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Problem Solving Butler: August 2026
August 14PS 1PS 2

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PS 1

When multiplying certain numbers, instead of taking 36 as one of the multipliers, Aman took 63. As a result, the product went up by 810. What is the correct product?

A. 810
B. 1080
C. 1620
D. 1890
E. 2160
____________________
PS 2

­A fruit basket contains the same number of apples and pears. If Eric eats 5 apples and 1 pear, there will be twice as many pears as apples. How many pears remain in the basket?

(A) 4
(B) 8
(C) 9
(D) 11
(E) 12
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Critical Reasoning Butler: August 2026
August 14CR 1CR 2

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CR 1

­Sure Enough Insurance is a large insurance company that has recently been experiencing financial difficulties. Claims are handled by claims coordinators who determine how much, if at all, Sure Enough must pay a policy holder who has made a claim. The aforementioned financial difficulties are forcing Sure Enough to fire 25% of its claims coordinators. To minimize the potentially harmful effects of these cuts, it is recommended that Sure Enough lay off coordinators whose average time of completing work on their assigned claims is the longest.

Which of the following, if true, most seriously calls into question the argument's conclusion?

A. No insurance payments are made by Sure Enough until a claims coordinator has completed work on the claim.

B. Other departments in Sure Enough Insurance do not have any job vacancies.

C. A significant increase in the amount of time it takes Sure Enough claims coordinators to complete work on claims could result in Sure Enough's loss of business to competitors.

D. Sure Enough's policy is to assign complex and lengthy claims to the most competent coordinators.

E. There is no significant difference between the premiums Sure Enough currently charges and those charged by its competitors.
___________________
CR 2

­Plan: As part of its Healthy Students Initiative, Happy Meadows Elementary School decided two years ago to raise its school lunch budget by 20 percent in order to serve healthier food to its students. Result The nutritional quality of Happy Meadows' school lunches is no better now than it was two years ago. Further information: the annual rate of inflation since the budget change has been below 4 percent, and all of the money budgeted for lunches has been received by the school cafeteria.

In light of the further information, which of the following, if true, would best explain the result that followed from the implementation of the plan?

A. The school cafeteria does not receive any outside funding.

B. The cafeteria's ordering process requires that all meals for a semester be planned before the semester starts.

C. The prices of healthy ingredients have increased at a rate much higher than the rate of inflation.

D. When the budget change occurred, the nutritional quality of Happy Meadows' school lunches was at an all-time low.

E. The most recent budget increase was only the second such increase in the last eight years
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Data Sufficiency Butler: August 2026
August 14DS 1DS 2

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DS 1

Maria has $2.45 consisting of coins each worth either $0.05 or $0.25. How many coins worth $0.05 does Maria have?

(1) Maria has fewer than 8 coins worth $0.05 each.

(2) Maria has more than 8 coins worth $0.25 each.
________________
DS 2

Angela and Maria each earn a different regular monthly salary. Each of them has a different percentage of that salary withheld every month by her employer. Is Angela's monthly salary after withholding greater than Maria's?

(1) Angela's monthly salary after withholding is 20 percent less than her regular salary; Maria's monthly salary after withholding is 25 percent less than her regular salary.

(2) Angela's monthly salary after withholding is $1000 less than her regular salary; Maria's monthly salary after withholding is $1200 less than her regular salary.­
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Problem Solving Butler: August 2026
August 17PS 1PS 2

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PS 1

­N workers can finish a job in 15 days. After working 5 days, additional 8 workers joined them. Together, they finished remaining job in 6 days. What is the value of n?

A. 15
B. 18
C. 24
D. 12
E. 9
_____________________
PS 2

Which of the following is equal to 37.5% of 2.4?

A. 0.8
B. 0.9
C. 1.0
D. 1.2
E. 1.5
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Critical Reasoning Butler: August 2026
August 17CR 1CR 2

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CR 1

The Japanese Gardens' coral reef, situated in the western tip of the Arabian Peninsula, is considered one of the most beautiful reefs on earth, contains many fish which are indigenous to it, and exhibits a unique construction of the subterranean landscape. However, it is not among the list of the 50 most visited diving areas.

All of the following may help resolve the seeming discrepancy above EXCEPT:

A. Most of the world's divers are from the Americas, over 7000 miles away from the Arabian Peninsula.

B. Due to severe underwater currents throughout most of the year, the Japanese Gardens can only be accessed during two months of the year.

C. Diving in the Japanese Gardens requires a high level of expertise.

D. While the vast majority of the diving areas on the 50 most visited diving areas' list are accessible from the beach, the Japanese gardens can only be accessed from a boat.

