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Critical Reasoning Butler: May 2025
May 25CR 1CR 2

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CR 1

In the year 1900, the average household net worth, the mean totality of wealth per one family unit, in Zeneru was $10,000, whereas, in the year 2000, accounting for inflation, it was $30,000. Thus, in 1900, people must have been considered middle class at a net worth that was considered poor in 2000.

Which of the following, if true, undermines the argument above?

A. In 1900, Zeneru’s population was considerably smaller than it was in 2000.
B. In 1900, more Zeneru residents engaged in manual labor than in 2000.
C. Many of the people who built up a considerable net worth in 2000 were only able to do so thanks to advanced technology that was unimaginable in 1900.
D. The proportion of households with a net worth below $10,000 was significantly smaller in 2000 than was the proportion of households with a net worth above $10,000.
E. Most of the gains in average net worth between 1900 and 2000 came from large numbers of Zeneru citizens who had moved out of the lowest levels of poverty.
______________________
CR 2

Demand made by Scottish floriculturist: Tariffs need to be imposed on less expensive flowers grown outside Scotland to maintain the price of flowers in this country; otherwise, our farms will be unable to stay in business.

Response from a Scottish florist: Scottish retailers and other businesses purchase about eighty percent of the flowers grown in Scotland. If the prices we pay are not competitive with those in Europe, our sales will drop, and then the demand for Scottish flowers will go down.

If the factual information presented by both companies is accurate, the best assessment of the logical relationship between the two arguments is that the florist’s argument

A) is self-serving and irrelevant to the proposal of the floriculturist
B) is circular, presupposing what it seeks to prove about the proposal of the floriculturist
C) establishes that even the floriculturist’s business will prosper if the floriculturist’s proposal is rejected
D) fails to give a reason why the proposal of the floriculturist should not be put into effect to alleviate the concern of the floriculturist for staying in business
E) shows that the proposal of the floriculturist would have a negative effect on the floriculturist’s own business
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Data Sufficiency Butler: May 2026
May 25DS 1DS 2

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DS 1

A tutoring center pays Clara each week for grading practice tests. In a given week, she earns p dollars for each of the first 24 tests she grades and p + 8 dollars for each test she grades beyond the first 24. If Clara graded 27 tests last week, what is the value of p?

(1) Clara earned 3p + 24 dollars for the tests she graded beyond the first 24.
(2) If Clara had graded 35 tests last week instead of 27 tests, she would have earned 8p + 64 dollars more.
____________________
DS 2

A cyclist followed a two-leg route from a riverside park to a lookout point. If the second leg of the route was twice as long as the first leg, what was the cyclist’s average (arithmetic mean) speed for the entire route?

(1) The cyclist’s average (arithmetic mean) speed was 12 kilometers per hour on the first leg and 24 kilometers per hour on the second leg.
(2) The cyclist spent the same amount of time on the first leg as on the second leg.
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Problem Solving Butler: May 2025
May 26PS 1PS 2

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PS 1

Palindrome is a number that reads the same right to left as it does left to right. For example: 2332. How many five–digit numbers are palindromes?

A. 450
B. 900
C. 1000
D. 1200
E. 1800

______________________
PS 2

An arithmetic progression is one wherein each subsequent term is the sum of the preceding term and a constant. If a, b, c, d, e, f, g, and h are eight integers in arithmetic progression with four of these terms being odd, which of the following may be true about the eight integers?

I. The average is not an integer.
II. The median is not an integer.
III. The sum of the average and median is an even integer.

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
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Critical Reasoning Butler: May 2025
May 26CR 1CR 2

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Dog breeders do not typically look to breed dogs that have unique appearances or exceptional intelligence, as there is little demand for such dogs. The only dog-owners willing to pay for dogs that have been bred to possess a unique combination of traits are those who intend to compete in dog shows. Therefore, innovation in dog-breeding is limited by what dog-show organizers consider attractive attributes.

Which of following is an assumption made in drawing the conclusion above?

A) The market for typical dog breeds cannot expand unless the market for specially bred dogs expands.
B) Dog breeding methods are likely to be improved more as a result of innovations developed by independent breeders than as a result of innovations developed by large pet companies.
C) Dog show organizers do not consider the possibilities offered by advanced breeding techniques when they determine what traits they find attractive in a dog.
D) Dog breeders lack interest in innovation primarily because they desire to breed dogs that can be reared easily by the average pet owner.
E) Dog show competitors do not produce a strong demand for innovations other than what is considered attractive by dog show organizers.

