Quiz: How would you do on the PSAT?

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Question 1

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

Answer 1

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:

Question 2

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

Answer 2

B: 

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 width) = (ride wingspan / ride width)

(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, (B).

Question 3

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

Answer 3

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, so (B) is correct.

Question 4

Which of the following is the best estimate for the slope of the line that best fits the data shown in the figure? (Assume that the blackbordered area is a square and that the scale of measurement is the same on every side.)

psat practice

A. -2

B. -1/2

C. 1/2

D. 2

Answer 4

A: A line with a downward slant has a negative slope, so you can immediately eliminate C and D. Mark the bordered area using equal measures, then estimate the slope of a line drawn through the center of the points. The line appears to fall 2 and run 1, so a good estimate for the slope is −2, (A).

Question 5

The following passage, adapted from an article in an encyclopedia of American culture, addresses some of the influences of the automobile on American life.

Interestingly, it was the process of building cars rather than the cars themselves that first brought a sea change to the American workplace. In 1914, a Ford plant in Highland Park, Michigan, used the first electric conveyor belt, greatly increasing the efficiency of automobile manufacturing. Assembly lines for the production of automobiles were quickly adopted and became highly mechanized, providing a new model for industrial business. In contrast to European manufacturers, which employed a higher percentage of skilled laborers to produce fewer and costlier cars, American companies focused on turning out a large quantity of affordable cars utilizing less-skilled laborers. Assembly-line production was a mixed blessing, as it enabled higher productivity and more affordable cars but resulted in less-satisfied workers with less-interesting jobs. The value of efficiency was emphasized over personal pride and investment in the work.

The author refers to European and American manufacturing practices (in bold) primarily to

A. demonstrate the quality difference between European and American cars.

B. argue for a return to a less mechanized but less efficient factory system.

C. highlight the positive and negative effects of the automobile on the American workplace.

D. suggest that greater efficiency and more skilled laborers can improve the American workplace.

Answer 5

C: Think about how the text in the question stem provides evidence for the author’s central idea. Eliminate any answer choices that don’t match the author’s purpose. For instance, “argue” in B does not match the author’s informative tone. The author describes how the assembly line impacts the American workforce in both good and bad ways. Choice (C) correctly supports this claim.

Question 6

As cars became more popular, their effect on population distribution was likewise profound. Unlike railroads, which helped concentrate the population in cities, the automobile contributed to urban sprawl and, eventually, to the rise of suburbs. People no longer needed to live near public transportation lines or within walking distance of their jobs, and so were drawn to outlying areas with less congestion and lower property taxes. Business districts became less centralized for similar reasons. Sadly, this movement toward suburbs exacerbated social stratification. Since cars were initially affordable only to wealthier people, the upper and middle classes moved out of cities. Many businesses followed, attracted by the educated, well-trained workforce. As good jobs also moved out of cities, the people who remained were further disadvantaged and even less able to leave. Though few anticipated it in the heady early days of suburban growth, by the century’s end cars had helped to further entrench social divisions in America by making possible great physical distances between rich and poor.

In the bolded lines above, what distinction does the author draw between the two types of transportation?

A. Railroads are a more efficient mode of transportation than automobiles.

B. Automobiles allow greater flexibility, while railroads operate on a fixed schedule.

C. Railroads promote clustered populations, while automobiles promote dispersed populations.

D. Automobiles replaced railroads as the preferred American mode of transportation.

Answer 6

C: Determine the author’s reasoning using context. The author uses the keyword “unlike” to show contrast. The passage states that railroads brought people together, while cars brought people apart. Choice (C) correctly expresses this idea.

Question 7

As cars became more popular, their effect on population distribution was likewise profound. Unlike railroads, which helped concentrate the population in cities, the automobile contributed to urban sprawl and, eventually, to the rise of suburbs. People no longer needed to live near public transportation lines or within walking distance of their jobs, and so were drawn to outlying areas with less congestion and lower property taxes. Business districts became less centralized for similar reasons. Sadly, this movement toward suburbs exacerbated social stratification. Since cars were initially affordable only to wealthier people, the upper and middle classes moved out of cities. Many businesses followed, attracted by the educated, well-trained workforce. As good jobs also moved out of cities, the people who remained were further disadvantaged and even less able to leave. Though few anticipated it in the heady early days of suburban growth, by the century’s end cars had helped to further entrench social divisions in America by making possible great physical distances between rich and poor.

As bolded above, “profound most nearly means”

A. absolute

B. unintelligible

C. far-reaching

D. thoughtful

Answer 7

C: On Vocab-in-Context questions, it’s often helpful to use a one-word paraphrase as your prediction. The author’s purpose is to explain how cars have “greatly” affected American life, so look for a similar word among the answer choices. Choice (C) matches. Choice A is extreme; an “absolute” effect would mean that there are no other influences. Choice B doesn’t make sense in context. Choice D is related to a common meaning of “profound,” as when an idea is described as profound. It doesn’t fit here, however, as “effects” cannot be “thoughtful.”

Question 8

In recent years, many parents have expressed concern that the atmosphere of violence (1) propagated by the American entertainment industry may be having a harmful effect on their children. Certainly these parents are correct that (2) violent acts such as murder, have become the pervasive theme of everything from feature films to television cartoons. But is this kind of depravity altogether new to the world of the (3) child. Haven’t parents for centuries been exposing their children to fairy tales that are at least as gory and violent?

How should word (1) be changed?

A. NO CHANGE

B. secreted

C. populated

D. advocated

Answer 8

A: When a single word is underlined, make sure that it is the word that best conveys the author’s intended meaning in the context of both the sentence and paragraph. No change is necessary. One of the definitions of “propagate” is “to cause to spread out” over a great area or population. This sense of the word is correct in the context of this sentence and paragraph.

Question 9

In recent years, many parents have expressed concern that the atmosphere of violence (1) propagated by the American entertainment industry may be having a harmful effect on their children. Certainly these parents are correct that (2) violent acts such as murder, have become the pervasive theme of everything from feature films to television cartoons. But is this kind of depravity altogether new to the world of the (3) child. Haven’t parents for centuries been exposing their children to fairy tales that are at least as gory and violent?

How should #2 be changed?

A. NO CHANGE

B. violent acts; such as murder; have become

C. violent acts, such as murder have become

D. violent acts, such as murder, have become

Answer 9

D: When an underlined sentence fragment includes a parenthetical remark, look for the answer that shows the correct way to punctuate that clause. Choice (D) is correct. “Such as murder” is a parenthetical remark because it is not necessary for the sentence to be complete. It is best set aside by two commas.

Question 10

In recent years, many parents have expressed concern that the atmosphere of violence (1) propagated by the American entertainment industry may be having a harmful effect on their children. Certainly these parents are correct that (2) violent acts such as murder, have become the pervasive theme of everything from feature films to television cartoons. But is this kind of depravity altogether new to the world of the (3) child. Haven’t parents for centuries been exposing their children to fairy tales that are at least as gory and violent?

How should #3 be changed?

A. NO CHANGE

B. child?

C. child!

D. child;

Answer 10

B: An underlined section that includes punctuation requires an assessment of the punctuation. Choose the answer that provides the correct punctuation for the sentence and context. Choice (B) is correct. The sentence cannot be correctly combined with the following sentence using a semicolon, so a question mark is the only appropriate option to follow the word “child.”