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Problem Solving Butler: July 2026
July 20PS 1PS 2

_______________________
PS 1

Machine M, working alone at its constant rate, processes one ton of a chemical product in 3/4 of the time that Machine N, working alone at its constant rate, does. If the two machines, working simultaneously at their respective constant rates, process one ton of the chemical product in 6 hours, how many hours will it take for Machine N working alone to process this amount?

A. 8
B. 9
C. 10
D. 12
E. 14
_______________________
PS 2

A contractor was hired to complete a certain construction job in 80 days. To meet this deadline, the contractor initially assigns 120 men, each working 10 hours per day at a constant rate. After 40 days with these 120 men, an inspection shows that only 3/8 of the job has been completed. At that point, how many additional men, working at the same rate and for 10 hours per day, must be hired to finish the job on time?

(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
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Critical Reasoning Butler: July 2026
July 20CR 1CR 2

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CR 1

Critics of strict "promotional gates" at the grade school level point to a recent study comparing students forced to repeat a grade with those promoted despite failing scores on an unscheduled, experimental competency test. Since there was no significant difference between the two groups' scores on a second test administered after completion of the next higher grade level, these critics argue that the retention policy has failed in its expressed purpose of improving students' basic skills.

Which of the following best expresses the argument made by critics of promotional gates?

A. Anxiety over performance on standardized tests often hinders a student s ability to master challenging new material.

B. A student's true intellectual development cannot be gauged by his score on a standardized competency test.

C. The psychological damage a child suffers by repeating a grade outweighs the potential intellectual benefits of a second chance at learning.

D. Strict requirements for promotion do not lead to harder work and greater mastery of fundamentals among students fearful of being held back.

E. Socioeconomic factors as well as test scores influenced whether a given student in the study was promoted or forced to repeat a grade.

____________________
CR 2

In its report for the quarter just ending, Company X announces that in some of its manufacturing processes it plans to begin converting from conventional fuels like oil and natural gas, which are rapidly becoming scarce, to synthetic fuels currently under development in the company's laboratories in Europe and the American far west. Implementation of this plan will almost certainly increase the company's expenses, since even if the synthetic fuels are rendered practical for use they can be expected to cost considerably more than conventional fuels.

Which of the following, if true, casts the most doubt on the argument above?

(A) Company X's synthetic fuels will not be ready for use in its manufacturing processes for at least a decade.

(B) Whatever increased expenses accrue from the development and use of synthetic fuels can and will be passed on to consumers of Company X's products.

(C) Company X's manufacturing processes can be adapted to the use of synthetic fuels at little or no expense.

(D) In time, the raw materials used to produce Company X's synthetic fuels will become as scarce as oil and natural gas.

(E) Long-needed conservation procedures will become practical when synthetic fuels are introduced and will compensate for the higher cost of the fuels.
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Data Sufficiency Butler: July 2026
July 20DS 1DS 2

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DS 1

A quality-control bin contains 30 sensor chips, some of which are faulty. If two chips are selected at random without replacement, is the probability that both selected chips are faulty less than 1/4?

(1) More than 40% of the chips in the bin are faulty.
(2) More than 50% of the chips in the bin are not faulty.

________________________
DS 2

Two workers, Ava and Ben, are hired to mow a field at a community park. If Ava and Ben work at their respective constant rates, by what percent is the time Ben would take to mow the field alone less than the time Ava would take to mow the field alone?

(1) Ben, working alone at his constant rate, would take 2 hours less to mow the field than Ava, working alone at her constant rate, would take.

(2) Ava and Ben, working simultaneously and independently at their respective constant rates, can mow the field in 3/5 of the time that Ben, working alone at his constant rate, would take to mow the field.
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Problem Solving Butler: July 2026
July 21PS 1PS 2

_________________________
PS 1

A certain factory normally produces 500 units per hour for a 7.5 hour workday. In a month with 22 workdays, no units are produced in the first 7 days because of a job action. By how many units must production increase on each of the remaining workdays of the month in order to meet normal production levels for the month?

A. 500
B. 688
C. 1750
D. 3750
E. 5500
_________________________
PS 2

A manager asked a team of 20 equally efficient employees to finish a project in 25 days. After 10 days, he found that the team had finished only one-fifth of the project. What is the minimum number of employees, who are twice as efficient as the original team members, that the manager should add to the current team in order to complete the project 5 days sooner?

A. 15
B. 25
C. 30
D. 60
E. 120
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Critical Reasoning Butler: July 2026
July 21CR 1CR 2

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CR 1

Shareholders and investment analysts have criticized the Vista Products Company for having slow and outdated computer systems in its factories when these systems are compared to Vista's competitor's systems. However, a Vista representative has claimed that such criticism is unfair. The representative noted that Vista spent more money last year per factory upgrading its computer systems than any of its competitors did.

Which of the following, if true, most seriously discredits the reasoning in the company representative's argument?

A. Overall spending per factory on computer systems is lower in Vista Product's industry than in other industries.

B. Vista Products is not as profitable as some of its competitors

C. Companies with fast, modern computer systems would have no need to spend large amounts of money to upgrade these systems.