_______________________
CR 2

Last year the total amount of bonuses offered by Xio Technologies reached a historic peak, and many are wondering if that record will be surpassed this year. Now, any bonus is received either by existing employees during their annual appraisals or by new employees in the form of a joining bonus. This year, the management has not been as generous in awarding annual bonuses as it was last year. Additionally, the recruitment calendar for this year indicates that the number of new employees joining the firm will be lower this year than it was the previous year, and new recruits this year will definitely receive no higher joining bonus than did those who joined last year. Hence, it can be established that the total amount of bonuses distributed this year will not outdo last year’s record.

In the argument given, the two portions in boldface play which of the following roles?

(A) The first is a claim challenged by the argument; the second is an explicit assumption that the challenge is based on.
(B) The first is a claim challenged by the argument; the second is a judgment advanced in support of the argument’s main conclusion.
(C) The first provides evidence in support of the argument’s main conclusion; the second is a judgment advanced in support of that main conclusion.
(D) The first provides evidence that supports the argument’s main conclusion; the second is an objection that has been raised against that main conclusion.
(E) The first and the second are each claims that have been advanced in support of a position opposed by the argument.
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Data Sufficiency Butler: May 2026
May 26DS 1DS 2

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DS 1

At the beginning of 2024, Elena divided $1,200 between two savings accounts, Account A and Account B. The amount placed in Account A earned simple interest at 9% per year, and the amount placed in Account B earned simple interest at 5% per year. If no additional deposits or withdrawals were made in either account, by the end of 2024 was the interest earned by Account A greater than the interest earned by Account B?

(1) Elena placed less than one-third of the $1,200 in Account A.

(2) By the end of 2024, the total interest earned by the two accounts was $74.

____________________
DS 2

At a training center, 4 interns and 6 mentors took the same certification test. What was the average (arithmetic mean) score of all 10 test-takers?

(1) The total score of the mentors was 180 points, and the average score of the interns was 5 points less than the average score of the mentors.
(2) If one of the interns had scored 20 points more, the average score of all 10 test-takers would have been 30.
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Problem Solving Butler: May 2026
May 27PS 1PS 2

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PS 1

In how many ways can 5 different balls be distributed among 3 children such that each child gets at least one ball?

A. 540
B. 360
C. 240
D. 180
E. 150
_______________________
PS 2

If |3 – x| < x + 5, which of the following must be true about x?

I. x > -2
II. x < 2
III. x > -1

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
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Critical Reasoning Butler: May 2026
May 27CR 1CR 2

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CR 1

Insurance Agent: Unlike most of our competitors, People Care Insurance offers employee incentives based on customer satisfaction rather than on sales numbers, meaning our salespeople have no incentive to sell the most expensive coverage package and have every incentive to meet your unique needs. Thus, when you buy insurance from us, you can be sure that you are not paying for coverage that you do not need.

Which of the following would, if true, most weaken the insurance agent’s reasoning?

A. Some cheaper coverage packages actually offer better coverage than do the more expensive ones.
B. Salespeople with a financial incentive to make higher sales typically provide more attentive service than do other salespeople.
C. People Care Insurance does not sell any basic coverage packages.
D. People Care Insurance is often understaffed, making it difficult for clients to fully discuss their concerns and options.
E. Ancillary benefits that come with less expensive coverage packages can be worth nearly as much as the package itself.
____________________
CR 2

Which of the following most logically completes the argument below?

The atmosphere exerts less pressure as altitude rises above sea level. Since the boiling point of all liquids decreases alongside air pressure, those who have scaled Everest have reported that water boils very quickly at the peak. The boiling point of water at any given pressure can be determined and the pressure for any altitude can be mathematically calculated. Therefore, physicists can determine the boiling point of water at the summit of Everest, since _______.

A. air pressure at sea level is higher than air pressure above sea level
B. air currents sometimes carry pressure from lower points in the atmosphere to higher points
C. the exact height of the summit is known
D. air pressure cannot be directly measured anywhere in the atmosphere
E. the boiling point of water is higher at sea level than it is above sea level
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Data Sufficiency Butler: May 2026
May 27DS 1DS 2

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DS 1

At a community center’s weekend open house, 360 registered visitors had access to two optional sessions: a gardening workshop and a budgeting seminar. How many of the registered visitors attended both sessions?

