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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.

________________________
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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Problem Solving Butler: May 2025
May 12PS 1PS 2

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PS 1

If x ≠ 0 and -1 < x < 1, among x, 1/x, and x^3, which may be the median?

I. 1/x
II. x
III. x^3

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
____________________
PS 2

If |10 – 3x| < 4, what range of values satisfy x ?

A. -14/3 < x < -2
B. -14/3 < x < 2
C. 2 < x < 14/3
D. x > 2 or x < 14/3
E. x < 2 or x > 14/3
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Critical Reasoning Butler: May 2025
May 12CR 1CR 2

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CR 1

Which of the following best completes the passage below?

In a recent voter survey, forty percent responded that they are somewhat undecided regarding the upcoming presidential election. However, the survey may undervalue the proportion of voters who are undecided, as ______.

A. some who claimed to be somewhat undecided may actually be very undecided
B. some decided voters taking the survey may have claimed that they are not in favor of any candidate
C. some undecided voters taking the survey may have claimed that they are in favor of one candidate
D. some who claimed to be undecided may have done so due to very firmly held opinions
E. some who will not be voting in the upcoming presidential election are probably somewhat undecided

______________________
CR 2

Cash-on-cash return is the ratio of the money earned on an investment in the first year to the total monetary investment, and it is a popular metric by which to express the value of a real estate investment scheme. The higher the cash-on-cash return on an investment, the more likely it is to attract investors. Therefore, a real estate firm that either estimates a higher first year return or allows a lower initial investment requirement will increase the likelihood that an investor will select an investment from the firm over other investment options.

Which of the following, if true, would most strengthen the conclusion drawn above?

A. Increasing both the first year return on an investment and its initial investment requirement without changing its competitive position is possible.
B. For certain types of investors, high initial investment options are preferable to low initial investment options.
C. Investors’ perception of a real estate investment’s first year return is based on real estate firms’ estimates of the first year return on the firms’ investment schemes.
D. The competitive position of a real estate investment can be affected by such factors as marketing and the reputation of the firm offering the investment.
E. Competing real estate investments are often geared towards appealing to different segments of the population of investors.
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Data Sufficiency Butler: May 2025
May 12DS 1DS 2

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DS 1

A city volunteer program recorded whether each of its 480 volunteers held each of three certifications: logistics, first aid, and radio operation. Every volunteer with first-aid certification also had logistics certification, and no volunteer held all three certifications. If 90 volunteers held only the radio-operation certification, how many volunteers held exactly two of the three certifications?

(1) 70 volunteers held only the logistics certification.
(2) 30 volunteers held none of the three certifications.
___________________
DS 2

A lab technician mixed two salt solutions, Solution A and Solution B. Solution A contained 12% salt, and Solution B contained 4% salt. If the resulting mixture contained 7% salt, how many liters of Solution A were used?

(1) The technician used 20 liters of Solution B.
(2) The resulting mixture was 32 liters.
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Problem Solving Butler: May 2025
May 13PS 1PS 2

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PS 1

Letters of the word “POLITICS” are shuffled to form all possible distinct combinations. In how many cases does ‘P’ come before ‘O’, and ‘O’ come before ‘L’?

A. 360
B. 720
C. 2520
D. 3360
E. 6720
________________________
PS 2

In a sequence S, each term, after the first term, is obtained by multiplying the previous term by a constant k, where k is an integer other than 1. If the 6th term of the sequence is 243 and the 3rd term is –9, what is the sum of the first five terms of the sequence?

A. 103
B. 101
C. -59
D. -61
E. -91
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Critical Reasoning Butler: May 2025
May 13CR 1CR 2

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CR 1

Management consultant: It is broadly true that pharmaceutical firms that employ sales representatives to persuade doctors to prescribe certain medications charge less for their products than do those that do not employ sales representatives. It is also true that each time the restrictions on the use of pharmaceutical sales representatives have been relaxed, the number of firms employing sales representatives has increased, and consequently, medical costs to consumers have declined. However, eliminating the requirement that the sales representatives must provide a detailed report comparing prices of their products with those of competing products would almost certainly increase rather than decrease medical costs. The firms would no longer be incentivized to lower drug costs when they begin employing sales representatives and if no longer required to provide the necessary price comparison report, many firms that now employ sales representatives would increase the medications’ price.

In the management consultant’s argument, the two portions in boldface play which of the following roles?

(A) The first is a generalization accepted as true by the management consultant; the second is presented as a consequence that follows from the truth of that generalization.
(B) The first is a cause-effect pattern that the management consultant predicts will not hold in the case at issue; the second offers a consideration supporting that prediction.
(C) The first is a cause-effect pattern that the management consultant argues will repeat in the case at issue; the second recognizes a circumstance in which that pattern would not hold.
(D) The first is evidence offered by the management consultant in support of a certain prediction; the second is that prediction.
(E) The first recognizes a consideration that weighs against the main position that the management consultant defends; the second is that position.

_________________________
CR 2

Public-private partnerships are cooperative arrangements wherein government and private sector entities work together to complete a project or provide a service to the population. Since the core purpose of the government is to provide material resources and services to ensure the well-being of the public, any task that can be performed more efficiently through a public-private partnership should be done so.

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

A. If the government decides to work with private sector entities on a project or service, it can usually take advantage of the strong competition that arises among the multiple firms interested in working on that project or service.
B. When a government agency decides to partner with a private entity on a project or service, the private entity sometimes hires government employees who formerly worked on similar projects and services.
C. Certain tasks, such as construction, are commonly conducted through public-private partnerships, whereas others such as defense and law enforcement are not.
D. For a government agency to manage a product or provide a service as effectively as a private sector entity can, the officials involved need to be experts in the relevant areas, as the people in charge of the same at the private entity are.
E. A successful public-private partnership requires the government to provide the private sector entity with information about the population that the private sector entity can potentially use to exploit people.
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Data Sufficiency Butler: May 2025
May 13DS 1DS 2

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DS 1

At a one-day music workshop, some registered participants attended the morning session, and some attended the afternoon session. If 40% of the registered participants did not attend the morning session, what percent of the registered participants attended the afternoon session?

(1) Of the registered participants who attended the morning session, 1 out of every 4 attended the afternoon session.

(2) The number of registered participants who attended the morning session but did not attend the afternoon session was 3 times the number of registered participants who attended neither session.

_______________________
DS 2

Lena and Marco are hired to paint a fence at a community park. If each of them paints at a constant rate, does Lena, working alone, take more time than Marco, working alone, to paint 120 square meters of the fence?

(1) Lena, working alone, would take 6 more hours to paint 18 square meters of the fence than Marco, working alone, would take to paint 6 square meters of the fence.

(2) Lena, working alone, would take twice as long to paint 4 square meters of the fence as Marco, working alone, would take to paint 1 square meter of the fence.
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Problem Solving Butler: May 2025
May 14PS 1PS 2

______________________
PS 1

If x is positive, which of the following may be the correct ordering of x, x^2, x^3 ?

I. x < x^2 < x^3
II. x^3 < x < x^2
III. x^3 < x^2 < x

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
______________________
PS 2

If |3x + 2| < 20 – x, which of the following reflects the range(s) of all possible values of x ?

A. x > 9/2
B. x < -11
C. -9/2 < x < 11
D. x > 9/2 or x < -11
E. -11 < x < 9/2
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