D. No investment analyst has visited every single Vista Products factory.

E. When assessing the overall quality of a company's operations, production line speed is more critical than the quality of the company's computer systems.
________________________
CR 2

Electrical engineers have developed an energy-efficient type of light bulb that can replace the traditional incandescent bulb. The new bulb, known as the electronic lamp, operates by using a high frequency radio signal rather than the filament featured in incandescent bulbs. Although the electronic lamp currently costs 20 times as much as its traditional counterpart, its use will prove more cost effective in the long run. While a 100-watt incandescent bulb lasts 6 months if burned for 4 hours daily, a 25-watt electronic lamp used for the same amount of time each day lasts up to 14 years.

The argument above assumes that

A. the typical household use of a light bulb is approximately 4 hours a day

B. aside from its greater efficiency, the electronic lamp resembles the incandescent light bulb in most aspects

C. the type of light cast by the electronic lamp is different from that cast by an incandescent bulb

D. the price of electronic lamps will decrease as they are produced in increasingly greater quantities

E. a 100-watt incandescent light bulb does not provide significantly more light than a 25-watt electronic lamp
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Data Sufficiency Butler: July 2026
July 21DS 1DS 2

_________________________
DS 1

In a pet store survey about dog and cat owners, it was found that 18% were cat owners, and 42% were male pet owners. What percentage are female dog owners?

(1) 34% of the owners are male dog owners.
(2) The ratio of female cat owners to male cat owners is 5 to 4.

_________________________
DS 2

When the members of group A are divided into subgroups of 13 people, m subgroups are formed, and no one is left over. When the members of group B are divided into subgroups of 11 people, n subgroups are formed, with 8 people left over. What is the total number of members in group B?

(1) m = n
(2) The total numbers of members in groups A and B are the same.
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Problem Solving Butler: July 2026
July 22PS 1PS 2

_______________________
PS 1

A cistern has a leak which empties it in 8 hrs. A tap is turned on which fills water into the cistern at 6 liters a minute, and it is now emptied in 12 hours. How many liters of water does the cistern hold?

A. 8640
B. 8740
C. 8840
D. 8540
E. 8940
_______________________
PS 2

If 1 millilitre of a certain chemical weighs 0.04 ounce, then the weight of 1 pint of this chemical is closest to which of the following number of ounces? (1 litre = 2.1 pints, rounded to the nearest tenthof a pint)

A. 8
B. 15
C. 19
D. 67
E. 84
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Critical Reasoning Butler: July 2026
July 22CR 1CR 2

_____________________
CR 1

Journalist: Residents of a natural area popular with tourists have long complained about the air pollution caused by tourists’ use of all-terrain vehicles (ATVs) on local trails. This problem will soon be solved, however, because of a new law requiring that all area tour companies cease using gasoline-powered ATVs and use only electric ones. Whereas a gasoline-powered ATV can emit as much air pollution as multiple cars, electric ATVs produce no emissions.

Which of the following is an assumption on which the journalist’s reasoning relies?

(A) The relatively high weights of electric ATVs do not cause them to cause more damage to local ecosystems than gasoline-powered ATVs.
(B) Few of the residents of the natural area will continue to use gasoline-powered ATVs after the new law goes into effect.
(C) ATVs used on trails do not kick up fine dust that remains airborne for relatively long periods of time.
(D) The vehicles that tourists use to travel to the natural area produce less pollution than the ATVs they ride once there.
(E) The process of mining the minerals used in production of the batteries in electric ATVs does not result in large amounts of air pollution.

_____________________
CR 2

Small Business Owner: Prescott’s grocery store was losing customers because of long checkout lines. To address this issue, Prescott’s installed self-checkout stations so that more customers could check out at a time and the lines would be shorter. This approach will not help Prescott’s retain customers, however, since most of the people who shop at Prescott’s dislike checking out their own groceries.

Which of the following, if true, could a Prescott’s manager use to effectively rebut the argument made by the small business owner?

(A) Prescott’s would not become more profitable if it were to hire more cashiers so that customers could check out quickly without having to check out their own groceries.

(B) Most of Prescott’s customers prefer checking out their own groceries over waiting in long checkout lines.

(C) Before Prescott’s installed the self-checkout stations, there were no times of day when the checkout lines at Prescott’s were generally sufficiently short to satisfy most customers.

(D) Prescott’s biggest spending customers tend also to be those customers least willing to wait in long lines.

(E) Prescott’s has personnel supporting self-checkout who can assist customers with solving any problems they experience while checking out.
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Data Sufficiency Butler: July 2026
July 22DS 1DS 2

________________________
DS 1

A shopper bought a tie and a belt during a sale. Which item did he buy at the greater dollar value?

(1) He bought the tie at a 20 percent discount.

(2) He bought the belt at a 25 percent discount
________________________
DS 2

­A coat sells for one price in children's sizes and another price in adult sizes. What is the price of 1 coat in an adult size?

(1) A man pays $230 for 1 adult coat and 1 children's coat.

(2) A woman pays $370 for 2 adult coats and 1 children's coat.
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