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Problem Solving Butler: April 2025
April 6PS 1PS 2

____________________
PS 1

If |2x – 2| < x + 1, which of the following represents the correct range of values of x ?

A. 1 / 3 < x
B. x < 3
C. 3 < x < 11
D. 1 / 3 < x < 3
E. 3 < x < 9
____________________
PS 2

If x^2 + 6x > 27, which of the following specifies all the possible values of x ?

A. x > 3
B. x < –9
C. –9 < x < 3
D. x > 3 or x < –9
E. x > 9 or x < –3
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Critical Reasoning Butler: April 2025
April 6CR 1CR 2

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CR 1

Political theorist: The principle of airspace reprisal states that nations denied access to a portion of another nation’s airspace should deny that nation access to a portion of their airspace in order to pressure the other nation to restore access. If every nation made decisions as per this principle, no nation would allow foreign aircraft to enter its airspace.

The political theorist’s argument relies on which of the following assumptions?

A) In the case of any two nations, at least one has denied access of a portion of its airspace to the other.
B) No nation should deny access to any portion of its airspace to foreign aircraft.
C) Disputes over airspace should be handled by the international court.
D) No nation actually makes decisions, as per the principle of airspace reprisal.
E) Nations close their airspace to foreign aircraft to safeguard their domestic airlines.
_____________________
CR 2

Professor Lebiski: The most basic human need is food. Before humans discovered that they could grow their own food, all they did was wander in the forests and forage for fruits and meat. With the evolution of grass, humans learned that certain plants, grown near water bodies, can be consumed as food. This provided them the incentive to spend their time cultivating these plants in one location rather than roaming around, hunting for food. This geographical stability must have gradually helped the evolution of agriculture and, with it, of civilization.

Professor Gomez: The core aspects of this evolution of civilization were climate and the availability of water for plants. It is, therefore, no surprise that all the early civilizations were near large rivers and in tropical areas.

Which one of the following most accurately characterizes Professor Gomez’s response to the argument furnished by Professor Lebiski?

A) Professor Gomez provides a counterargument that highlights a flaw in Professor Lebiski’s argument.
B) Professor Gomez builds on Professor Lebiski’s argument and provides additional evidence.
C) Professor Gomez discards Professor Lebiski’s argument on the basis of the examples provided.
D) Professor Gomez’s argument is incompatible with that of Professor Lebiski.
E) Professor Gomez repeats Professor Lebiski’s argument with little additional information.
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Data Sufficiency Butler: April 2025
April 6DS 1DS 2

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DS 1

At the Northgate distribution center, a sorting line can run in one of two modes: automated mode, in which it processes 180 parcels per hour, and manual-check mode, in which it processes 45 parcels per hour. For a certain batch, was the line’s average (arithmetic mean) processing rate greater than 120 parcels per hour?

(1) The batch contained 240 parcels.
(2) More than 3/4 of the parcels in the batch were processed in automated mode.

_____________________
DS 2

During an overnight run, a server handled two types of jobs: validation jobs and migration jobs. Every validation job took the same amount of time, and every migration job took the same amount of time. If each migration job took 6 minutes longer than each validation job, what was the average (arithmetic mean) processing time per job for all the jobs handled in that run?

(1) The total time spent on validation jobs was three times the total time spent on migration jobs.
(2) The server handled five times as many validation jobs as migration jobs.
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Can anyone help while I open these questions I am not able to see the options. Just the choices-A,B,C,D,E
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vrinda6
Can anyone help while I open these questions I am not able to see the options. Just the choices-A,B,C,D,E
Hi,
These are DS questions and since all DS questions have same options, they aren’t mentioned for every question.
Please check this - data-sufficiency-answer-choices-455275.html
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vrinda6
Can anyone help while I open these questions I am not able to see the options. Just the choices-A,B,C,D,E
Hi,

These are data sufficiency questions. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.
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Critical Reasoning Butler: April 2025
April 6CR 1CR 2

_____________________
CR 1

Political theorist: The principle of airspace reprisal states that nations denied access to a portion of another nation’s airspace should deny that nation access to a portion of their airspace in order to pressure the other nation to restore access. If every nation made decisions as per this principle, no nation would allow foreign aircraft to enter its airspace.

