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Problem Solving Butler: January 2025
January 13PS 1PS 2

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PS 1

p, q, r, s are positive integers. When p is divided by q, the remainder is 6; when r is divided by s, the remainder is 11. Which of the following is the least possible value of q + s?

A. 15
B. 16
C. 17
D. 18
E. Greater than 18
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PS 2

What is the highest integer k for which 1260^k perfectly divides 500! ?

A. 123
B. 82
C. 81
D. 1
E. 0
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Critical Reasoning Butler: January 2025
January 13CR 1CR 2

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CR 1

Looking to bolster the domestic luxury cars industry, a member of parliament has introduced a bill that would levy additional taxes on the import of luxury cars. The reasoning behind the bill is that the taxes will raise the prices of foreign luxury cars above those of the luxury cars by their domestic counterparts, prompting consumers to buy luxury cars produced domestically instead.

Which of the following statements, if true, provides the strongest evidence that the reasoning put forward by the member of parliament is flawed?

A. Projected increases in the price of international shipping will increase the cost of importing luxury cars.
B. Each year, the imports of luxury cars account for thirty percent of the total sales amount from luxury cars sold in the country.
C. Most of the wholesalers currently dealing only in domestic luxury cars cannot afford to import foreign ones.
D. Some wholesalers of imported luxury cars are willing to pay the additional taxes for importing luxury cars.
E. Regular upkeep of imported luxury cars is already significantly more expensive than that of domestic luxury cars.
______________________
CR 2

People tend to evaluate the importance of a public issue according to its salience, meaning people are more likely to think that an issue is important if it comes to their attention frequently and in an aggressive manner. By volume of discussion and due to selection bias, social media emphasizes issues that are relatively frivolous but eye-catching over relatively more serious but non-sensational issues.

It can be concluded on the basis of the statements above that, if they are true, which of the following is most probably also true?

A. The language used on social media to describe relatively frivolous issues is sensationalist and fails to accurately respect the traditional boundaries of news coverage.
B. Those who discuss public issues on social media tend to overestimate the importance of relatively frivolous but eye-catching issues compared to serious but non-sensational ones.
C. Discussion on serious but non-sensational issues is neglected on social media in favor of discussion on frivolous but eye-catching issues.
D. None of the issues concerning other people that are discussed on social media is so salient in people’s minds as their own personal issues.
E. Social media is the medium that focuses people’s attention most strongly on frivolous issues.
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Data Sufficiency Butler: January 2025
January 13DS 1DS 2

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DS 1

Cars A and B are stationed in “Townville” and “Cityburg”, respectively. The two cities are connected by parallel highways and are 100 miles apart. The two cars begin their journeys simultaneously, moving in opposite directions, each heading towards the other car’s point of departure. If the two cars cross each other after 30 minutes, which car is closer to its destination city at the point of crossing?

(1) Car B averaged a speed of 40 miles per hour for the entire trip.
(2) When the two cars crossed each other, car A had averaged a speed of 80 miles per hour.

_______________________
DS 2

The average duration of Rasmus’s commute across Monday, Tuesday, and Wednesday was 3 hours. What was the median length of Rasmus’s commute over the three days?

(1) On Tuesday, Rasmus’s commute took 3 hours.
(2) On Monday, Rasmus’s commute took 2.5 hours.
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Just a quick question if anyone can answer:

The difficulty level of the questions mentioned throughout the forum is base on the updated focus edition or the old one?

Not sure if this is the right place ask this question
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Yes, it’s updated as per the focus edition.

anu12345678765
Just a quick question if anyone can answer:

The difficulty level of the questions mentioned throughout the forum is base on the updated focus edition or the old one?

Not sure if this is the right place ask this question
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Yes, it’s updated as per the focus edition.
Thanks a lot!
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Problem Solving Butler: January 2025
January 14PS 1PS 2

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PS 1

The value of \((\frac{4}{5})^{(\frac{1}{10})}\) is closest to which of the following?

A. 1
B. 1/2
C. 0
D. –1/2
E. –1

_________________________
PS 2

What is the digit at the units place in the total integer value of 27^31 – 19^27 ?

A. 0
B. 2
C. 4
D. 6
E. 8
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Critical Reasoning Butler: January 2025
January 14CR 1CR 2

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CR 1

By restricting roads leading through residential areas to just private vehicles and commercial vehicles specifically authorized to travel through residential areas, most commercial traffic would be forced onto alternate routes. A reduction in the volume of commercial traffic would ease traffic gridlocks in residential areas.

The conclusion drawn in the argument depends on which of the following assumptions?

A) Alternate routes would be as suitable as the roads leading through residential areas for most drivers of commercial vehicles.
B) Most commercial vehicles that use the roads leading through residential areas are not authorized to travel through residential areas.
C) Most alternate routes are not suitable for private traffic
D) Private vehicles are at greater risk of getting caught in traffic gridlocks than are commercial vehicles.
E) Eventually, reduction in traffic gridlocks will lead to increases in private traffic.
______________________
CR 2

Economist: Operating a store in a shopping mall generally generates more value for owners than running a standalone shop outside a shopping mall does, due to the economies of scale. Store owners who operate out of the same mall can collectively bear the cost for services that would be unaffordable to them individually. Moreover, since a specialized cleaning company handles the upkeep of common areas, storeowners in a shopping mall spend less time and resources on maintenance that owners of standalone shops do.

The two portions in boldface play which of the following roles in the economist’s argument?

