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Problem Solving Butler: June 2026
June 15PS 1PS 2

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PS 1

A crowd of 40,000 is watching a football game. A family of four has to leave after one of their children has a tantrum. The number of people in the crowd after the family leaves is how many times the number of people in the family?

(A) 999
(B) 1,000
(C) 9,999
(D) 10,000
(E) 39,996
_____________________
PS 2


The table shows the number of seats available at each price tier for a concert venue. What is the average (arithmetic mean) cost of a ticket to the concert?

(A) $75
(B) $100
(C) $125
(D) $150
(E) $175
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Critical Reasoning Butler: June 2026
June 15CR 1CR 2

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CR 1

Auto Manufacturer: For the past three years, the Micro has been our best-selling car. This year, however, sales of the Micro have been down for two consecutive quarters. Therefore, we are going to make certain features, like leather seats and CD players, standard on the Micro, rather than require buyers to pay extra for them. This will make the Micro more attractive to buyers, thus stimulating sales.

Auto Dealer: Most people who buy the Micro do so because of its low cost. Adding new standard features will raise the base price of the Micro, costing us sales.

In the argument above, the two statements in bold play which of the following roles?

(A) The first is a conclusion; the second suggests that this conclusion is based on evidence that is irrelevant to the issue at hand.

(B) The first presents a hypothesis; the second casts doubt on the evidence on which that hypothesis is based.

(C) The first provides a conclusion; the second weakens the assumption on which that conclusion relies.

(D) The first offers evidence that is disproved by the second.

(E) The first presents a conclusion; the second supports the conclusion but offers a different interpretation of how it will impact the speaker’s business.

__________________________
CR 2


The growth of the market for self-portraits of 19th century artists has not stopped increasing in the past twenty years, due to a concomitant rise in both the number of museums and in the interest of collectors in Eastern Asia. However, the fact that the market has been growing for the past two decades does not mean it cannot shrink as well. An international financial crisis may change the current direction the market is taking.

In the argument, the two portions in boldface play which of the following roles?


A. The first is a fact that has caused further occurences; the second is a fact which clarifies the first.

B. The first is a piece of evidence that is dependent on following pieces of evidence; the second is a prediction which limits the scope of the first.

C. The first is a fact that in turn has caused other facts to come into effect; the second is a conclusion deduced from both the first and other facts.

D. The first is a fact which resulted from following facts; the second is a premise which weighs against the first.

E. The first is a fact brought about by other facts; the second is the conclusion of the argument.
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Data Sufficiency Butler: June 2026
June 15DS 1DS 2

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DS 1

Last week, did Cafe Luna sell more lunch boxes than Cafe Porto?

(1) More than 15% of the lunch boxes sold by Cafe Porto last week were sold on Friday, and fewer than 15% of the lunch boxes sold by Cafe Luna last week were sold on Friday.

(2) On Friday of that week, Cafe Luna sold more than 900 lunch boxes, and Cafe Porto sold fewer than 900 lunch boxes.
_____________________
DS 2

At a print shop, Nora, Ethan, and Maya bind booklets at their respective constant rates. If Maya can bind one booklet in 12 minutes, can Nora, Ethan, and Maya, working simultaneously and independently, bind at least 35 booklets in 1 hour?

(1) Nora can bind one booklet in less than 2 minutes.

(2) Ethan takes more than 25 minutes to bind one booklet.
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Problem Solving Butler: June 2025
June 16PS 1PS 2

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PS 1

If \(p =\frac{0.7197}{(0.294)(0.739)}\), then p satisfies which of the following inequalities?

(A) 0 < x ≤ 1
(B) 1 < x ≤ 2
(C) 2 < x ≤ 3
(D) 3 < x ≤ 4
(E) 4 < x ≤ 5

_____________________
PS 2

Which of the following numbers is closest to 1/2?

(A) 9/16
(B) 10/19
(C) 13/24
(D) 16/30
(E) 19/36
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Critical Reasoning Butler: April 2026
June 16CR 1CR 2

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CR 1

A corporation’s recent financial report indicates that customers in its Quarx stores, which play upbeat music through an in-store audio system, spend on average 25 percent more per shopping trip thancustomers in its Cubix stores, which advertise specials over the audio system. Clearly, hearing music has a greater impact than hearing advertisements on how much money customers spend when shopping.

Which of the following, if true, would most strengthen the argument above?

(A) A study conducted by a psychologist found that hearing music makes shoppers feel financially secure, so they are more likely to make impulse purchases.

(B) Customers who hear advertisements for things they dislike form a negative association between their shopping experience and what they heard, making them less likely to return to the store where they heard the advertisement.

(C) Stores that play music tend to carry products that are essential to daily life, while those that advertise specials often stock unessential, fun items that the stores hope consumers will decide to buy on a whim if offered a special price.

(D) An economist who studied consumer shopping habits found that about half the population likes to listen to music while shopping, while the other half reports either disliking music or not noticing that music is playing.

(E) According to a recent sociological study, customers say that hearing specials announced while they are shopping is irritating, but they often take advantage of the discounts offered in those announcements.
____________________
CR 2

Zeta Manufacturing, a producer of low-cost chairs and tables, plans to start production on a more expensive line of furniture. The company’s research shows that consumers are currently reluctant to purchase products made by Zeta Manufacturing because of concerns about the products’ quality. The company is certain that selling a more expensive line will alleviate these concerns.

