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Problem Solving Butler: December 2025
December 30PS 1PS 2

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PS 1

If y = 160x + 42, where x is a positive integer, which of the following cannot be a factor of y?

I. 14
II. 28
III. 42

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

Which of the following represents the value of 15! ?

A. 2^7 x 3^5 x 5^3 x 7^2 x 11^1 x 13^1
B. 2^9 x 3^4 x 5^2 x 7^2 x 11^1 x 13^1
C. 2^10 x 3^5 x 5^3 x 7^2 x 11^1 x 13^1
D. 2^11 x 3^4 x 5^3 x 7^2 x 11^1 x 13^1
E. 2^11 x 3^6 x 5^3 x 7^2 x 11^1 x 13^1
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Critical Reasoning Butler: December 2025
December 30CR 1CR 2

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CR 1

Which of the following most logically completes the argument below?

Standard dumpsters found in suburban neighborhoods next to forested land attract racoons, as the racoons forage for discarded food in the dumpsters at night. The racoons, in turn, attract foxes and bobcats, their natural predators who feed primarily on the racoons, into the neighborhoods. The town of Bonne’ Borough intends to rectify this situation by replacing their current dumpsters with lockable ones that will not attract racoons. This change is likely to result in a drop in the population of foxes and bobcats in Bonne’ Borough, since __________.

A. without a local concentration of the racoons on which foxes and bobcats prey, these predators expend much more energy on hunting, requiring much more prey for each fox and bobcat
B. foxes and bobcats are not likely to prey on other animals that might be attracted to the dumpsters
C. the sanitation department is capable of replacing the current dumpsters with lockable ones within a relatively short time and without disrupting regular sanitation services.
D. foxes and bobcats do not start hunting before sundown
E. foxes and bobcats primarily rely on smell to track prey and therefore gain no advantage from the fact that there is more light in the neighborhoods than in the forested land
__________________________
CR 2

Smithson University’s English department recently found that, because the Literary Analysis elective is not particularly relevant to contemporary society, the elective attracted few students. So, to attract more students to the literary analysis elective, the department proposed a curriculum emphasizing the use of literary analysis in producing articles of mass media and understanding their impact on the consumer.

Which of the following, if true, provides the strongest reason to expect that the proposed curriculum will be successful in attracting students?

A. Several of the foundational principles of literary analysis are involved in producing articles of mass media and understanding their impact on the consumer.
B. Knowledge of literary analysis is becoming increasingly important in understanding the role of mass media in contemporary society.
C. In contemporary society, the production of articles of mass media and the understanding of how they impact the consumer is of major importance in business, politics, and recreation.
D. Fewer students are interested in literary analysis today than there were 20 years ago.
E. An executive at a major mass media publisher has offered to deliver a guest lecture that could be useful in explaining the proposed curriculum.
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Data Sufficiency Butler: December 2025
December 30DS 1DS 2

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DS 1

In a class of 80 students, how many students play volleyball?

(1) 55 students in the class play basketball.
(2) The number of students playing both basketball and volleyball is equal to the number of students playing neither.
______________________________
DS 2

Of the students who dine in a cafeteria, each student either likes or dislikes coffee and each student either likes or dislikes tea. Of these students, 50% dislike coffee; of those who dislike coffee, 1/3rd also dislike tea. How many students like tea but dislike coffee?

(1) 240 students dine in the cafeteria.
(2) 120 students like coffee.
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Data Sufficiency Butler: December 2025
December 31DS 1DS 2

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DS 1

In a group, everybody speaks English or French. What percentage of members speak only English?

(1) 80% members speak English.
(2) 60% members speak French.
____________________________
DS 2

Mitchell intends to deposit for a year, $10,000 in a savings account in either LeMarche Brothers Bank or Orion Bank. The rate of interest offered by LeMarche Brothers Bank is x percent per year, and the rate of interest offered by Orion Bank is y percent per year. If x > y, how much more interest will Mitchell earn if he saves his money with LeMarche Brothers Bank rather than with Orion Bank?

(1) x = y + 1.5
(2) x = 1.5y
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Critical Reasoning Butler: December 2025
December 31CR 1CR 2

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CR 1

If the state’s construction firms continue to harvest wood at the current pace, all viable tree farms will soon be exhausted, and woodlands will need to be used to maintain a steady supply of wood. Levying heavy taxes on each ton of wood harvested will induce the firms to reduce their consumption; these taxes will, therefore, protect the state’s woodlands.

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

(A) The construction firms will reduce the amount of wood they consume by reducing the number of projects they take on.
(B) The taxes will not significantly affect the profits of most construction firms, even if they do not reduce the amount of wood they consume.
(C) Tree farms outside the state’s borders could be used as a source of wood for the state’s construction industry.
(D) Most of the state’s residents consider the beauty of the woodlands an important issue.
(E) The taxes will not induce the construction firms to illegally harvest wood from the woodlands.

