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Problem Solving Butler: April 2025
April 1PS 1PS 2

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PS 1

A set of 7 different integers has a median of 9, range of 10, and average of 9. What is the lowest possible value of the smallest integer in the set?

A. 6
B. 5
C. 4
D. 3
E. 2
______________________
PS 2

Which of the following can never be correct?

I: \(x < x^2 < 1-x\)

II: \(x < x^2 < \frac{1}{x}\)

III: \(x < \frac{1}{x} < x^2\)

IV: \(x < \frac{1}{x} < x^2 < x^3\)

A. II only
B. II and III only
C. II and IV only
D. I, II, and IV only
E. I, II, III, and IV only
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Critical Reasoning Butler: April 2025
April 1CR 1CR 2

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CR 1

Charities will soon start scrutinizing major donors for any signs of financial wrongdoing. Even though the screening processes are estimated to disqualify up to ten percent of all prospective donors, they will still fail to identify one-third of all donors who have committed financial maleficence. Therefore, about five percent of actual donors will still provide unethically sourced money.

Which of the following inferences about the consequences of instituting the new screening processes is best supported by the passage above?

A. Incidences of financial wrongdoing are likely to rise by five percent.
B. The amount of money available to charities is likely to decrease.
C. The funding for social initiatives by charities is likely to fluctuate across a wider range.
D. Donations made solely for the benefit of the donor are likely to become rarer.
E. Potential first-time donors are likely to increase in number by ten percent.
_______________________
CR 2

A recent law ruled that all aviation companies have the right to refuse service to an individual if allowing the individual to fly would entail an eighty percent chance that he or she would suffer respiratory issues. The lawmakers justified the law, saying that the law protected both the aviation companies and their passengers.

The effectiveness of the law in regulating the behavior of aviation companies could be most questioned if which of the following were true?

A. The best interests of aviation companies often conflict with the best interests of their passengers.
B. An aviation company might lose passengers if the company, by screening passengers for risk of respiratory issues, seemed to suggest that taking its flights entailed a high risk of respiratory issues.
C. Flying might involve health risks other than the risk of respiratory issues.
D. Passengers who have an eighty percent chance of suffering from respiratory issues may not know that their risk is so great.
E. There is no legally accepted method for reliably determining the risk of a passenger suffering respiratory issues as a result of flying.
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Data Sufficiency Butler: April 2025
April 1DS 1DS 2

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DS 1

At a lakeside park, two cyclists, Maya and Tessa, started riding at the same time from the entrance toward the marina along the same straight path, each at a constant speed. Tessa rode faster than Maya, reached the marina, turned around immediately, and began riding back toward the entrance before meeting Maya on the path. What was the distance from the entrance to the marina?

(1) When they met, Maya had covered 3/5 of the distance from the entrance to the marina.

(2) When they met, Tessa had covered 2,100 meters.

________________________
DS 2

Two buses, R and S, each traveling at a constant speed, departed from the depot at the same time and traveled along the same route toward Central Square station. Bus R traveled faster than Bus S, reached Central Square station, turned around immediately, and began traveling back toward the depot before meeting Bus S along the route. What was the distance between the depot and Central Square station?

(1) When the two buses met, Bus S was 250 kilometers from Central Square station.
(2) Bus R traveled 3 times as fast as Bus S.
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- Why these passages make test-takers panic (and how to stop).
- How to apply our core reading strategies to abstract cultural topics.
- How to find the author's purpose when the passage feels like a subjective essay.

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Problem Solving Butler: April 2025
April 2PS 1PS 2

_____________________
PS 1

If a^3 > b^2 > c, which of the following may be true?

I. a > b > c
II. c > b > a
III. a > c > b

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
_____________________
PS 2

The average weight of students in a class of 20 was 80 pounds. Five new students joined and the weight increased to 84 pounds. If weights of the five new students are in integers, weight of no two students is same, and the lightest new student weighs 84 pounds, what is the highest possible weight of the heaviest new student?

A. 100
B. 116
C. 158
D. 164
E. 172
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Critical Reasoning Butler: April 2025
April 2CR 1CR 2

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CR 1

High marginal tax rates do not lead to a large middle class; if this was the case, the nations with the highest marginal tax rates would also have the largest middle classes. The reality is that if marginal tax rates are adjusted to allow different countries to be reliably compared to one other, no such correlation is found.

If the statements above are all true, which of the following can properly be inferred on the basis of them?

A. Increasing a country’s marginal tax rates will not necessarily result in the growth of its middle class.
B. Reliably comparing the marginal tax rates of one country with another’s is not possible.
C. Nations with high marginal tax rates tend to restrict the growth of the upper class.
D. When countries are arranged in descending order by population, the least-populous countries generally have the lowest marginal tax rates and the smallest middle classes.
E. Nations with the highest marginal tax rates never have proportionally small middle classes.
_____________________
CR 2

Executive: My only opponent for the post of CEO has a corporate restructuring plan that goes against the goals of many on the board of directors. Nonetheless, some of these same members support him for the position due to his push for greater vertical integration. In order to win these members’ votes, I must prove to the members that my opponent does not align with their goals with regard to corporate restructuring.

Which of the following would, if true, most strongly suggest that the executive’s plan is unlikely to succeed?

A. On some topics, the executive and his opponent are in strong agreement.
B. Most of the members of the board of directors who support the executive care very much about vertical integration, but do not know much about corporate restructuring.
C. Sometimes, long-term corporate restructuring goals come into conflict with short-term corporate restructuring goals.
D. Many of the members of the board of directors who support the executive’s opponent for his push for greater vertical integration also support his corporate restructuring plan and are fully aware of its implication.
E. Some members of the board of directors are concerned about both the corporate restructuring plan and vertical integration.
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Data Sufficiency Butler: April 2025
April 2DS 1DS 2

___________________
DS 1

A museum curator will select 4 paintings from a collection to feature in a special exhibition. How many paintings are in the collection?

(1) The probability that two paintings from the collection, Sunrise Harbor and Winter Field, will both be selected is 2/15.
(2) The number of different 4-painting groups that could be selected is 210.
___________________
DS 2

A pipeline inspection team was assigned to inspect a newly laid pipeline. According to the inspection plan, all of the first 60 kilometers of the pipeline were inspected, 2/3 of the next 150 kilometers were inspected, and no part of the pipeline beyond the first 210 kilometers was inspected. How long was the pipeline?

(1) A total of 160 kilometers of the pipeline was inspected.
(2) The length of the pipeline that was inspected was at least 16/21 of the total length of the pipeline.
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Problem Solving Butler: April 2025
April 3PS 1PS 2

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PS 1

The intake of students in a bachelor’s degree program of four years is supposed to increase by 1/4th of the intake in the inception year for each of the first five years. If the enrollment in the year of inception was x and no student failed or dropped out over these five years, how many students were studying in the four years of the degree program towards the end of fifth year?

A. 4x
B. 5x
C. 5.5x
D. 6.5x
E. 7.5x
______________________
PS 2

10 years ago, Jack was twice as old as Renee. Two years from now, Jack will be 1.5 times as old as Renee. What was the sum of the ages of Jack and Renee 5 years ago?

A. 28
B. 36
C. 46
D. 50
E. 56
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