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Problem Solving Butler: May 2025
May 5PS 1PS 2

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PS 1

If x is positive, which of the following may be the correct ordering of \(\frac{1}{x}\), \(x\), \(x^2\), \(x^3\) ?

I. \(\frac{1}{x} < x < x^2 < x^3\)

II. \(\frac{1}{x} < x^3 < x^2 < x\)

III. \(x^3 < x^2 < x < \frac{1}{x}\)

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

______________________
PS 2

If |x| > 5 – 2x, which of the following represents the correct range of values of x ?

A. x > 5/3
B. x > 5
C. 5/3 < x < 5
D. -5 < x < -5/3
E. No such real value of x exists
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Critical Reasoning Butler: May 2025
May 5CR 1CR 2

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CR 1

Over the last fifteen years, the consumption of beef has decreased significantly in many parts of the world. This decrease has coincided with an increasing public awareness of the adverse environmental effects of cattle ranching. Thus, the decrease in beef consumption must have been caused by the consumers’ awareness of the environmentally damaging effects of cattle ranching.

Which of the following, if true, most seriously calls into question the explanation above?

A. On average, people consume twenty percent less beef today than they did fifteen years ago.
B. Habitual beef eaters may suffer mild gastrointestinal distress for a few weeks or so after significantly reducing their beef consumption.
C. Beef prices increased steadily in the last fifteen years because of the degradation of land used to graze cattle.
D. The consumption of poultry, fish, and other forms of seafood has increased over the last fifteen years.
E. Gourmet beef sales have held steady as sales of regular beef have declined.
________________________
CR 2

A promising student of taekwondo once asked his coach how long it would take him to earn his black belt, signifying the end of his training. Thinking carefully, the coach replied, “If you practice three hours a day for six days a week, you could earn your black belt in five years.” Unhappy, the student asked, “What if I practice eight hours a day, every day?” The coach then said, “If you do so, you will probably never move beyond a blue belt.”

The main point that the coach makes here is that in martial arts, a critical value is

A. curiosity
B. patience
C. dedication
D. vigor
E. resolution
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Problem Solving Butler: May 2025
May 5PS 1PS 2

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PS 1

At two specialty food stalls, Green Market and Riverside Market, the prices per kilogram of almonds, walnuts, and pecans were as follows:

Green Market Riverside Market
Almonds $14 $16
Walnuts $16 $18
Pecans $18 $20

Marcus bought certain quantities of almonds, walnuts, and pecans at Riverside Market. How much money would he have saved if he had bought those same quantities at Green Market instead?

(1) The total weight of nuts Marcus bought was 4.5 kilograms.

(2) For every 2 kilograms of walnuts Marcus bought, he bought 3 kilograms of pecans and 5 kilograms of almonds.
_____________________
PS 2

At a certain car dealership, what percent of the cars both weigh more than 1,800 kilograms and cost more than €40,000?

(1) 55% of all the cars at the dealership weigh more than 1,800 kilograms.

(2) Of the cars at the dealership that weigh more than 1,800 kilograms, 20% cost more than €40,000.
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Problem Solving Butler: May 2025
May 6PS 1PS 2

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PS 1

In how many ways can a group of 6 people be divided into three groups, with each group consisting of 2 people?

A. 12
B. 15
C. 60
D. 90
E. 120
________________________
PS 2

In how many ways can 7 different chocolates be distributed among 3 children if each child can get any number of chocolates?

A. 35
B. 84
C. 120
D. 210
E. 2187
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Critical Reasoning Butler: May 2025
May 6CR 1CR 2

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CR 1

The indigenous tribes of the Western Hemisphere were first introduced to horses through the Europeans. The use of horses revolutionized the hunting and transportation capabilities of these tribes. However, tribes that started using horses soon began to suffer from outbreaks of diseases such as salmonellosis, which can be transmitted from horses to humans. Yet, such outbreaks were rare among the Europeans, although they used horses more extensively.

If true, which of the statements below best explains the discrepancy in the outbreak of diseases such as salmonellosis?

A. Generational exposure to domesticated horses allowed the Europeans to develop stronger immune responses to horse borne diseases.
B. Horses raised in Europe were more susceptible to disease than those raised in the Western Hemisphere were.
C. After their introduction into the Western Hemisphere, horses became status symbols among the indigenous tribes, due to the horses’ exotic nature and impressive size.
D. Many Europeans who worked with horses were also exposed to horse borne diseases other than salmonellosis.
E. Before the discovery that horses transmit diseases such as salmonellosis, such conditions were attributed to an imbalance of fluids within the body.
_______________________
CR 2

Economist: Universal Basic Income (UBI) may help mitigate wealth disparity and alleviate socioeconomic issues caused by increased industrial automation in many countries. However, since the long-term feasibility of UBI is unknown, I do not recommend its implementation.

Cabinet Member: This position is quite different from your usual stand. You routinely recommend traditional economic measures that carry a significant risk of failure, so it seems unlikely that feasibility concerns are the true reason behind your reluctance to support UBI.

The flaw in the Cabinet Member’s argument is its failure to take into consideration that

A. the factors that affect the feasibility of UBI are different from those that affect the risk of traditional economic measures
B. the economist may not believe that UBI has been definitively proven to be effective
C. the risk of failure of established measures can be weighed against the benefits of such measures, but the risk of failure of unestablished measures cannot
D. it takes time for the feasibility risks inherent in an economic policy to become apparent
E. if wealth disparity and the socioeconomic issues caused by increased industrial automation are not addressed, they can lead to severe social unrest
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Data Sufficiency Butler: May 2025
May 6DS 1DS 2

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DS 1

Elena left Riverton and drove to Lakehurst, which is 420 kilometers away. At the same time, Marta left Lakehurst and drove along the same route to Riverton. If neither driver ever exceeded the speed limit of 80 kilometers per hour, did Marta reach Riverton before Elena reached Lakehurst?

(1) After 4 hours of driving, they passed each other at a point 140 kilometers from Riverton.

(2) Marta’s average (arithmetic mean) speed for the entire trip was 70 kilometers per hour.
________________________
DS 2

The table below shows the numbers of four pastry box types sold by a bakery in March and in April.

March April
Classic 260 232
Chocolate 180 188
Berry 150 161
Pistachio 210 219

If the selling price of each box type stayed the same from March to April, did the bakery earn more revenue from the sales of these four box types in April than in March?

(1) The Pistachio box was priced lower than each of the other three box types.

(2) The Classic box was priced higher than each of the other three box types.
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