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Data Sufficiency Butler: June 2026
June 24DS 1DS 2

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DS 1

At a community center, 360 people enrolled in at least one of two weekend classes, pottery and photography. If 80 of these people did not enroll in photography, how many enrolled in both classes?

(1) Of the 360 people, 70 did not enroll in pottery.
(2) A total of 290 people enrolled in pottery.
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DS 2

At a distribution center, stations A and B scan packages at their respective constant rates. How many more hours does it take station B, working alone, to scan a new shipment of packages than it takes station A, working alone?

(1) The ratio of the time it takes station B, working alone, to scan the shipment to the time it takes station A, working alone, to scan the shipment is 4 to 1.

(2) The ratio of the time it takes stations A and B, working together, to scan the shipment to the time it takes station A, working alone, to scan the shipment is 4 to 5.
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Problem Solving Butler: June 2026
June 24PS 1PS 2

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PS 1

Sophie, working at a constant rate, can complete a job working alone in 34 hours. Julien, working at a constant rate, can complete the same job twice as fast as Sophie. Sophie takes a 1 hour break after each 2 hours she works, and Julien takes a 1 hour break after each 3 hours he works. If they start working at the same time and follow these break patterns, after how many hours from the start will the job be completed?

A. 12
B. 13
C. 14
D. 15
E. 16
____________________
PS 2

Ann takes 50 percent more time to complete a job working alone than Ann and Bob take to complete the job when working together. By what percent does Bob take more time to complete the job working alone than Ann and Bob take to complete the job when working together?

A. 50%
B. 75%
C. 100%
D. 150%
E. 200%
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Problem Solving Butler: June 2026
June 25PS 1PS 2

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PS 1

7 technicians and 8 trainees can complete a piece of work in 7 days, and 8 technicians and 11 trainees can complete the same work in 6 days. If each technician works at a constant daily rate, and each trainee works at a constant daily rate, what is the ratio of the work done per day by a technician to that done per day by a trainee?

A. 1:10
B. 6:1
C. 8:1
D. 10:1
E. 12:1
_____________________
PS 2

Clara can complete a job working alone in 48 days. Hugo can complete the same job working alone in 32 days. They begin working together, and after 8 days Hugo leaves. How many additional days will Clara, working alone, need to complete the remaining work?

A. 28
B. 32
C. 36
D. 40
E. 48
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Critical Reasoning Butler: June 2026
June 25CR 1CR 2

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CR 1

Space Enthusiast: The fact that the government has ignored space science is reprehensible. In the past five years the current administration has spent less than 2.5 billion dollars on promising missions to explore the outer planets and understand the fundamental properties of our universe and the origins of life.

Politician: Your claims are erroneous and absurd. The current administration has allocated over 4 billion dollars for exactly the sort of scientific space missions you claim we do not support!

The apparent contradiction in the claims of the space enthusiast and the politician could best be resolved if which of the following was true?

A. Many space missions require billions of dollars and, often, decades of development and flight before returning any useful scientific data.

B. Politicians often select space missions for funding based not on the mission's potential scientific return but rather on an assessment of the mission's appeal to the public sense of imagination and adventure.

C. Without government funding, projects as complex as space missions to explore the outer planets are unlikely to ever come to fruition.

D. Often the budgetary allocations assigned to one agency or project are instead called upon to fund emergency needs of a different agency or project.

E. Many politicians support space exploration very strongly, albeit sometimes for selfish reasons ranging from creating jobs in their voting districts to seeking exciting ways of inspiring the public
_____________________
CR 2

Justin: Under current state law, employers must provide worker’s compensation insurance, which provides income to employees who cannot work due to injuries sustained at the workplace, to all full-time employees. This form of insurance is vital in protecting workers from financial ruin in the event they are suddenly unable to work.

Bharti: I disagree with your assessment. The high premiums employers are forced to pay for worker’s compensation insurance force many of them out of business, thereby serving to increase the state’s unemployment rate. Since unemployed people are statistically unlikely to carry health insurance, the state-mandated worker’s compensation scheme actually renders workers more vulnerable to financial devastation in the event of bodily injury.

Which of the following, if true, should Justin cite in order to respond most effectively to Bharti’s counterargument?

(A) In addition to carrying worker’s compensation insurance, most employers in the state also provide health insurance for full-time employees.

(B) Patients without health insurance and who have no money typically receive inferior treatment at hospital emergency rooms.

(C) People are statistically more likely to sustain debilitating injuries at the workplace than elsewhere.

(D) The state agency that compensates injured workers under the current insurance scheme is financially able to pay all foreseeable claims.

(E) Many workers file fraudulent worker’s compensation claims, and state regulators often fail to detect such fraud.
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Data Sufficiency Butler: June 2026
June 25DS 1DS 2

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DS 1

Rina and Maya start at the same time from a trailhead and ride bicycles at their respective constant speeds along the same straight path toward a ranger station 54 miles away, with Rina riding faster than Maya. When Rina reaches the ranger station, she immediately turns around and rides back along the same path until she meets Maya. How many miles has Maya ridden when they meet?

(1) Rina rides 2 times as fast as Maya.
(2) Rina rides 18 miles per hour faster than Maya.
______________________
DS 2

At a volunteer orientation, 8 participants are in a training group. If three participants are randomly selected without replacement, what is the probability that all three selected participants have prior volunteer experience?

(1) If two participants are randomly selected from the group without replacement, the probability that neither participant has prior volunteer experience is greater than 0.5.

