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Problem Solving Butler: June 2026
June 30PS 1PS 2

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PS 1

Daniel can complete a piece of work alone in 10 days, and Stefan can complete the same work alone in 5 days. The work carries a total payment of 1,200 euros. Daniel, Stefan, and a third person, Oliver, work together and complete the work in 2 days. If the payment is divided in proportion to the amount of work done by each person, what is Oliver’s share of the payment?

A. 300 euros
B. 360 euros
C. 400 euros
D. 480 euros
E. 600 euros
_____________________
PS 2

Andreas and Bruno each work at a constant rate. Andreas can clear a garden plot working alone in 50 days. He works for 5 days and then leaves. The remaining work is cleared by Bruno working alone in 30 days. In how many days can Andreas and Bruno clear the entire plot if they work together from the start?

A. 16 2/3
B. 18 3/4
C. 20
D. 22 1/2
E. 25
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Critical Reasoning Butler: June 2026
June 30CR 1CR 2

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CR 1

­Many physicians cater to their patients’ insistence that they be given antibiotics for a common cold. However, these illnesses are viral in nature, and such medications have no effect on viruses. This course of treatment is troublesome, as antibiotics have dangerous side effects and unnecessary use of these drugs can lead to resistant bacteria. So clearly doctors need to stop prescribing antibiotics to treat the common cold.

Which of the following best describes the role of the two boldfaced portions above?

A. The first is a phenomenon that the argument addresses; the second is evidence used by the author to support his position.
B. The first is a phenomenon that the argument addresses; the second is the author’s primary conclusion.
C. The first is evidence used by the author to support his conclusion; the second is that conclusion.
D. The first is a circumstance that the author tries to explain; the second is that explanation.
E. The first is a circumstance that the author tries to explain; the second is the author’s primary conclusion.
___________________
CR 2

Most research scientists who work for corporate consulting firms have low levels of job satisfaction. However, Expert Consulting is known throughout the industry for research scientists who experience very high levels of job satisfaction. Expert Consulting attributes its success in cultivating happy employees to its programs enabling staff scientists to work on their own research projects in addition to working for clients.

Which of the following, if true, most strongly supports Expert Consulting’s explanation of its success in cultivating happy employees?

A. Some scientists experience low job satisfaction when they must work more than full time.
B. Most scientists at corporate consulting firms come from academic programs that they entered because they enjoyed pursuing their own research questions
C. Many of Expert Consulting’s senior staff scientists divide their time between working on their own research projects and working for clients.
D. Working on their own research projects shields scientists from exposure to other industries in which they might find better paying jobs.
E. The cost of living near Expert Consulting is relatively low compared to areas in which some other scientific consulting firms.
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Data Sufficiency Butler: June 2026
June 30DS 1DS 2

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DS 1

During a 10-day craft fair, a print studio sold only posters and banners. Each poster sold for $18 and cost $10 to produce, while each banner sold for $30 and cost $16 to produce. If the studio sold 110 posters and banners in total during the fair, was its profit from these sales more than $1,200?

(1) The studio used 290 ounces of ink to produce the items sold, with each poster requiring 1 ounce and each banner requiring 4 ounces.

(2) The studio sold more banners than posters.
_____________________
DS 2

A stationery shop sells only notebooks and planners. Each notebook sells for $30 and costs the shop $25, while each planner sells for $20 and costs the shop $12. In June, the shop sold 140 notebooks and planners in total. Was the shop’s profit from these sales more than $900?

(1) The shop’s profit from planners was less than its profit from notebooks.

(2) The shop’s revenue from notebooks was greater than its revenue from planners.
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Problem Solving Butler: July 2026
July 1PS 1PS 2

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PS 1

Alex can do three times as much work per hour as Bruno. As a result, Alex takes 12 hours fewer than Bruno to complete a certain job. In how many hours can Bruno complete the job working alone?

A. 12 hours
B. 15 hours
C. 18 hours
D. 24 hours
E. 30 hours


_______________________
PS 2

Lucas can process four times as many data files per day as Martin. Consequently, Lucas takes 30 days fewer than Martin to complete a large data-processing task. If Lucas and Martin work together, how many days will they take to complete the task?

A. 7
B. 8
C. 9
D. 10
E. 12
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Critical Reasoning Butler: July 2026
July 1CR 1CR 2

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CR 1

­Incumbent candidate for governor: As the people of our great state know, my administration has created unprecedented economic prosperity and job growth. Just look at the unemployment rate, which has reached its lowest point in nearly twenty years!

