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29 Jan 2026, 22:45
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| Problem Solving Butler: January 2025 | ||
| January 30 | PS 1 | PS 2 |
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PS 1
If 3p^5 = 96 and 7q = 32, what is the value of p/q?
A. 16/7
B. 7/16
C. ±16/7
D. ±7/16
E. Cannot be determined from the given information
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PS 2
p, q, r, s are positive integers. When p is divided by q, the remainder is 7; when r is divided by s, the remainder is 12. Which of the following may be a value of q + s?
A. 15
B. 17
C. 19
D. 20
E. 23
29 Jan 2026, 22:47
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| Critical Reasoning Butler: January 2025 | ||
| January 30 | CR 1 | CR 2 |
__________________________
CR 1
Some Egyptologists consider Pharaoh Rameses II’s decision to draft the Treaty of Kadesh, which ended the fifteen-year long Egyptian-Hittite War, to be one of the pivotal decisions made by the Pharaoh that allowed him to cement his legacy as the greatest of the Egyptian Pharaohs.
Which of the following, if true, would most weaken the claim that the signing of the Treaty of Kadesh was one of the pivotal decisions made by Pharaoh Rameses II that allowed him to cement his legacy as the greatest of the Egyptian Pharaohs?
A. Egypt secured access to lucrative Hittite ports and a large amount of arable land as a result of the treaty.
B. The treaty was signed at a time when both the Hittite army and the Egyptian army were engaged in military innovation.
C. The Treaty of Kadesh established the Hittite Kingdom as a military ally of Egypt, against the increasingly powerful Assyrian Empire.
D. Ramses II had drastically underestimated the strength of the Hittite army.
E. The Treaty of Kadesh was signed after internal conflict forced the Hittite Kingdom to pursue diplomatic ties with the kingdoms surrounding it.
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CR 2
Sandra is a dog walker who usually looks after twelve dogs. In the morning, Sandra picks the dogs up from their owners’ homes and then takes them to a local park to exercise and entertain before dropping them back at their respective owner’s home. Every Sunday, the owners pay Sandra at an hourly rate for the services she rendered that week. Typically, Sandra’s weekly income is adequate, but it is not always consistent, particularly when it rains, as the owners often choose to keep their dog indoors in bad weather.
Which of the following plans, if implemented, is most likely to make Sandra's weekly income both consistent and adequate?
A) Combine resources with a friend who looks after dogs under similar arrangements, enabling the two dog walkers to cooperate in looking after double the dogs that Sandra currently does.
B) Employ a permanent assistant and invest in protective gear to shield the dogs from the cold.
C) Replace payment by actual hours of pet care services provided with a fixed weekly fee based upon the number of hours of pet care that Sandra would typically be expected to provide.
D) Raise her hourly rate enough to provide adequate income, even if half of the dogs Sandra usually takes to the park are kept indoors for a full workweek.
E) Raise her daily hours of availability, so that dog-owners can have Sandra exercise their pets for more time every day at the current hourly rate.
29 Jan 2026, 22:50
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| Data Sufficiency Butler: January 2025 | ||
| January 30 | DS 1 | DS 2 |
_________________________
DS 1
Murtaugh Dynamics and O.R.E Machinery are sister firms. Rounded to the nearest thousand, what was the combined 2022-2023 revenue for the two firms?
(1) Rounded to the nearest thousand, the 2022-2023 revenues for Murtaugh Dynamics and O.R.E Machinery were $200,000 and $150,000 respectively.
(2) The exact revenue figures for Murtaugh Dynamics and O.R.E Machinery were each within 0.4% of the rounded figures.
_________________________
DS 2
A game was played by each student in two sections of a class - A and B. If the two sections had the same number of students, was the median score the same in the two sections?
(1) No two students in the same section got the same score.
(2) The highest score as well as the lowest score was the same in the two sections.
