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Problem Solving Butler: January 2025
January 30PS 1PS 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
_______________________________
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
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Critical Reasoning Butler: January 2025
January 30CR 1CR 2

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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.

__________________________
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.
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Data Sufficiency Butler: January 2025
January 30DS 1DS 2

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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.
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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.
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Problem Solving Butler: February 2025
February 2PS 1PS 2

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PS 1

‘W’ is the smallest positive integer that has 12 factors. What is the remainder when W is divided by 11 ?

A. 2
B. 5
C. 6
D. 8
E. 9
_________________________
PS 2

What is the rightmost non-zero integer in the integer value of 16! ?

A. 1
B. 2
C. 4
D. 6
E. 8
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Critical Reasoning Butler: February 2025
February 2CR 1CR 2

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CR 1

Which of the following most logically completes the passage?

Federal officers analyzing the stagnant industries of the Alcappian region divided the industries into two categories: consumer goods manufacturing and the service industry. According to the analysts, unlike the service providers, most of the manufacturing companies in the region were not profitable. Some economists’ recommendation to focus federal aid on the service industry alone, however, will not necessarily improve the economic situation of the region, since ________.

A. most manufacturing industry companies have been in the Alcappian region for at least a decade, whereas some of the service companies were established in the region in the last decade
B. over the last thirty years, a third of the least profitable manufacturing companies have closed business, and their employees have emigrated from the Alcappian region
C. a significant portion of the revenue of service providers in the region is accounted for by contracts to manufacturing industry companies
D. Local service industry companies do not provide all the services needed by the companies in the Alcappian region
E. Neither industry has greater profitability, relative to the overall size of the industry, than the profitability of the ever-growing shipping industry in the region
___________________________
CR 2

Those who are suspicious of government attempts to regulate industry suggest that the well-being of workers would be better served if workers’ unions were established for each profession and radically empowered to establish and enforce the worker protection guidelines currently enforced by the government.

Which of the following, assuming that it is a realistic possibility, argues most strongly against the suggestion above?

A. Workers’ unions might compete for influence over the labor market.
B. Workers’ unions might not always agree on the best way to serve the well-being of the workers.
C. If they wished to expand their operations, workers’ unions might be forced to accept funding from private organizations.
D. Because of their lack of experience, many workers’ unions might not be able to establish better worker protection guidelines than the current guidelines established by the government.
E. Some groups of workers may continue to be mistreated despite the best efforts of the workers’ unions, even if the unions are not hindered by a lack of resources.
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Data Sufficiency Butler: February 2025
February 2DS 1DS 2

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DS 1

The average weight of five people is 160 pounds. If no two people weigh the same, what is the weight of the third heaviest person?

(1) If the weights in pounds of five people are arranged in increasing order, the difference between any two consecutive terms is 10 pounds.
(2) If the weights in pounds of five people are arranged in increasing order, the difference between any two consecutive terms is the same.
_________________________
DS 2

Some Nitrogen was added into each of the 5 Nitrogen cylinders in a lab. If the standard deviation of the volume of Nitrogen in the 5 cylinders before the addition was 10 gallons, what was the standard deviation of the same after the addition?

(1) 7 gallons of Nitrogen was added into each of the cylinders.
(2) The average volume of Nitrogen in the 5 cylinders was 30 gallons before the addition and 37 gallons after the addition.
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Check out this New and Tricky Work and Rate problem from GMAT Club Tests. Give it a try, post your solution, and earn kudos for a correct answer:

https://gmatclub.com/forum/sophie-worki ... 53955.html
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Check out this New and Tricky Work and Rate problem from GMAT Club Tests. Give it a try, post your solution, and earn kudos for a correct answer:

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2. https://gmatclub.com/forum/ann-takes-50 ... 53956.html
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