_______________________________
CR 2

Angel investors are protected from the legal liabilities of labor violations committed by the startups they invest in. A lawyer argues that this protection is in part why the rate of labor violations in startups is so high, as it negates any motivation on the part of the investor to determine whether the startups manage their employees ethically. If angel investors were more selective, startups would have to display compliance with labor laws to secure capital from them.

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

A. Before angel investors were protected from the legal liabilities incurred by the startups they invest in, there were fewer labor violations in startups than there are now.
B. The liability of an angel investor for labor violations committed by a startup in which the investor has invested depends on the level of involvement the investor has with the startup.
C. Most angel investors are well aware that they are protected from the legal liabilities of labor violations committed by the startups they invest in.
D. There is an upper limit to the amount of involvement an angel investor can have with a startup, while maintaining protection from the legal liabilities of labor violations committed by the startup, but few exceed this limit.
E. When angel investors were not protected from the legal liabilities incurred by the startups they invest in, frequent labor violations occurred in startups as a result of the lack of capital with the startups.
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Problem Solving Butler: December 2025
December 31PS 1PS 2

_______________________________
PS 1

The number 11 can be written as the sum of the square roots of four different positive integers. What is the sum of these positive integers?

A. 37
B. 39
C. 41
D. 46
E. 54
_______________________________
PS 2

Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 19 / 17
B. 133 / 60
C. 19 / 112
D. 17 / 48
E. 177 / 320
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hi everyone.....
Happy some last hour of this year :):):):)
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Problem Solving Butler: January 2025
January 1PS 1PS 2

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PS 1

Both a and b are perfect squares, and the product a x b is divisible by 10 as well as by 15. By which of the following, the product a x b may not be divisible ?

A. 300
B. 150
C. 125
D. 50
E. 20
_____________________________
PS 2

What are the last two digits (at tens place and units place) in the total numerical value of the following product?

243 * 8770 * 3137 * 7789 * 58263 * 3177 * 9931

A. 10
B. 30
C. 50
D. 70
E. 90
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Critical Reasoning Butler: January 2025
January 1CR 1CR 2

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CR 1

Like most manufacturers of high-end racing bicycles, Pedal Max earns most of its profits on replacement parts rather than on the bicycles themselves. As Pedal Max cannot sell its replacement parts as cheaply as other manufacturers can, it plans to redesign its high-end racing bicycles so that they will accept only newly-designed Pedal Max replacement parts, which will be sold at the same price as Pedal Max’s current replacement parts.

Which of the following, if true, most strongly supports Pedal Max’s projection that its plan will lead to an increase in its sales of replacement parts?

A. The new Pedal Max high-end racing bicycles will be introduced at prices higher than the prices Pedal Max charges for its current bicycle models.
B. It is likely that, in the foreseeable future, high-end racing bicycle manufacturers will have to increase the prices charged for replacement parts.
C. According to comprehensive market research, riders of high-end racing bicycles find the new Pedal Max bicycles considerably better than other high-end racing bicycles they had ridden.
D. A rival to Pedal Max recently announced similar plans to introduce high-end racing bicycles that will accept only the replacement parts produced by that rival.
E. The newly designed Pedal Max replacement parts will cost a bit more to manufacture than Pedal Max’s current replacement parts do.
___________________________
CR 2

Film critic: Last year, fewer articles analyzing French films were published in journals of film studies than in previous years. The total number of films produced in France dropped considerably the year before last, so it is likely that the low number of articles was due to the decline in the total number of films made in France.

Which of the following, if true, most seriously undercuts the film critic’s argument?

A. Every article analyzing French films that was submitted for publication last year was actually published.
B. Over the last several years, the availability of French films to international film academics has fallen.
C. Recently, the editorial policies of several journals of film studies were changed, decreasing the likelihood that articles concerning French films will be accepted for publication.
D. Films in languages other than French are produced in France, every year.
E. The number of journals of film studies was the same last year as in previous years.
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Data Sufficiency Butler: January 2025
January 1DS 1DS 2

______________________________
DS 1

In a class of 100 students, how many students play volleyball?

(1) 60 students in the class play basketball and 24 students play volleyball but not basketball.
(2) The number of students who play both basketball and volleyball is equal to the number of students who play neither.
______________________________
DS 2

$30,000 were invested into an index fund on January 1, 2010. During what year did the value of this fund exceed $40,000?

(1) The investment rose in value by 10 percent each year.
(2) On January 1, 2015, the value of the investment was $48,315.3
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Problem Solving Butler: January 2025
January 2PS 1PS 2

______________________________
PS 1

5^n is a factor of 125! - 100!, where n is a positive integer. What is the highest possible value of n ?

A. 5
B. 7
C. 18
D. 24
E. 31
______________________________
PS 2

Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 19 / 11
B. 13 / 9
C. 91 / 28
D. 17 / 48
E. None of these
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