E. As in many of the diving areas on the 50 most visited diving areas' list, one must train for at least two weeks before one can dive in the Japanese Gardens.

________________________
CR 2

­Every year, thousands of students graduate from fine art programs conducted by schools all over the country. Most art galleries and museums, however, only lend about 1% of their exhibit space to unknown contemporary artists. It is clear that a successful career as an artist is more like a fantasy than a possible achievement.

Which of the following, if true, casts the most doubt on the argument's conclusion?

A) Fine art programs have always been popular because they offer students a true opportunity to express themselves.

B) Although some art galleries are government institutions, many are private companies that operate in a similar way to ordinary retailers.

C) The development of the Internet, and communications technology in general, has created a constant need for talented artists of all kinds.

D) Last year, 61% of people under the age of 30 who filed for unemployment benefits had degrees in the fine arts.

E) Because today's art market is a global one, individual artists must compete with thousands of others from all over the world, if they are to become successful.
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Data Sufficiency Butler: August 2026
August 17DS 1DS 2

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DS 1

The cost of each bottle of water is the same and the cost of each bottle of cola is the same. What is the difference in the cost of 1 bottle of water and 1 bottle of cola?

(1) 2 bottles of water and 5 bottles of cola cost $40
(2) 6 bottles of water and 15 bottles of cola cost $120
________________________
DS 2

­Working together, Machine A and Machine B can produce a total of 200 widgets in 4 hours. How many hours would it take Machine A, working alone, to produce 200 widgets?

(1) Working alone, Machine B takes 5 hours to produce 50 widgets.

(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.
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Problem Solving Butler: August 2026
August 19PS 1PS 2

____________________
PS 1

­Your aim is to run a 10km race in 1 hour. During the race, when you pass the 6km mark, you look at your watch and realize that the time elapsed since the start is 40 minutes. What average pace, in minutes per 1000m, should you target for the rest of the race to achieve your time goal?

A. 8
B. 5
C. 6
D. 2
E. 10
____________________
PS 2

­In a leap year that begins on a Tuesday, what is the number of Mondays, Tuesdays, and Wednesdays?

(A) 155
(B) 156
(C) 157
(D) 158
(E) 159
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Critical Reasoning Butler: August 2026
August 19CR 1CR 2

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CR 1

Country X has the world's highest rate of skin cancer, a disease caused mainly by overexposure to ultraviolet (UV) radiation. There are three types of skin cancer: basal cell carcinoma, squamous cell carcinoma, and melanoma. Every year, 2.7% of the population in Country X is diagnosed with basal cell carcinoma, 1.3% with squamous cell carcinoma, and 0.8% with melanoma. The population of Country X buys more sun block than the population of any other country in the world.

Which of the following, if true, contributes most to a resolution of the above paradox?

(A) Ultraviolet radiation in Country X is stronger than anywhere else in the world.

(B) Awareness of the potential damage of exposure to the sun in Country X is high.

(C) Country X is the world leader in sunglasses and hat sales.

(D) The rate of cancer cases other than skin cancer in Country X is lower than the rate of skin cancer.

(E) 3.9% of the population in Country X are diagnosed with bowel cancer.


_______________________
CR 2

­Company X discovered that employees that have lunch before 13:00 are more productive than employees who have lunch after 13:00, or skip lunch altogether. The company management concluded that in order to increase employee productivity, it needs to encourage employees to have their lunch no later than 13:00.

Which of the following, if true, most strongly supports the company's conclusion?

(A) Having lunch at the same time every day is known to increase productivity.

(B) The majority of employees who have lunch before 13:00 are 25-30 year old women.

(C) Jane, who is the most productive employee of Company X, never has lunch before 13:30.

(D) Company Y, a competitor of Company X, which boasts the highest employee productivity rate in the industry, closes its employee dining room at 13:00.

(E) Employees who have lunch after 13:00 are usually not hungry before 13:30.
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Data Sufficiency Butler: August 2026
August 19DS 1DS 2

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DS 1

­A university awarded grants in the amount of either $7,000 or $10,000 to some incoming freshmen. The total amount of all such awards was $2,300,000. Did the university award more $7,000 grants than $10,000 grants to its incoming freshmen?

(1) A total of 275 freshmen received grants in one of the two amounts.
(2) The amount of money awarded in $10,000 grants was $200,000 more than the amount of money awarded in $7,000 grants.

___________________________
DS 2

Of the 9,000 people who voted in a recent election, how many women voted for candidate X?

(1) The percentage of women voting for candidate X was twice the percentage of women voting against candidate X.
(2) 3000 men voted for candidate X.
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