Which of the following is an assumption that lies behind Zeta Manufacturing’s decision to produce a more expensive line of furniture?

A. Consumers believe that items that are equal in quality are equal in cost.

B. Consumers make a connection between the cost of a product and its quality.

C. Consumers are less attracted to low cost than they are to high quality.

D. Companies increase their profitability when they sell more expensive products.

E. People expect to purchase furniture infrequently because furniture is durable
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Data Sufficiency Butler: June 2026
June 16DS 1DS 2

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DS 1

A course advisor is paid a monthly enrollment bonus. In any month in which she enrolls at least 10 students, she earns a total bonus of b dollars for the first 10 students enrolled, plus 0.05b dollars for each additional student enrolled, where b is positive. If she enrolled at least 10 students last month, did she enroll at least 25 students last month?

(1) Last month, her total enrollment bonus was 1.75b dollars.

(2) Last month, her total enrollment bonus was $1,050.

____________________
DS 2

A custom print shop produced event posters last year. The shop’s total cost for the posters was $48,000 plus a licensing fee equal to 20% of the shop’s total revenue from poster sales. If the shop sold every poster it produced and its revenue from poster sales was not greater than its total cost for the posters, did the shop sell fewer than 8,000 posters last year?

(1) Last year, the shop sold the posters for an average (arithmetic mean) price greater than $8 per poster.

(2) Last year, the shop’s total revenue from poster sales was less than $55,000.
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Problem Solving Butler: June 2026
June 17PS 1PS 2

______________________
PS 1

p = 400,000 x 500,000,
q = 0.235 x 10^12,
r = (100,000 + 25,000)(10^3)^2,
s = 500,000,000/0.004

Which of the following is true of the numbers shown above?

(A) p = q < r < s
(B) r < s = p < q
(C) r = s < p < q
(D) p < r = s < q
(E) q < p = r < s
______________________
PS 2

\(\frac{4x+3y-15}{24} = y - \frac{x}{8} - \frac{1}{2}\)

What is the value of x - 3y ?

(A) -2
(B) -3/7
(C) 3/7
(D) 2
(E) The answer cannot be determined
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Critical Reasoning Butler: June 2026
June 17CR 1CR 2

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CR 1

Occupational safety advocate: Logging is one of the most dangerous occupations in the United States. A company has developed a chainsaw that will instantly shut off if there is kickback of the chain, which studies have shown to be the most common cause of chainsaw injuries. The logging industry should adopt this new chainsaw as standard equipment in order to prevent most of the logging-related deaths that occur each year.

Which of the following statements, if true, most seriously weakens the occupational safety advocate’s argument?

(A) Loggers are sometimes killed by problems with chainsaws other than the kickback of the chain.

(B) Injuries from falling trees cause the vast majority of deaths in the logging industry.

(C) The new chainsaw is inexpensive and easy to learn how to use.

(D) There are other, equally safe chainsaws available, but the logging industry has not adopted them.

(E) The chainsaw manufacturer’s claims about its product are supported by a study conducted by a government agency.
______________________
CR 2

The use of fingerprint analysis to identify criminal suspects dates back to the late 1800s, although the theory behind the technique existed long before it was actually used in practice. In fact, the hypothetical possibility was so intriguing to Mark Twain that he used fingerprint identification as a plot device in his quasi-memoir Life on the Mississippi nearly a decade before fingerprints were used to solve a crime in real life. Since then, fingerprint analysis has become a standard law enforcement technique for real and fictional detectives alike. Yet, despite its widespread use, the practice has never been subjected to rigorous scientific study, and some of the assumptions that underpin its use—such as the notion that each person has a unique set of fingerprints—may not be accurate. The time has come for the legal community to acknowledge that fingerprint analysis is an unsubstantiated forensic science and to advocate for more research in the field.

In the argument given, the two portions in boldface play which of the following roles?

(A) The first is a detail that supports the author’s main idea, and the second raises a contrary opinion.

(B) The first is a detail that supports one opinion, and the second is a contrary opinion held by the author.

(C) The first introduces an opinion, and the second contradicts that opinion.

(D) The first is a detail that supports the author’s main idea, and the second is additional evidence for the author’s main idea.

(E) The first is a detail that supports a claim made in the argument, and the second is the author’s main point.
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Data Sufficiency Butler: June 2026
June 17DS 1DS 2

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DS 1

At a charity event, 80 volunteers were assigned to exactly one of two roles: setup crew or check-in desk. If one volunteer is selected at random from the 80 volunteers, is the probability greater than 3/10 that the selected volunteer is a woman on the setup crew?

(1) There were 45 men among the 80 volunteers.

(2) There were 22 volunteers on the setup crew.

____________________
DS 2

Maya bought a framed print at an art gallery and paid a total of $96. If the $96 total consisted of the pre-tax price of the framed print plus sales tax on that pre-tax price, was the sales tax rate less than 20%?

(1) The pre-tax price of the framed print was less than $80.

(2) The sales tax Maya paid on the framed print was less than $19.20.
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