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Problem Solving Butler: April 2025
April 9PS 1PS 2

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PS 1

Among the following functions, for which one is f(a – b) = f(a) * f(–b) for all integer values of a and b?

A. f(t) = t/10
B. f(t) = t + 10
C. f(t) = 10t
D. f(t) = 10^t
E. f(t) = t^10

_______________________
PS 2

The compensation of person A is a fixed salary of $3,000 plus $30 for each additional computer sold after the first 40. The compensation of person B is straightaway $60 per computer sold. For a sale of how many computers each is the compensation of A 25% more than that of B?

A. 30
B. 40
C. 50
D. 60
E. 70
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Critical Reasoning Butler: April 2025
April 9CR 1CR 2

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CR 1

Last year the total amount of bonuses offered by Xio Technologies reached a historic peak. Now, many wonder if this year will see a new record. All bonuses are given either to existing employees during their annual appraisals or to new, as a joining bonus. This year, the management has not been as generous in awarding annual bonuses as it was last year. Moreover, this year’s recruitment calendar indicates that the number of new employees joining the firm will be lower this year than it was the previous year, and new recruits this year will definitely receive no higher joining bonus per employee than did those who joined last year. Hence, it can be established that the total amount of bonuses distributed this year will not outdo last year’s record.

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

(A) The first is an objection rejected by the argument; the second is the argument’s main conclusion.
(B) The first is an objection rejected by the argument; the second presents a conclusion that could be drawn if that objection were allowed to stand.
(C) The first is a claim advanced to support a position opposed by the argument; the second is a claim advanced to support the argument’s main conclusion.
(D) The first is a prediction that, if accurate, would support the argument’s main conclusion; the second is that main conclusion.
(E) The first is a prediction that, if accurate, would support the argument’s main conclusion; the second is a conclusion the argument draws to support that main conclusion.
_______________________
CR 2

Medical article: Detailed psychological interviews with hundreds of physicians have shown that those who rated their attitude towards patients highly also reported higher levels of job satisfaction. This finding suggests that a better attitude towards patients helps physicians avoid circumstances that can lower job satisfaction.

In evaluating how strong the article’s argument is, it would be most useful to know whether

A. physicians rate their attitude towards patients higher than a professional assessment from their superiors would
B. physicians’ assessment of their own attitude towards patients may be influenced by factors they are ignorant of
C. physicians’ rating of their attitude towards patients tends to fall for some time during interactions with uncooperative patients
D. low job satisfaction has a significant negative impact on physicians’ attitude towards patients
E. beyond a certain level, maintaining a good attitude towards patients tends to lower physicians’ job satisfaction
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Data Sufficiency Butler: April 2025
April 9DS 1DS 2

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DS 1

A bakery packed 150 dessert boxes in two batches. If each box contained between 2 and 5 eclairs, inclusive, was the average (arithmetic mean) number of eclairs per box greater than 3.5?

(1) The median number of eclairs per box was 4.5.
(2) The second batch contained 110 boxes and had an average (arithmetic mean) of 4.2 eclairs per box.
______________________
DS 2

At a print shop, premium brochures cost $14 each and standard flyers cost $9 each. For an event, Nora ordered only premium brochures, and Eli ordered only standard flyers. How many premium brochures did Nora order?

(1) If Nora had ordered as many premium brochures as Eli ordered standard flyers, Nora’s order would have cost $45 more than Eli’s order.
(2) If Nora had ordered standard flyers instead, in the same quantity as the premium brochures she actually ordered, her total cost would have been $35 less.
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Problem Solving Butler: April 2025
April 10PS 1PS 2

_______________________
PS 1

If abc < 0 and bcd > 0, which of the following is definitely negative ?

A. \(a^2b^3c^3d\)

B. \(a^2b^4c^4d^2\)

C. \(a^3b^4c^5d\)

D. \(a^3b^4c^4d\)

E. \(a^3b^5c^4d^2\)

_______________________
PS 2

If |3 – x| < x + 5, which of the following may be true about x ?

I. x > –1
II. x < 2
III. x < –2

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 10CR 1CR 2

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CR 1

Those who suffer from dissociative identity disorder are said to develop multiple personalities, called alters, so distinct from their own that some may even complain of imagined ailments. However, when supposedly blind alters are asked in writing whether they can see, they respond, “No.” Some psychiatrists attempt to explain this result by suggesting that blind alters are one part of a disassociated psyche, and it is actually another part of the psyche that responds to the question.

Which of the following challenges indicates the most serious weakness in the attempted explanation described above?

A. Why do all the supposedly blind alters respond identically in the situation described?
B. Why must the observed fact be provided a special explanation?
C. Why do the supposedly blind alters develop the delusion that they cannot see?
D. Why does the part of the psyche that answers not reply, "Yes"?
E. Why are the separate parts of the psyche the same for all subjects?
_________________________
CR 2

As per the out-of-Africa theory, the earliest homo sapiens to leave Africa crossed the Red Sea and spread along the coast of Asia, making their first major settlement in the Deccan (India, Asia) roughly 45,000 years ago. However, the discovery of 46,000 to 49,000 years old homo sapiens settlement in the Bacho Kiro caves (Bulgaria, Europe) suggests that the earliest homo sapiens to leave Africa actually spread towards Europe, migrating along either the Danube river or the Mediterranean coast.

Which of the following, if it were discovered, would be relevant evidence against the conjecture above?

A. The oldest positively identified homo sapiens fossil is dated to be 58,000 years old.
B. 6,000 years ago, the depth of the Red Sea, between Africa and Asia, was considerably lower, due to glaciation.
C. The climate at the Bacho Kiro site is more temperate than that at the oldest known Deccan site.
D. The site in Bulgaria where the fossils dated to be 46,000 to 49,000 years old has been continuously occupied since the time.
E. Some Asian sites of homo sapiens migration predate any sites found in Europe.
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Data Sufficiency Butler: April 2025
April 10DS 1DS 2

_______________________
DS 1

Last season, a football team scored 35 more goals than it conceded. Was the difference between the number of goals the team scored and the number of goals it conceded greater this season than it was last season?

(1) This season, the team scored 10% more goals than it scored last season.
(2) This season, the team conceded 20% more goals than it conceded last season.
_______________________
DS 2

A local arts center hosted a weekend illustration workshop. A community college club reserved spots for its members and paid a one-time reservation fee. If each registration cost $24.50, did the club purchase fewer than 14 registrations?

(1) The club’s total payment, including the one-time reservation fee, was $342.
(2) The one-time reservation fee was $18.
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