The political theorist’s argument relies on which of the following assumptions?

A) In the case of any two nations, at least one has denied access of a portion of its airspace to the other.
B) No nation should deny access to any portion of its airspace to foreign aircraft.
C) Disputes over airspace should be handled by the international court.
D) No nation actually makes decisions, as per the principle of airspace reprisal.
E) Nations close their airspace to foreign aircraft to safeguard their domestic airlines.
_____________________
CR 2

Professor Lebiski: The most basic human need is food. Before humans discovered that they could grow their own food, all they did was wander in the forests and forage for fruits and meat. With the evolution of grass, humans learned that certain plants, grown near water bodies, can be consumed as food. This provided them the incentive to spend their time cultivating these plants in one location rather than roaming around, hunting for food. This geographical stability must have gradually helped the evolution of agriculture and, with it, of civilization.

Professor Gomez: The core aspects of this evolution of civilization were climate and the availability of water for plants. It is, therefore, no surprise that all the early civilizations were near large rivers and in tropical areas.

Which one of the following most accurately characterizes Professor Gomez’s response to the argument furnished by Professor Lebiski?

A) Professor Gomez provides a counterargument that highlights a flaw in Professor Lebiski’s argument.
B) Professor Gomez builds on Professor Lebiski’s argument and provides additional evidence.
C) Professor Gomez discards Professor Lebiski’s argument on the basis of the examples provided.
D) Professor Gomez’s argument is incompatible with that of Professor Lebiski.
E) Professor Gomez repeats Professor Lebiski’s argument with little additional information.
CR1 - A
CR2 - E
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CR 1 - A

CR 2 - E
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Problem Solving Butler: April 2025
April 7PS 1PS 2

____________________
PS 1

Jack and Lily are playing quiz. They start with 50 chocolates each and Jack asks questions. For each correct answer, Jack gives Lily four chocolates and for each incorrect answer, Lily gives three chocolates to Jack. If at the end of the quiz, Lily gave only one-third answers correct and is left with 36 chocolates, how many questions did Jack ask her?

A. 7
B. 14
C. 21
D. 36
E. 43
____________________
PS 2

If x > y > z, which of the following may be true?

I. x^4 > y^4 > z^4
II. z^4 > y^4 > x^4
III. y^4 > x^4 > z^4

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
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Critical Reasoning Butler: April 2025
April 7CR 1CR 2

_____________________
CR 1

Which of the following most logically completes the argument?

Energy department officials in Haydenburg responded to the city council’s plan to offer tax breaks to major corporations headquartered in the city by pointing out that doing so would attract more corporate headquarters, which tend to consume large amounts of electricity, driving up energy prices. Responding to the officials, the city council pointed out that modern conservation measures are most effective in reducing the energy consumption of tech firms, and such tax breaks attract tech firms the most. However, this outcome cited by the city council is unlikely to negate the outcome pointed out by the energy department officials, since _____.

A. more corporations headquartering in a city reduces the average number of conservation measures deployed unless tax breaks are offered
B. the plan to offer tax breaks will have to be rolled out sector by sector and may take a year to be effective for all sectors
C. a corporation headquartered in Haydenburg will spend a lower proportion of its revenue on energy once the tax breaks are applied
D. the tax breaks will not induce more corporations to headquarter in Haydenburg if the city does not have adequate infrastructure to support them
E. corporate headquarters that do not employ conservation measures consume disproportionately high amount of energy
_____________________
CR 2

A firm that owns and manages apartment buildings throughout Sinolia pays for repairs suggested by safety inspectors only if the repairs are first approved as being “free of tenant error” by a review panel appointed by the company. The purpose of this rule is to save the company the money it might otherwise spend on unneeded repairs. Recently, the firm announced that as part of a cost saving initiative, it has decided to abandon the rule.

