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04 Jan 2026, 23:00
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| Problem Solving Butler: January 2025 | ||
| January 5 | PS 1 | PS 2 |
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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
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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
04 Jan 2026, 23:04
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| Critical Reasoning Butler: January 2025 | ||
| January 5 | CR 1 | CR 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.
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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.
04 Jan 2026, 23:08
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| Data Sufficiency Butler: January 2025 | ||
| January 5 | DS 1 | DS 2 |
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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.
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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.