(A) The first is a premise, for which no evidence is provided; the second is the only conclusion of the argument.
(B) The first is a conclusion that supports the second; the second is the main conclusion of the argument.
(C) The first is the only conclusion of the argument; the second is a premise, for which no support is provided.
(D) The first is the main conclusion of the argument; the second is another conclusion that supports the first.
(E) Both are premises, for which no support is provided, and both support the only conclusion of the argument.
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Data Sufficiency Butler: January 2025
January 14DS 1DS 2

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DS 1

Which burns for longer, a candle made of 100 grams of beeswax or one made of 100 grams of soy wax?

(1) A candle made of 100 grams of beeswax burns longer than a candle made of 80 grams of soy wax.
(2) A candle made of 100 grams of soy wax burns for shorter than a candle made of 80 grams of beeswax.

_______________________
DS 2

The per sofa selling price at a showroom this year was $40 more than this price last year. What was the revenue of the showroom last year?

(1) The showroom sold 20% more number of sofas this year than it did last year.
(2) The showroom earned $30,000 more revenue this year than it did last year.
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I was wondering the same and would appreciate any insights from people who’ve applied for deferral before.
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hi, i got to know about a rule of focus edition ..that you have to send your scores within 48 hrs to 5 business schools, if you fail to do so then you will have to pay 35 $ for each school . If we sit for the exam on 18th january, that means its towards the end of round 3 applications ( atleast in India) , so will have to send the scores immediately , right?

somebody please confirm this rule

i was planning to give the exam early but apply in round 1
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vanshitabajaj26
hi, i got to know about a rule of focus edition ..that you have to send your scores within 48 hrs to 5 business schools, if you fail to do so then you will have to pay 35 $ for each school . If we sit for the exam on 18th january, that means its towards the end of round 3 applications ( atleast in India) , so will have to send the scores immediately , right?

somebody please confirm this rule

i was planning to give the exam early but apply in round 1
Hi vanshitabajaj26,

The 48-hour window starts from the time you receive your official score report. If you're applying in R1, you can send your scores now. Those schools will be able to access your score report for as long as your score remains valid.
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Problem Solving Butler: January 2025
January 15PS 1PS 2

__________________
PS 1

What is the highest integer k for which 135^k perfectly divides 200! ?

A. 97
B. 49
C. 40
D. 32
E. 1

__________________
PS 2

What is the sum of the digits of the highest prime factor of 200! ?

A. 13
B. 15
C. 19
D. 23
E. Greater than 23
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Critical Reasoning Butler: January 2025
January 15CR 1CR 2

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CR 1

As part of a study conducted by the Lexington University’s Psychology Department, two groups of volunteers from the university’s classical music program performed Claude Debussy’s Claire de Luna. Then, one group was provided verbal feedback in a jovial tone, while the other was provided verbal feedback in a neutral tone. Some volunteers, chosen randomly from each group, were then encouraged to enjoy a warm beverage of their choice. Among those who received verbal feedback in a neutral tone, those who accepted a beverage were significantly less likely to volunteer for another, similar experiment than those who did not accept a beverage. The researchers concluded that some of the volunteers chose not to volunteer again, partly because they received feedback in a neutral tone.

Which of the following would, if true, most help to support the researchers' conclusion?

A. Among the volunteers who received feedback in a jovial tone, those who accepted a beverage were significantly less likely to volunteer for another, similar experiment than those who did not accept a beverage.
B. Just as many volunteers from one group were encouraged to enjoy warm beverages as from another group.
C. Most of the volunteers encouraged to enjoy a beverage accepted one.
D. The volunteers were not more disposed to drinking warm beverages under typical circumstances than the general population was.
E. Those who received feedback in a jovial tone were, on average, more likely to volunteer for another, similar experiment than those who received feedback in a neutral tone were.

________________________
CR 2

Looking to improve student performance in the suburb of Backport, the Mayor of Grantsville has decided to initiate a series of improvement projects for the three public schools that serve the suburb. The Mayor plans to fund these improvements over the course of the next four years by raising property taxes in the neighboring suburb of Gadsen. Although these improvements are surely needed, the Mayor’s plan to fund them should be rejected because it would unfairly force the residents of Gadsen to absorb the entire cost of initiatives from which they receive no benefit.

Which of the following, if true, would provide the Mayor with the strongest counter to the objection that her plan is unfair?

A. Even with the proposed tax increase, property taxes in Gadsen would remain less than property taxes levied in most of the other suburbs of the city.
B. The public schools that serve the suburb of Gadsen are overcrowded and residents of the suburb benefit when some families choose to send their children to schools in neighboring suburbs.
C. The residents of Gadsen benefit from the commuter roads leading to the city center, and the maintenance of these roads is funded out of general income tax revenues from both Backport and Gadsen.
D. Any attempt to finance the improvements by raising property taxes in Backport would result in fewer families with school-going children moving to Backport and so would be at least partially self-defeating.
E. The only alternative way to fund the proposed improvement initiatives now being considered is through a regional income tax surcharge, which would affect the residents of Backport and the residents of Gadsen alike.
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Data Sufficiency Butler: January 2025
January 15DS 1DS 2

_______________________
DS 1

If all workers in a workshop are equally efficient, how long will it take 10 workers to pack 30 items?

(1) Five workers take 12 minutes to pack 15 items.
(2) When four workers worked for five minutes each followed by five workers working for eight minutes each, 15 items were packed.

_______________________
DS 2

What is the average age of the 12 people on a certain jury?

(1) The oldest juror is 61, and the youngest is 29.
(2) Average age of the 10 youngest jurors is 40.
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