(1) Of the 360 registered visitors, 140 attended the gardening workshop, and 180 attended the budgeting seminar.

(2) The number of registered visitors who attended neither session was 40 greater than the number who attended both sessions.
______________________
DS 2

At a music audition, judges assigned scores to 9 applicants. Among the applicants, 3 tied for the lowest score of 14 points, and 2 tied for the highest score of 65 points. If the median score of the 9 applicants was 50 points, what was the average (arithmetic mean) score of the 9 applicants?

(1) If the applicants who received 14 points or 65 points are not considered, the median score of the remaining applicants is 56 points.

(2) If the applicants who received 14 points or 65 points are not considered, the range of the remaining scores is 12 points.
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Problem Solving Butler: May 2026
May 28PS 1PS 2

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PS 1

Ida had five cards with matching envelopes – same in design, different in color. She removed the cards from all envelopes and randomly put them back. What is the probability that exactly one card got into the matching envelope?

A. 3/16
B. 5/8
C. 3/8
D. 1/4
E. 1/2

_______________________
PS 2

A set has ten positive integers – six even and four odd. Two integers are picked randomly and multiplied. What is the probability that the product is even?

A. 2/15
B. 7/15
C. 8/15
D. 2/5
E. 13/15
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Critical Reasoning Butler: April 2026
May 28CR 1CR 2

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CR 1

Archaeological examination of the ancient city of Helike, located in Achaea, revealed a pattern of geological damage and collapsed buildings that resembles the pattern formed after tsunamis level down settlements. Thus, archaeologists have theorized that the destruction was caused by a well-documented tsunami that struck Acahea in 373 BCE.

Which of the following, if true, most strongly supports the archaeologists' hypothesis?

A. Ceramic funeral urns that are often found in graves dating from years before and after 373 BCE were also found in several graves near Helike.
B. Inscriptions utilizing a form of the Hellenic alphabet that was certainly used in Achaea after 373 BCE were found in Hellike.
C. Most contemporary accounts of Achaean history mention that a severe tsunami struck the region in 373 BCE.
D. Several coins minted in styles current in Achaea in the century between 350 BCE and 200 BCE were found in Helike.
E. Excavation in Helike found fragments of pottery created before 373 BCE in abundance but did not find any fragments of pottery created after 373 BCE.
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CR 2

Opioid painkillers, such as oxycodone, are administered intravenously, meaning they are injected directly into the bloodstream. Such painkillers must be injected intravenously because if taken by any other method, the opioids will be processed by the liver before the opioids enter the bloodstream, rendering them useless by the time they reach their target cells. Certain non-opioid painkillers, however, contain chemical agents that are not processed by the liver. Therefore, such non-opioid painkillers can be administered in several different ways.

The statements above most strongly support a claim that the research accomplishment of which of the following would be beneficial to the users of opioid painkillers?

A. Determining, in a systematic way, what chemicals are naturally found in the human bloodstream and whether they tend to be processed by the liver.
B. Chemically altering, by procedures that work in the laboratory, the non-opioid painkillers that are not processed by the liver into opioids.
C. Permanently rendering the liver incapable of processing painkillers.
D. Combining oxycodone with compounds that prevent oxycodone from being processed by the liver but do not affect how target cells react to oxycodone.
E. Determining the amount of time each non-opioid painkiller takes to reach its target cells.
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Data Sufficiency Butler: May 2026
May 28DS 1DS 2

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DS 1

A delivery van traveled from Westport Depot to Lakeview Market in 7 hours. If the trip consisted of a 4-hour first leg at one constant speed and a 3-hour second leg at a different constant speed, what was the van’s average (arithmetic mean) speed for the entire trip?

(1) If the van had traveled for 8 hours at its first-leg speed and for 6 hours at its second-leg speed, it would have traveled 700 kilometers.
(2) If the van had traveled for 1 hour at each of those two speeds, it would have traveled 110 kilometers.
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DS 2

A juice bar mixed apple juice and berry concentrate to make 6 liters of a fruit drink. If apple juice cost $4 per liter, and berry concentrate cost $10 per liter, was the volume of apple juice used greater than the volume of berry concentrate used?

(1) Less than 4 liters of berry concentrate were used.

(2) The total cost of the apple juice and berry concentrate used to make the 6 liters of fruit drink was less than $39.
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