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Problem Solving Butler: February 2025
February 20PS 1PS 2

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PS 1

x is the sum of the cubes of reciprocals of the first 50 positive integers. Which of the following is true ?

A. 0 < x < 1
B. 1 < x < 1.4
C. 1.4 < x < 1.8
D. 1.8 < x < 2
E. x > 2

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PS 2

Which is the smallest integer, greater than 1, to leave a remainder of 1 when divided by each of the first five prime numbers?

A. 211
B. 421
C. 1891
D. 2311
E. 2371
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Critical Reasoning Butler: February 2025
February 20CR 1CR 2

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CR 1

One potential solution to the problem of road congestion in Gainley county is to provide rail transit between major city centers lying 50 to 80 miles apart. Successfully implementing this plan would cost far less than expanding existing roads and would reduce the number of cars clogging up both roads and parking spaces.

Which of the following, if true, could proponents of the plan above most appropriately cite as a piece of evidence for the soundness of their plan?

A. Major repairs to Gainley’s intercity road network would be necessary for building an effective rail transit system.
B. A large proportion of drivers are from outside Gainley and are traveling over 100 miles to visit Gainley’s major city centers.
C. Over 60 percent of all drivers departing from rural areas of Gainley county are driving to rural destinations over 90 miles away.
D. Several new express roads are being built in areas that are currently served by rail transit systems.
E. The majority of vehicles leaving Gainley’s biggest city center heads for a destination in another major city center about 65 miles away.

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CR 2

Adaptive reuse is the practice of converting an existing building to serve a purpose other than its original one and is widely seen as a preferable and economical alternative to tearing down defunct buildings. Adaptive reuse is profitable, as demonstrated by the reuse programs already in operation. A city official has suggested requisitioning funds for a project that would ensure that sixty percent of all defunct buildings in the city are converted to a new purpose within ten years.

Which of the following, if true, most seriously calls into question the advisability of implementing the proposal?

A. Existing adaptive reuse programs have been voluntary, with the property owners being willing to invest heavily in the projects.
B. Many of the buildings that cannot be reused are also difficult to tear down.
C. Existing adaptive reuse programs have had recurrent difficulties in finding buyers for their buildings because many buildings are far from one another and are, therefore, unsuitable for most buyers wanting to have a presence in all areas of the city.
D. Some of the buildings that are candidates for adaptive reuse are the ones that can most easily be torn down and built over.
E. Existing adaptive reuse programs have been limited to the approximate twenty-five percent of defunct buildings that can feasibly be refurbished to match new buildings in utility and price.
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Data Sufficiency Butler: February 2025
February 20DS 1DS 2

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DS 1

The rate at which a certain investment appreciates is R. If R is a function of the federal interest rate i, such that R = xi^3 + yi^2 + z, where x, y, and z are constants and i > 0. Is there a value of i for which R is 0?

(1) x > y > z
(2) x > 0

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DS 2


The table shows the distribution of revenue for a chain of 56 stores. Is the range of the revenue greater than $32,000?

(1) The highest-earning store generated $62,000 in revenue.
(2) The lowest-earning store generated $25,000 in revenue.
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Reading Comprehension Butler: February 2025
February 20RC 1
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Problem Solving Butler: February 2025
February 23PS 1PS 2

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PS 1

Three alloys - A, B, and C contain only Copper and Zinc in the ratio 1:2, 2:3, and 1:4 respectively. The three alloys are mixed in the ratio 2:3:5 to form a new alloy. What is the ratio of Copper and Zinc in the new alloy?

A. 29 : 61
B. 37:59
C. 43:107
D. 61:29
E. 107:43
_______________________
PS 2

In a class of 75, each student is enrolled for at least one of the three sports - Soccer, Hockey, or Baseball. 39 students are enrolled for Soccer, 29 are enrolled for Hockey, and 35 are enrolled for Baseball. If 7 students are enrolled for all the three, how many students are enrolled for exactly two of the three sports?

A. 7
B. 14
C. 17
D. 21
E. 28
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Critical Reasoning Butler: February 2025
February 23CR 1CR 2

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CR 1

Gaida and Carcassa are two neighboring cities in Lamoraland; the average net worth of residents of Gaida is $100,000, and the average net worth of residents of Carcassa is $120,000. Therefore, if a newlywed couple from Gaida moved to Carcassa before starting a family, their children would be expected to accumulate a greater net worth than if the family had remained in Gaida.

Which of the following, if true, would most seriously weaken the conclusion drawn in the passage?

A. Carcassa is home to a many of the richest Lamoralanders who inherited wealth from their forefathers.
B. The Mayor of Gaida has falsely claimed that statistics published regarding his city are inaccurate.
C. Financial planners do not believe that moving to Carcassa will significantly improve the net worth of the average Gaidan.
D. Twenty percent of all Gaidans can expect to accumulate a net worth of $250,000.
E. Most regions of Carcassa have a minimum wage higher than the average minimum wage in Gaida.

__________________________
CR 2

Galen: I do not think I shall take up a factory job with Agone Industries. The company is not concerned with ensuring the safety of its workers.

Arie: But, last month the company proactively agreed to adhere to the government’s latest round of worker safety requirements.

Galen: If Agone Industries has proactively agreed to adhere to safety requirements, these requirements must not be very stringent.

The biggest logical flaw in Galen’s reasoning is identified by which of the following?

A. The facts put forward by Galen do not support the claim that Agone Industries is not concerned with ensuring the safety of its workers.
B. Galen assumes without any logical basis that worker safety is the most important factor to be considered in deciding whether to accept a factory job.
C. In making the choice to not accept the factory job, Galen does not consider any issue besides worker safety.
D. Galen attacks Agone Industries on moral grounds rather than on its commitment to worker safety.
E. Galen employs circular logic, employing an unsubstantiated assertion to dismiss the validity of information that weakens his argument.
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Data Sufficiency Butler: February 2025
February 23DS 1DS 2

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DS 1

The regular ticket price for a certain showing of a film was $30, but loyalty card holders paid a discounted price of only $20. Last Tuesday, what was the ratio of the number of discounted tickets to the number of regularly priced tickets purchased for the showing?

(1) Last Tuesday, the total sale of all tickets for the showing was $4,800.
(2) Last Tuesday, the ratio of total discounted ticket sale for the showing to the total regular ticket sale was 2 to 5.
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DS 2

If Kyle’s total post-tax income in 2009 was $64,000, what was his total post-tax income in 2014?

(1) Kyle’s pre-tax income in 2014 was 50 percent more than that in 2009.
(2) Kyle paid 40 percent more in taxes in 2014 than what he did in 2009.
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NEW - Reading Comprehension Butler!

Reading Comprehension Butler: February 2025
February 23RC 1
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