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Problem Solving Butler: May 2025
May 15PS 1PS 2

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PS 1

What is the sum of the multiples of 4 from 60 to 100, both inclusive?

A. 240
B. 800
C. 860
D. 880
E. 960
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PS 2

In how many ways can 10 identical chocolates be distributed among three children such that each child gets at least one chocolate?

A. 36
B. 66
C. 72
D. 78
E. 84
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Critical Reasoning Butler: May 2025
May 15CR 1CR 2

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CR 1

The ancient Spartans relied on conquest far more than did citizens of other, similarly sized Greek cities. Historians have hypothesized that it was a paucity of agricultural resources that drove the Spartans to subjugate so much foreign territory. This hypothesis is difficult to confirm directly, as sufficiently detailed records of Spartan agricultural output did not survive the medieval periods. However, careful comparison between the pattern of Sparta’s conquests and climate records kept by nearby civilizations show that the Spartans launched a higher number of military campaigns during years when regional agriculture suffered due to inclement weather. This indicates that there is some merit to the hypothesis.

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

A. The first presents an explanatory hypothesis; the second states the argument’s main conclusion.
B. The first presents an explanatory hypothesis; the second presents evidence in order to support an alternative explanation.
C. The first presents an explanatory hypothesis; the second presents evidence that tends to support this hypothesis.
D. The first describes a position opposed by the argument; the second presents evidence to undermine the support for the opposed position.
E. The first describes a position opposed by the argument; the second states the argument’s main conclusion.

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CR 2

A software has been designed to help nuclear power plants determine the necessity of an emergency shutdown, in the event of a drop in coolant pressure by analyzing the drop and comparing it against a database of 10,000 simulated nuclear coolant failure scenarios. The software is meant to help nuclear power plant workers determine whether a disruption in the plant’s coolant flow is severe enough to lead to a meltdown, necessitating an emergency shutdown.

In order to assess the effectiveness of the software for its stated purpose, it would be most helpful to establish which of the following?

A. Whether the nuclear coolant failure scenario database will receive regular updates of new simulations.
B. Whether nuclear power plant workers routinely misjudge the severity of drops in coolant pressure.
C. Whether a significant number of nuclear safety professionals will vouch for the software.
D. Whether the database also includes simulations of scenarios wherein coolant flow is stable.
E. Whether the use of this software will enable nuclear power plant workers to make sound decisions regarding the necessity of an emergency shutdown, before a meltdown occurs.
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Data Sufficiency Butler: May 2025
May 15DS 1DS 2

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DS 1

A regional express train normally travels from Northgate Station to Lakeside Station by its regular route and has a fixed scheduled travel time for that route. On one day, because of track maintenance, the train traveled from Northgate to Lakeside by a detour route instead. Was the train’s travel time that day more than 2 hours longer than the scheduled travel time?

(1) The train’s average (arithmetic mean) speed on the detour route differed from its average (arithmetic mean) speed on the regular route by no more than 20 kilometers per hour.
(2) The distance the train traveled on the detour route differed from the distance on the regular route by no more than 40 kilometers.
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DS 2

At a science quiz, Team Atlas consisted of Elena, Hugo, and Liam, and Team Nova consisted of Mia, Theo, and Nora. If a team’s score was the average (arithmetic mean) of the three scores earned by its members, what was Team Atlas’s score?

(1) Elena scored 15 points more than Mia, Hugo scored 6 points fewer than Theo, and Liam scored 18 points fewer than Nora.

(2) If Mia had scored 18 points more, Team Nova’s score would have been 20% greater than Team Atlas’s score.
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