Opposing candidate for governor: That’s preposterous. You overlook the fact that the unemployment rate is just as much a function of the number of people in the labor market as much as it is of the number of people employed. Your greatest contribution to the economy has been a series of retirement parties and moves to other states!

The opposing candidate’s reply to the incumbent proceeds by:

(A) Supplying a statistic that undermines the incumbent’s conclusion.

(B) Suggesting that the incumbent’s statistic is factually inaccurate.

(C) Offering a statistic that sheds additional light on the statistic supplied by the incumbent.

(D) Claiming that the incumbent used a statistic irrelevant to his conclusion.

(E) Pointing out that the incumbent cited a statistic that does not necessarily support his conclusion.
_______________________
CR 2

­Professor Edwards must have revealed information that was embarrassing to the university. After all, to have been publicly censured by the head of the university, as Edwards was, a professor must either have revealed information that embarrassed the university or have been guilty of gross professional negligence, and Edwards’s professional behavior is impeccable.

Which one of the following arguments exhibits a pattern of reasoning most similar to that in the argument above?

(A) According to company policy, employees who are either frequently absent without notice or who are habitually late receive an official warning. Since Ms. Jensen has never received such a warning, rumors that she is habitually late must be false.

(B) Any employee of Wilkins, Waddel, and Sloan, who discussed a client with a member of the press will either be fired or demoted. But since Wilkins employees never discuss their clients at all, no Wilkins employee will ever be demoted.

(C) Anyone promoted to supervisor must either have worked on the shop floor for three years or have an influential sponsor. Daniels, therefore, has an influential sponsor, since he was promoted to supervisor after a year on the shop floor.

(D) To earn a merit salary increase, an employee of TGX must either bring in new clients or develop innovative products. No innovative products were developed at TGX this year, so TGX employees must have brought in many new clients.

(E) Anyone who is either awarded a letter of commendation or who receives a bonus must be recommended by a company officer. Simon has been recommended by a company officer and will receive a bonus, so he must not have been awarded a letter of commendation.
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Problem Solving Butler: July 2026
July 1DS 1DS 2

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DS 1

At the beginning of a charity event, Lena had only red wristbands and blue wristbands, with at least one wristband of each color. During the morning shift, she handed out 1/9 of the red wristbands. If Lena did not receive any additional wristbands that day, did she have more than 27 wristbands at the beginning of the event?

(1) The number of red wristbands Lena handed out during the morning shift was 50% as many as the number of blue wristbands she had at the beginning of the event.

(2) The number of red wristbands Lena handed out during the morning shift was 75% as many as the number of red wristbands she handed out during the afternoon shift.

____________________
DS 2

A vendor bought 40 identical phone chargers for $35 each. The vendor sold some of the chargers at one price and the rest at another price. What was the vendor’s gross profit from selling all 40 chargers?

(1) If the vendor had paid $5 less for each charger, the gross profit would have been $1,900.

(2) If each charger had sold for $3 more, the gross profit would have been $1,820.
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Problem Solving Butler: July 2026
July 2PS 1PS 2

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PS 1

A team of T technicians, each working at the same constant rate, can complete a task in 60 days. If 8 additional technicians, each working at the same constant rate as the original technicians, join the team, the task is completed 12 days earlier. What is the value of T?

(A) 30
(B) 32
(C) 35
(D) 40
(E) 45

______________________
PS 2

Liam, Emma, and Noah together earn €600 per day. Liam and Noah together earn €380 per day, and Emma and Noah together earn €320 per day. How much does Noah earn per day?

(A) €80
(B) €90
(C) €100
(D) €110
(E) €120
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Critical Reasoning Butler: July 2026
July 2CR 1CR 2

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CR 1

During a period of low growth after a recent and remarkable boom in the solar energy sector, Company X, a major manufacturer of solar-powered generators, attributed its success during the boom to the sale of excess inventory it had discovered in one of its warehouses.

Which of the following tests would most help to evaluate the company’s hypothesis as to the cause of its success?

