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Problem Solving Butler: January 2025
January 23PS 1PS 2

______________________
PS 1

Which of the following is not an integer ?

A.\(\frac{25! }{ (5)^6}\)

B. \(\frac{10! }{ (3)^4}\)

C. \(\frac{9! }{ (2)^7}\)

D. \(\frac{12! }{ (3!)^5}\)

E. \(\frac{20! }{ (11)^2}\)
______________________
PS 2

How many factors of 72^2 are multiples of 6 ?

A. 30
B. 24
C. 20
D. 15
E. 5
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Critical Reasoning Butler: January 2025
January 23CR 1CR 2

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CR 1

In an interview to a business daily, a senior manager at Windsor Hotels recently stated that the hotel is poorly managed, mentioning the hotel’s inability to modify its marketing strategy in response to a recent surge in its number of unoccupied rooms. A senior manager’s negative comments are generally detrimental to the image of the company, but in this case, the negative comments were also unjustified. Although an increased number of unoccupied rooms at a hotel often indicates that the hotel is losing clients to competitors, in Windsor Hotels’ situation, it does not. Rather, the increase in the number of unoccupied rooms can be attributed entirely to the cancellation, earlier this year, of two of the city’s biggest events.

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

(A) The first states the position opposed by the argument as a whole; the second states the conclusion of the argument as a whole.
(B) The first states the position opposed by the argument as a whole; the second provides evidence to undercut the support for the position being opposed.
(C) The first states the position opposed by the argument as a whole; the second is evidence that has been used to support the position being opposed.
(D) The first is evidence that has been used to support a position opposed by the argument as a whole; the second provides information to undercut the force of that evidence.
(E) The first is evidence that has been used to support a position opposed by the argument as a whole; the second states the conclusion of the argument as a whole.
_____________________
CR 2

To compete with a number of newer restaurants, Rick’s Café has begun offering a free appetizer to every customer who orders more than $40 worth of food. The manager of Rick’s Café claims that the offer has been a huge success in increasing sales, since the number of customers whose orders exceed $40 has increased by twenty-seven percent since the offer began.

Which of the following, if true, most seriously weakens the claim of the manager?

A. Most people who began eating at Rick’s Café after the offer began spending more than $40 each time they eat there.
B. Most people who typically spend less than $25 on a restaurant meal would not be persuaded to spend more by any offer.
C. Nearly all who have begun spending $40 or more at Rick’s Café since the offer began are regular patrons who have increased the average amount spent during one meal at Rick’s Café, but have begun visiting less frequently.
D. Since the offer began, most of the people who spend $40 or more at Rick’s Café are people who have never eaten there before and who always spend more than $40 when eating at restaurants.
E. Most people who received a free appetizer through the offer will continue to eat at Rick’s Café after the offer ends.
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Data Sufficiency Butler: January 2025
January 23DS 1DS 2

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DS 1

If 40 percent of the people who bought a particular smartphone bought a smartwatch, what percent of the smartphone buyers bought headphones?

(1) 50 percent of people who bought the smartphone and the smartwatch also bought headphones.
(2) 80 percent of people who bought the smartphone and the headphones also bought the smartwatch.
__________________________
DS 2

Over the course of a certain month, Olga, a saleswoman, sold 20 cars, and each of her 7 colleagues sold at least 1 car. Did Olga sell as many or more cars than at least 4 of her colleagues?

(1) The average (arithmetic mean) of the number of cars sold by Olga’s 7 colleagues is 12.
(2) The median of the number of cars sold by Olga’s 7 colleagues is 18.
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In the final episode of AMA with GMAT Ninja, we break down why RC feels slippery—especially when sentences get dense, you keep rereading, and inference questions feel like guessing. We’yzsmiWO8a64er note-taking (too much vs too little), and reducing constant look-backs to the passage

👉 *Watch Live on YouTube* https://www.youtube.com/watch?v=yzsmiWO8a64
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From the set of numbers x, y, t, z and w, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc and (x,y)=(y,x)

A. 10
B. 14
C. 15
D. 16
E. 30

Why we are not taking empty set in count for final answer.
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dhilavikash
From the set of numbers x, y, t, z and w, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc and (x,y)=(y,x)

A. 10
B. 14
C. 15
D. 16
E. 30

Why we are not taking empty set in count for final answer.

This question is discussed HERE: https://gmatclub.com/forum/from-the-set ... 96122.html
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Test your GMAT skills in Real Test Conditions - Join our Live GMAT Quiz and see how you stack up against other test takers https://www.youtube.com/watch?v=LVTXzc3aFf8
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Problem Solving Butler: January 2025
January 26PS 1PS 2

__________________
PS 1

If \((\frac{1}{50})^a(\frac{1}{20})^4 = \frac{1}{50} (100)^{-6}\), a = ?

A. 3
B. 4
C. 5
D. 6
E. 7

__________________
PS 2

What is the highest integer k for which 125^k perfectly divides 200! ?

A. 49
B. 48
C. 16
D. 13
E. 1
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Critical Reasoning Butler: January 2025
January 26CR 1CR 2

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CR 1

A new town ordinance that requires all home owners to install burglar alarms and other anti-theft measures on their property has received stiff opposition from those who believe that citizens of a free society must be allowed to freely take risks, as long as those risks do not harm others. Resultantly, they conclude that it should be each home owner’s decision to install the anti-theft measures.

Which of the following, if true, most seriously weakens the conclusion drawn above?

A. Many new homes come with pre-installed anti-theft measures.
B. Property owners who do not install anti-theft measures, on average, experience greater monetary loss due to burglary than those who do install such measures.
C. Banks are required to install extremely stringent anti-theft measures.
D. The rate of burglary in states that do not have laws mandating the installation of anti-theft measures is greater than that in states that do have such laws.
E. Theft insurance rates are higher for everyone because of the need to pay for the increased losses sustained by those without anti-theft measures.
_________________________
CR 2

Lunacorp and Salem Industries are two sanitation firms that employ an equal number of workers who work the same number of hours per week. According to each company’s end of year report, the employees of Lunacorp took fewer sick leaves last year than did the employees of Salem Industries. Therefore, employees of Lunacorp are less likely to fall ill than are employees of Salem Industries.

Which of the following, if true, would most strengthen the conclusion above?

A. Lunacorp’s expenditure on new job-related medical claims is greater than Salem Industries’.
B. Salem Industries holds more health inspections than does Lunacorp.
C. Salem Industries’ infirmary is more modern than Lunacorp’s.
D. Salem Industries provides sanitation services for environments that are more hazardous for its employees to work in than does Lunacorp.
E. Salem Industries provides more types of health-care benefits than does Lunacorp.
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