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Problem Solving Butler: May 2025
May 11PS 1PS 2

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PS 1

A six–faced dice is thrown five times. What is the probability of getting a six exactly two times?

A. 5^3/6^5

B. (10 x 5^3)/6^5

C. (15 x 5^3)/6^5

D. (30 x 5^3)/6^5

E. 1/6^2

______________________
PS 2

The format of a soccer tournament is as follows:

Two pools contain four teams each. Each team in a pool plays a game with all the other teams in the pool. The top two teams in each pool reach the semi–finals. The top team from one pool plays the second team from the other pool. The winners of the semi–finals play each other for finals and the losers of semi–finals play each other for the third spot. In all, how many games are played in the tournament?

A. 14
B. 15
C. 16
D. 27
E. 28
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Critical Reasoning Butler: May 2025
May 9CR 1CR 2

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CR 1

The Patrolling Police is a sitcom that deals with funny situations that policemen often get into. The sitcom is so poorly made - with half-baked stories, poor actors, and immature direction – that most people poke fun at it. However, the sitcom still enjoys a wide viewership. This paradox has perplexed many who assumed that a sitcom has to be well made for it to be successful.

Which one of the following, best explains the paradox mentioned above in the argument?

A) People who watch TV for more than eight hours a day account for a large portion of viewership enjoyed by The Patrolling Police.
B) There are no other popular shows run during the time when The Patrolling Police is aired every night.
C) People who follow family-oriented TV shows do not prefer to watch The Patrolling Police.
D) TV show viewership surveys are not accurate because people tend to overemphasize their viewing habits.
E) People watch The Patrolling Police to poke fun at it.

____________________________
CR 2

Typically, newspapers run only a few in-depth and complex stories in each issue. In-depth and complex stories represent a higher standard of journalism but do not attract as many subscribers. However, this year in-depth and complex stories are the ones that newspapers have published most often- a clear sign that newspapers are assigning more importance to achieving a higher standard of journalism than to attracting subscribers.

Which of the following, if true, most seriously weakens the argument above?

A. This year’s bestselling newspaper has not published any in-depth and complex stories.
B. No newspaper has publicized that it would be prioritizing achieving a higher standard of journalism this year.
C. Because of changing market trends, the stories that attracted the most subscribers this year were more complex and in-depth than most others.
D. Because of declining interest in newspapers, all types of stories attracted fewer subscribers than in any previous year.
E. Subscription rates were lower this year than they had been in most of the years when in-depth and complex stories were rarely published.
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Data Sufficiency Butler: April 2025
May 11DS 1DS 2

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DS 1

A warehouse manager recorded the weights of all the crates in one shipment. How many crates were in the shipment?

(1) The average (arithmetic mean) weight and the median weight of the crates in the shipment were both 18 kilograms.

(2) In the shipment, one crate weighed more than 18 kilograms, and one crate weighed less than 18 kilograms.

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DS 2

During a trivia contest, Sophia completed a set of trivia questions. Each question in the set could have been answered correctly, answered incorrectly, or left unanswered. If a correct answer was worth 5 points, an incorrect answer reduced the score by 3 points, and an unanswered question reduced the score by 2 points, did the set contain fewer than 7 questions?

(1) Sophia’s final score was 18 points.

(2) Sophia answered at least one question correctly, answered at least one question incorrectly, and left at least one question unanswered.
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