118 inches; the length of the amusement park ride is 36 feet, 9 inches or 441 inches; the length of the wingspan on the ride is unknown. Set up a proportion. Try writing the proportion in words first.

(real wingspan / real length) = (ride wingspan / ride length)
(2,118 / 2,646) = ( / 441)
441 x 2118 = 2646(x)
934,038 = 2,646x
353 = x

The ride’s wingspan should be 353 inches, which is equal to 29 feet, 5 inches.

Question 3: Math

If a + 2 > 5 and a − 4 < 1, then which of the following could be a value for a ?

A. 3
B. 4
C. 5
D. 6

B: There is only one variable here, so solve each inequality for a and then eliminate incorrect answer choices.
First inequality: a + 2 > 5, so a > 3.

This means you can eliminate A because 3 is not greater than itself. Second inequality: a − 4 < 1, so a < 5.

This means you can eliminate C and D because neither 5 nor 6 is less than 5. The number 4 is the only answer choice that is both greater than 3 and less than 5.

Question 4: Reading & Writing

Amazingly, there was a period from 1908 to 1940 when you could order an entire house by mail from Sears. In fact, Sears issued a completely separate catalog—Sears Modern Homes—specifically to market these homes by mail. Over the 33 years of the program, buyers had the choice of some 370 home designs and floor plans. What’s more, the homes offered were not just simple cottages: designs ranged from modest, two-room bungalows to impressive, multi-story mansions that featured 42 intricate decorative elements, servants’ quarters, and wrap-around porches.

Which choice best states the main idea of the text?

A) The Sears Modern Homes catalog offered more mail-order houses than any other catalog of the time.

B) It was once possible to purchase a variety of houses through a mail catalog.

C) Two-room bungalows were the most popular home type ordered from Sears.

D) The Sears Modern Homes catalog was a separate publication from the standard Sears Catalog.

B: On the Main Idea question above, use the main idea identified in the first sentence of the passage to make a prediction of the correct answer in your own words: houses could be ordered from Sears by mail. This prediction matches (B), which also addresses the emphasis in the rest of the passage on the variety of available houses. Choices (A) and (C) make claims that are not supported by the passage, and choice (D) mentions just one detail from the passage rather than summarizing the big picture of the passage.

Question 5: Reading & Writing

The Sears Catalog, a mail-order catalog first introduced in 1887, offered a vastly larger selection and lower prices than a local store could do. From pocket watches to patent medicines, from women’s gowns to water pumps, from hunting rifles to horse-drawn plows, ____________ offered it all.

Which choice completes the text so that it conforms to the conventions of Standard English?

A) they
B) this
C) it
D) the catalog

D: First, eliminate choice (A), “they,” as the “Sears Catalog” is singular and this choice is a plural pronoun. Next, consider the singular pronoun “this” in choice (B). In context, this pronoun is ambiguous, as the first sentence refers to both the “Sears Catalog” and “a local store”; the blank must refer to the “Sears Catalog,” but “a local store” is closer to the blank. Thus, eliminate (B), as well as the ambiguous pronoun in (C). Choice (D) clarifies that the catalog offered a big selection.

Question 6: Reading & Writing

Archeologists have typically dated the begin- ning of human occupation of the majority of the American continents to approximately 13,000 years ago. This assumption was based upon both a lack of human archeological evidence and the premise that humans could not have traversed past broad North American glaciers prior to this timeframe. However, archeologist Ciprian Ardelean has dated what may be stone flaking tools in Chiquihuite cave in current-day Mexico to at least 18,000 years ago. If the Chiquihuite cave findings are indeed human artifacts, Ardelean implies that ______

Which choice most logically completes the text?

A) the stone flaking tools are among the most technologically advanced that have been discovered in the American continents.B. Automobiles allow greater flexibility, while railroads operate on a fixed schedule.

B) most other human archeological evidence from the American continents has been misdated.

C) glaciers were an impassable obstacle for the humans that occupied the American continents over the past 20,000 years.

D) human occupation of certain parts of the American continents occurred earlier than archeologists previously thought.

Difficulty: Medium

Category: Information and Ideas

Getting to the Answer (D): The question stem asks which choice logically flows from the ideas in the passage. The sentence with the blank identifies that the correct answer will be something that is implied if the cave artifacts were made by humans, so look for details about these artifacts as you read the passage. The previous sentence states that Ardelean dated the tool artifacts to at least 18,000 years ago. Determine why this dating is significant. The contrast transition “However” indicates that this date contrasts with other dates; the previous sentences explain that human occupation in the Americas was previously thought to have started only 13,000 years ago. With such a clear contrast word, many students would choose the predict-and-match strategy for this question. You can predict that the archeologist would imply that the new artifacts date human occupa- tion earlier than was previously thought. This matches (D).

