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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

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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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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

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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

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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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Critical Reasoning Butler: January 2025
January 2CR 1CR 2

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CR 1

The Sekhon class jet turbine, composed of a new and improved steel alloy, will cost more than thrice as much as the current model of jet turbines does. However, replacing older turbines with newer models should still reduce costs. Not only will installation time be reduced, but the Sekhon class turbines should last longer.

Which of the following must be studied in order to evaluate the argument presented above?

A. How likely is the use of the Sekhon class jet turbine to reduce the need for future repairs, in comparison with the use of the current model of jet engines
B. How much the cost of producing the current model of jet turbines has dropped, following the advent of the Sekhon class jet turbine
C. How long it takes to install a new jet turbine versus how long it takes for the jet to be cleared for flight
D. How much more care is taken in the manufacture of the Sekhon class jet turbines produced with the new alloy than in the manufacture of the current jet turbines.
E. How much more affordable jet turbines produced with the new alloy will become as the production procedures standardize and become applicable on a larger scale.

____________________________
CR 2

Alpha Deliveries has recently switched at least partly from older packaging using rigid materials to new packaging made from flexible plastics. The question has been raised whether it can be concluded that for a given level of output Alpha’s operations now cause fewer resources to be consumed than it did formerly. The answer is yes since the amount of raw material, energy, and manpower needed to produce and use the flexible plastic packing material is less than that needed to produce and use rigid packing material, provided the level of output is held constant.

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

(A) The first identifies the content of the argument’s conclusion; the second provides support for that conclusion.
(B) The first expresses the argument’s conclusion; the second questions that conclusion.
(C) The first provides support for the argument’s conclusion; the second identifies the content of that conclusion.
(D) The first provides support for the argument’s conclusion; the second questions that conclusion.
(E) Each provides support for the argument’s conclusion.
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Data Sufficiency Butler: January 2025
January 2DS 1DS 2

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DS 1

The revenue through television sales for Jacy, an electronic appliances firm, was what percent greater this year than it was last year?

(1) Jacy sold 20% more television units this year than the same last year.
(2) For Jacy, the average selling price per television unit this year was 10% less than the same last year.
__________________________
DS 2

A processed coffee manufacturer sources coffee beans from precisely 3 farms. If the available stock decreased by 20% from the first farm and 30% from the second farm, by what percentage must the manufacturer increase the amount of beans sourced from the third farm to offset a decrease in available stock from the first two farms?

(1) Before the recent decrease, the total amount of beans sourced from the first, second, and the third farm was in the ratio 1:1:2.
(2) Before the recent decrease, the manufacturer sourced 50 kilograms of coffee beans from the first farm.
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Problem Solving Butler: January 2025
January 5PS 1PS 2

____________________________
PS 1

For an integer n, the function f(n) is defined as product of all even integers from 1 to n. Which of the following is a factor of f(12) + 1 ?

A. 2
B. 3
C. 5
D. 7
E. 9
____________________________
PS 2

What is the digit at the units place in the total integer value of 19^31 – 18^16 ?

A. 1
B. 3
C. 5
D. 7
E. 9
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Critical Reasoning Butler: January 2025
January 5CR 1CR 2

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CR 1

The country of Sewell was recently hit by a devastating earthquake, prompting the government to request foreign aid. However, direct donations of medical supplies can depress prices of medical supplies in Sewell and drive local producers out of business, further increasing Sewell’s dependence on foreign aid to provide medical care for its people.

Which of the following, if true, is the strongest counter-argument against the argument above?

A. Cash aid would be thirty to fifty percent more expensive to donor countries than the direct donation of medical supplies, since the donor governments already hold a surplus of medical supplies for which they are incurring storage costs.
B. Since Sewell’s hospitals are nationalized, extra medical supplies will not depress the official price, and the government can use the cash it raises from selling donated medical supplies to fund reconstruction efforts.
C. If the medical supplies donated to the government of Sewell are given free to the people, the people will use the money they would have had to spend on medical supplies for other necessities, not medical supplies.
D. Due to logistical disruptions, local producers have produced much lower amounts of medical supplies than usual.
E. Many of Sewell’s poorest live in villages where there are no hospitals, so the benefit of the donated medical supplies will be felt by those who already have access to better medical care than the poor in the villages do.
_____________________________
CR 2

Journalist: For several years, the centrist party has been exhorting its wealthy donors and corporate sponsors to purchase traditional media outlets to propagate its political message, although this practice has earned it considerable criticism. The party has not invested much into reaching out to voters through digital media, even though doing so can lead to greater voter engagement without incurring ethical criticisms. Thus, many political scientists argue that the centrist party’s actions do not serve even its own political interests. However, the party is strongest in rural areas, where digital connectivity is low; the party’s most loyal base is voters above the age of 50, who do not heavily consume digital media; and conversely, the party is most firmly opposed by the demographics that are most engaged in political discussions through digital media. Therefore, the political scientists’ conclusion is likely incorrect.

In the journalist's argument, the two boldface portions play which of the following roles?

(A) The first supports the conclusion of the journalist's argument; the second questions that conclusion.
(B) The first expresses the conclusion of the journalist's argument; the second provides support for that conclusion.
(C) The first supports the conclusion of the political scientists' argument; the second expresses that conclusion.
(D) Each supports the conclusion of the journalist's argument.[/color]
(E) The first expresses the conclusion of the political scientists' argument; the second expresses the conclusion of the journalist's argument.
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Data Sufficiency Butler: January 2025
January 5DS 1DS 2

_______________________________
DS 1

Company M has two divisions – X and Y. Both the divisions have exactly two types of employees – operators and executives. Is the ratio of operators versus executives greater in division X than that in division Y ?

(1) The ratio of operators to executives for the division X is less than that for the company M.
(2) More than half the executives in company M are employees of Division X, and more than half the operators in company M are employees of division Y.
_______________________________
DS 2

For an aging power plant, the ratio of electricity produced to electricity consumed was 99:1 last month. How much electricity did the plant produce last month?

(1) The difference between the electricity produced and electricity consumed last month was 490,000 MWH.
(2) The plant’s electricity consumption last month was 5,000 MWH.
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