Which of the following, if true, provides the strongest justification for the firm’s decision?

A. Tenants often register a lack of satisfaction with safety inspectors who do not suggest any repairs to address their concerns.
B. Safety inspectors often suggest certain repairs that are useful but not altogether necessary for the safety of the tenant.
C. There is a strong negative correlation between approvals of repairs by the firm-appointed review panel and the cost estimates of the repairs.
D. The firm’s review panel does not supersede the safety inspectors’ prerogative, to select the type of repair the panel members prefer in cases where more than one type of repair is possible.
E. The review process is expensive and practically always results in the approval of the suggested repairs.
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Data Sufficiency Butler: April 2025
April 7DS 1DS 2

_______________________
DS 1

Today, Laura invested a total of $12,500 at two banks. She invested part of the money at Bank A, which pays 9% annual interest compounded annually, and the remainder at Bank B, which pays 8% annual interest compounded semiannually. How much did Laura invest in Bank A?

(1) After 1 year, the total value of Laura’s two investments at the banks will be $13,541.
(2) After 2 years, the amount in the Bank B investment will be $8,728.34 greater than the amount in the Bank A investment.

_______________________
DS 2

A delivery fleet currently has 108 vehicles of two types: vans and trucks. Are more than 75 percent of the vehicles vans?

(1) If the fleet added 12 trucks, then 30 percent of the vehicles would be trucks.
(2) 7/9 of the vehicles in the fleet are electric vans.
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Bunuel
Critical Reasoning Butler: April 2025
April 7CR 1CR 2

_____________________
CR 1

Which of the following most logically completes the argument?

Energy department officials in Haydenburg responded to the city council’s plan to offer tax breaks to major corporations headquartered in the city by pointing out that doing so would attract more corporate headquarters, which tend to consume large amounts of electricity, driving up energy prices. Responding to the officials, the city council pointed out that modern conservation measures are most effective in reducing the energy consumption of tech firms, and such tax breaks attract tech firms the most. However, this outcome cited by the city council is unlikely to negate the outcome pointed out by the energy department officials, since _____.

A. more corporations headquartering in a city reduces the average number of conservation measures deployed unless tax breaks are offered
B. the plan to offer tax breaks will have to be rolled out sector by sector and may take a year to be effective for all sectors
C. a corporation headquartered in Haydenburg will spend a lower proportion of its revenue on energy once the tax breaks are applied
D. the tax breaks will not induce more corporations to headquarter in Haydenburg if the city does not have adequate infrastructure to support them
E. corporate headquarters that do not employ conservation measures consume disproportionately high amount of energy
_____________________
CR 2

A firm that owns and manages apartment buildings throughout Sinolia pays for repairs suggested by safety inspectors only if the repairs are first approved as being “free of tenant error” by a review panel appointed by the company. The purpose of this rule is to save the company the money it might otherwise spend on unneeded repairs. Recently, the firm announced that as part of a cost saving initiative, it has decided to abandon the rule.

Which of the following, if true, provides the strongest justification for the firm’s decision?

A. Tenants often register a lack of satisfaction with safety inspectors who do not suggest any repairs to address their concerns.
B. Safety inspectors often suggest certain repairs that are useful but not altogether necessary for the safety of the tenant.
C. There is a strong negative correlation between approvals of repairs by the firm-appointed review panel and the cost estimates of the repairs.
D. The firm’s review panel does not supersede the safety inspectors’ prerogative, to select the type of repair the panel members prefer in cases where more than one type of repair is possible.
E. The review process is expensive and practically always results in the approval of the suggested repairs.
CR1 - E;
Goal is to counter the council’s against energy department. E says that disproportionate impact by those who don’t employ the new method would drive the cost up

CR2 - E
Logic of this CR is to provide reason that can show that panel is not serving the purpose. E clearly targets the cost benefit.
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