Choice (A) can be eliminated because it is out of scope; the passage does not address how advanced the stone tools were. Choices (B) and (C) can be eliminated because they distort the details in the passage. For (B), the passage states that Ardelean dated the stone tools from Mexico as relatively old, but the passage never suggests that he contests the dating of other archeological artifacts. For (C), the passage states that archeolo- gists assumed humans couldn’t go past glaciers earlier than 13,000 years ago, but it never suggests that Ardelean thinks glaciers were “impassable”; if anything, his older dating of artifacts suggests that humans got around the glaciers.

Question 7: Reading & Writing

The following text is from Washington Irving’s 1820 short story “The Legend of Sleepy Hollow.”

In the bosom of one of those spacious coves which indent the eastern shore of the Hudson, . . . there lies a small market town or rural port, which by some is called Greens- burgh, . . . Not far from this village, perhaps about two miles, there is a little valley or rather lap of land among high hills, which is one of the quietest places in the whole world. A small brook glides through it, with just murmur enough to lull one to repose; and the occasional whistle of a quail or tapping of a woodpecker is almost the only sound that ever breaks in upon the uniform tranquility. I recollect that, when a stripling, my first exploit in squirrel-shooting was in a grove of tall walnut trees that shades one side of the valley. I had wandered into it at noontime, when all nature is peculiarly quiet, and was startled by the roar of my own gun.

Which choice best states the function of the underlined sentence in the text as a whole?

A) It describes a feature of the setting that also reflects a trait of the character introduced in the sentences that follow.B. unintelligible

B) It elaborates on the setting that is described in the previous sentence.

C) It presents a counterpoint to the claim that is made in the previous sentence.

D) It establishes a conflict that will likely be addressed later in the story.

Difficulty: Hard

Category: Craft and Structure

Getting to the Answer (B): The question stem asks for the function of an underlined sentence, so think about the structure of the passage as you read. Ask yourself, Why did the author include this sentence? The passage begins by discussing the setting of the story, with a valley described as “one of the quietest places in the whole world.” The underlined sentence gives additional details about the valley (its murmuring brook, its occasional bird noises) that support the claim that it is quiet. The remaining sentences introduce a character (the narrator) into the quiet setting that has been described. While some students might predict an answer here, others might choose the elimination strategy. If you would choose the latter, evaluate the answer choices with the structure you just found in mind. Eliminate (A), as the character is not described as quiet; rather, he fires a loud gun. Choice (B) is correct; the underlined sentence uses details to elaborate on the description of the setting as quiet. Choice (C) is opposite; the underlined sentence is not a counterpoint, but rather supporting evidence, for the claim that the valley is quiet. Eliminate (D) as well, since the underlined sentence does not imply conflict, just a quiet setting.

Question 8: Reading & Writing

On January 8, 1918, more than half a year before the final battles of World War I, U.S. President Woodrow Wilson shared with Congress his vision for improved postwar international relations. One of Wilson’s fourteen goals for the postwar world included the creation of an international organization for collective security. The Treaty of Versailles, which officially ended the war in 1919, included the establishment of such an international organization, the League of Nations. Wilson actively advocated throughout the United States in support for the Treaty of Versailles. ______ the U.S. Congress never approved the treaty or joined the League of Nations.

Which choice completes the text with the most logical transition?

A) Moreover,

B) However,

C) Indeed,

D) Therefore,

Difficulty: Medium

Category: Expression of Ideas

Getting to the Answer (B): The question stem asks for the most logical transition, so as you read the passage, identify what ideas are being connected by the transition. The first idea, located in the sentence before the transition, is that Wilson advocated for the Treaty of Versailles. The second idea, located in the sentence with the transition, is that Congress never approved the treaty. These ideas contrast, so many students would predict that the correct answer will be a contrast transition word. This prediction matches (B), which is correct. Choices (A) and (C) are incorrect because they are continuation transitions, while the ideas in the passage contrast. Choice (D) is incorrect because it creates an illogical cause-and-effect relationship; Congress failed to approve the treaty despite, not due to, Wilson’s support for it.