(2) If one participant is randomly selected from the group, the probability that the participant has prior volunteer experience is less than 0.3.
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Problem Solving Butler: June 2026
June 26PS 1PS 2

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PS 1

20 archivists, each working at the same constant rate, can catalog a collection in 15 hours. After how many hours from the start should 8 archivists be reassigned and stop working so that the remaining archivists finish cataloging the entire collection in 10 hours after the reassignment?

A. 6
B. 7
C. 8
D. 9
E. 10

____________________
PS 2

Nina, Oscar, and Elena each work at a constant rate. Nina and Oscar can complete a piece of work in 10 hours. Oscar and Elena can complete the same work in 15 hours. Elena and Nina can complete the same work in 12 hours. How many hours will Elena take to complete the work working alone?

A. 30
B. 32
C. 36
D. 40
E. 48
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Critical Reasoning Butler: June 2026
June 26CR 1CR 2

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CR 1

­National Park Ranger: Young people are missing out on important opportunities to appreciate nature. While members of older generations spend hours and even days in our park, younger people simply stop by long enough to take the perfect photograph and then move on.

Which of the following is a required assumption of the park ranger's argument?

A) Younger people whose visits to the park consist of a quick photograph seldom look at that photograph after they have left the park.

B) People who spend multiple days at the park spend the majority of their time appreciating nature.

C) Members of older generations did not spend considerably less time in the park during their visits in their younger years.

D) Younger people are the only visitors to the park whose visits last just long enough to take a photograph.

E) The amount of time one spends in a park is a reliable measure of how much one appreciated nature on that visit.

____________________
CR 2

Despite the anti-virus protection program installed on its computers, SmartTech has received many complaints from consumers that their computers had become infected with viruses. In order to reduce the number of its computers vulnerable to viruses, the CEO of SmartTech Corp. has had the company's engineers install three different virus-blocking programs on each computer before shipping them to consumers. Nevertheless, customer reports of computer viruses have risen since the institution of this initiative.

Which of the following, if true, most helps to explain why acting on the CEO's plan failed to achieve her goal?

A. The installation of the three anti-virus programs has led to increased labor costs, taking away resources from other company departments.

B. When more than one anti-virus program is installed on a machine, the programs can become less effective.

C. Many consumers have found that it is more difficult to use a computer with three anti-virus programs than with one.

D. Corporations that are already vulnerable to hackers often use SmartTech's computers but have stopped doing so since the increased viruses.

E. SmartTech has lost approximately 25 percent of its clients as a result of its computers' vulnerability to viruses, though it regained a third of these with its recovery efforts.
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Data Sufficiency Butler: March 2026
June 26DS 1DS 2

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DS 1

A training program has a roster that includes only advanced students and beginner students. If the probability of randomly selecting an advanced student from the roster is 5/6, how many advanced students must be added to the roster so that the probability of randomly selecting an advanced student becomes 7/8?

(1) There are 44 more advanced students than beginner students.

(2) The ratio of advanced students to beginner students is 5 to 1.

_______________________
DS 2

Alloy A is 30 percent copper by weight, and Alloy B is 12 percent copper by weight. If Alloy A and Alloy B are combined to produce an alloy that is 18 percent copper by weight, how many kilograms of Alloy B are used?

(1) To produce the final alloy, 40 kilograms of Alloy A are used.
(2) The final alloy weighs 120 kilograms.
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Problem Solving Butler: June 2026
June 29PS 1PS 2

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PS 1

Alan and Brian each work at a constant rate, and Alan can do twice as much work per day as Brian. Working together, they complete a piece of work in 20 days. In how many days can Alan complete the work working alone?

A. 20 days
B. 24 days
C. 30 days
D. 40 days
E. 60 days
__________________
PS 2

Luca, working at a constant rate, can complete a data migration working alone in 24 days, while Marco, working at a constant rate, can complete the same migration working alone in twice that time. They start working together, but Luca stops working 6 days before the migration is finished. How many total days does it take to finish the migration under this schedule?

A. 16 days
B. 18 days
C. 20 days
D. 24 days
E. 30 days
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Critical Reasoning Butler: June 2026
June 29CR 1CR 2

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CR 1

Due to an obscure technicality in food labeling known as the batter-coating rule, French fries are legally considered fresh vegetables. The batter-coating rule stipulates that any vegetable that has been processed – such as a cucumber that has been waxed or a strawberry that has been sweetened – is still considered fresh as long as it is perishable, and French fries are the result of processing a vegetable.

Which of the following is an assumption on which the argument depends?

A. French fries are healthy.
B. French fries are unhealthy.
C. French fries are perishable.
D. French fries are waxed and sweetened.
E. The potato industry lobbied heavily to redesignate the French fry as a vegetable.
___________________
CR 2

Which of the following best completes the passage below?

At a recent meeting on environmental threats off the coast of the state of Maine, most participants favored uniform controls on the quality of food fed to salmon species in fish farms located along the coast of the state. Such controls were overwhelmingly supported without regard to whether or not specific environmental damage could be linked to a particular type of food being used. What must, of course, be shown, in order to mitigate the risk of excessively restrictive controls, is that _____ .

(A) all agreed upon controls that are uniform in nature will be implemented without any delay

(B) all fish foods that will be the subject of controls are known to actually cause environmental damage off the coast of Maine

(C) the meeting participants favoring uniform controls are primarily from an industry that competes with the salmon farmers

(D) all of the chemicals that are ingredients in some of the controlled substances are known to cause environmental damage

(E) the environmental damage that has historically been caused by the dangerous fish foods is not reversible in the foreseeable future, if ever
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