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22 Jan 2026, 01:52
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Bookmarks
| Problem Solving Butler: January 2025 | ||
| January 22 | PS 1 | PS 2 |
_________________________
PS 1
What is the remainder when 21^32 is divided by 50?
A. 1
B. 11
C. 21
D. 31
E. 41
_________________________
PS 2
If P is a positive integer, which of the following is not possible for any value of x?
A. \(-(P^x) = (-P)^{(-x)}\)
B. \(-(P^x) = (-P)^x\)
C. \((P)^{(-x)} = -(P)^x\)
D. \((-P)^x = (-P)^{(-x)}\)
E. \((-P)^x = -(P^x)\)
22 Jan 2026, 01:54
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| Critical Reasoning Butler: January 2025 | ||
| January 22 | CR 1 | CR 2 |
____________________________
CR 1
Salmon meat is frequently used in gourmet cooking and retails at high prices. Meat from less valuable white fish, however, can be dyed to give it salmon’s distinct red/pink hue. Only experienced chefs are able to distinguish between genuine salmon and counterfeit salmon prepared in this manner. However, only ten percent of white fish caught can be dyed and much of the meat from these fish is not of a high enough quality for making the treatment worthwhile. Thus, surely the vast majority of salmon sold is genuine.
A serious flaw in the reasoning of the argument is that
A. comparisons between the price of salmon sold for gourmet cooking and its value for personal consumption are not mentioned
B. it does not consider the difficulty that a chef would have in distinguishing between genuine salmon and dyed white fish
C. the possibility that white fish may be used in gourmet cooking, even if it has not been dyed is overlooked
D. it treats the currently available method of dying white fish to resemble salmon as if it were the only method that can be used to do so
E. it does not consider how rare white fish dyed red/pink is in comparison with how rare genuine salmon is
____________________________
CR 2
The participants sorted into the experimental group of a consumer focus test were instructed to use a new brand of degreasing agent to clean their car engines for a month. Afterward, the members of this group reported a drop in their cars’ acceleration speed, while the control group, those who did not use the degreasing agent, did not report any drop. The detrimental effects on the cars were attributed to a petroleum solvent that is the principal active ingredient in the degreasing agent.
Which of the following, if true, would best help explain how the degreasing agent might produce the observed effect?
A. Chemical analysis of the degreasing agent determined that a concentrated form of the agent was used.
B. Subjects in the focus group did not know whether they were cleaning their car engines with the new degreasing agent or some other substance that is harmless.
C. As the primary use of the degreasing agent is as a cleaning agent, its negative effects are rarely noticed by car owners.
D. The petroleum solvent that is a constituent of the degreasing agent is also sold separately as a heavy-duty industrial cleaner.
E. A high level of the petroleum solvent degrades engine components responsible for the acceleration process.
22 Jan 2026, 01:57
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| Data Sufficiency Butler: January 2025 | ||
| January 22 | DS 1 | DS 2 |
______________________
DS 1
Anne is participating in a shooting event. If she shoots five times, what is the probability that she hits the bull’s eye at least once?
(1) The probability of her hitting the bull’s eye is 20% in each shoot.
(2) The probability of her not hitting the bull’s eye is 80% in each shoot.
______________________
DS 2
Company M has two divisions – X and Y. Both the divisions have exactly two types of employees – operators and executives. Is the total number of employees in Division X greater than that in division Y?
(1) The division X has 10% executives and division Y has 25% executives.
(2) The company M has 15% executives.