A. Comparing the length of the low-growth period to the length of the preceding boom

B. Comparing the boom experienced by Company X to those experienced by similarly-sized manufacturers of solar powered generators that did not have inventory on hand

C. Calculating average sales increases within the individual divisions of Company X

D. Comparing the total number of generators sold by Company X during the boom to the total number sold by Company X during the period of low growth

E. Using economic theory to predict the next economic boom for Company X

______________________
CR 2

Senovia can be looked upon as an example of stability within an unstable region. Of the 4 countries in the Senovian Mountain region, Senovia is the only one to have the same borders today as it did 20 years ago.

Which of the following if true, would most weaken the conclusion presented above?

A. After years of dispute between Senovia and its neighbors, the United Nation redrew the country’s borders to match their original shape last year.

B. Two of Senovia’s neighbors split from one another to create independent countries 10 years ago.

C. Many countries in the region are more interested in acquiring new territory than they are in stabilizing existing borders.

D. Senovia has had unsteady economic growth during the 20 years in question.

E. As more countries in the Senovian Mountain region have joined global alliances, border disputes have become less likely.
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Data Sufficiency Butler: July 2026
July 2DS 1DS 2

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DS 1

A training program gave a final exam to all participants. Each participant was either an intern or a full-time employee. Was the percentage of interns who passed the exam greater than the percentage of all participants who passed the exam?

(1) The percentage of full-time employees who passed the exam was greater than the percentage of all participants who passed the exam.

(2) Less than 2/5 of all participants who passed the exam were interns, and less than 3/5 of all participants who failed the exam were full-time employees.
______________________
DS 2

At the end of Monday, a bookstore display had only hardcover books and paperback books, and 7/12 of the books on the display were hardcovers. On Tuesday, the store added hardcover books and paperback books to the display and removed none of the books that were already there. After the additions, was the fraction of paperback books on the display less than it had been at the end of Monday?

(1) Less than 1/2 of the books added on Tuesday were paperbacks.

(2) After the additions on Tuesday, the total number of books on the display was 1/3 greater than it had been at the end of Monday.
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Problem Solving Butler: July 2026
July 3PS 1PS 2

____________________
PS 1

Two pumps, X and Y, can fill a tank in 10 and 20 minutes, respectively. Both are turned on simultaneously, but after 5 minutes, pump X is turned off. How much additional time will pump Y take to fill the tank completely?

(A) 4 minutes
(B) 5 minutes
(C) 6 minutes
(D) 7 minutes
(E) 8 minutes

____________________
PS 2

A group of workers, each working at the same constant rate, can complete a task in 90 days. If 12 additional workers, each working at the same constant rate as the original workers, join the group, the task is completed 15 days earlier. How many workers were there in the group initially?

(A) 55
(B) 60
(C) 65
(D) 70
(E) 75
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Critical Reasoning Butler: July 2026
July 3CR 1CR 2

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CR 1

­Many people experience deficiencies in their intake of certain essential vitamins and minerals, such as vitamin D, calcium, and zinc. Many companies sell supplements that allow people to increase their intake of individual vitamins and minerals. People can also purchase multivitamins. The leading multivitamin brands provide vitamin D, calcium, and zinc in doses equal to those found in many of the individual supplements.

Which of the following statements is most strongly supported by the information above?

(A) Not all people switching from individual calcium supplements to multivitamins need to increase the number of pills they take daily.

(B) People who are not deficient in vitamin D, calcium, or zinc should not take multivitamins.

(C) It would be more cost-effective for people to take a multivitamin than to take individual supplements.

(D) Multivitamins are the most effective way of increasing one's intake of certain essential vitamins and minerals.

(E) Multivitamins contain some vitamins that are not available individually.
________________________
CR 2

­In Clark County, recent legislation requires that all new homes built with a pool be equipped with door alarms that sound when any door leading to the pool area is opened. The state legislature claims that this will save lives because parents will be alerted when their children enter the pool area. However, many homeowner's associations have protested the new law. The homeowner's associations conclude that few lives will be saved because children are supervised in pool areas over ninety-five percent of the time by their parents.

Which of the following, if true, would most seriously weaken the homeowner's associations' argument?

(A) Many parents have formal training in CPR to resuscitate children that have fallen into a pool and drowned.

(B) Since new homes with pools represent a small fraction of the homes in Clark County, the law will be rather narrow in scope.

(C) The cost of the new door alarms is not prohibitive for most new home buyers.

(D) Clark County has an excellent system of emergency medical technicians, all of whom are trained to resuscitate children that have fallen into pools and drowned.

(E) Most of the deaths that result from a child falling into a pool occur when parents are home with their child but not supervising the child's activities.
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