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Problem Solving Butler: April 2025
April 15PS 1PS 2

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PS 1

If 3x + y = 41 and |2y| > 15, how many pairs of values {x, y} exist where x and y are both positive integers ?

A. 10
B. 11
C. 12
D. 33
E. 38
______________________
PS 2

If 2x – y = 31 and |2y| < 10, how many pairs of values {x, y} exist where x and y are both positive integers ?

A. 5
B. 4
C. 3
D. 2
E. 1
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Critical Reasoning Butler: April 2025
April 15CR 1CR 2

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CR 1

The ancient techniques of herbal medication, most of which are from eastern countries, are gaining popularity in the West for the right reasons. Western medical science has seen tremendous progress in the last several decades and has now even begun to understand how the human brain works. Under these circumstances, it is foolish to blindly follow ancient herbal treatments as if there is little we can do but to follow them as they are.

It can be inferred from the passage above that the author would be most likely to favor

A) a ban on ancient techniques of herbal medication
B) a mix of both modern medicine and ancient herbal medication
C) critical assessment of how ancient herbal medication contributed to the advancement of medical science
D) increased reliance on western medical science in the West
E) assessment of ancient herbal medication with the help of modern western medical science
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CR 2

All wasp hives have only one female capable of reproduction. This female, commonly known as the queen, attracts male drones by producing a specialized hormone. However, at the end of her reproductive life, the queen produces an enzyme that halts the production of this hormone. This enzyme can be synthesized and, on being ingested by a queen, effectively renders her sterile, destroying the hive.

Which of the following, if true, most strongly supports the view that it would NOT be advisable to try to eradicate environmentally invasive wasps by spraying infested areas with the enzyme mentioned above?

A. Many species of wasps are vital to the well-being of the ecosystem.
B. Many environmentally destructive, invasive insect species are not wasps.
C. Most species of wasps have at least some natural predators.
D. Since wasps of different species are capable of swiftly producing new queens, several sprayings would be necessary.
E. Although laboratories have been able to synthesize the enzyme, there are no facilities capable of producing it on a large scale.
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Data Sufficiency Butler: April 2025
April 15DS 1DS 2

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DS 1

Before the start of the fall service cycle, the city transit authority revised Route G by increasing service frequency and adding a stop near a busy office district. Based on those changes, the authority expected the average (arithmetic mean) number of riders on Route G each weekday to increase by 20 percent. Did the average (arithmetic mean) number of riders on Route G each weekday actually increase by more than 25 percent?

(1) The actual average (arithmetic mean) number of riders on Route G each weekday was 500 higher than expected.
(2) The actual average (arithmetic mean) number of riders on Route G each weekday was less than 12,600.
_______________________
DS 2

During two 7-day promotional weeks, Week 1 and Week 2, a bike-share service tracked the total number of bicycles rented. If in Week 1, 20 percent of the bicycles rented were rented on Sunday, while in Week 2, 15 percent of the bicycles rented were rented on Sunday, were more bicycles rented in Week 2 than in Week 1?

(1) On each day from Monday through Saturday in Week 2, the number of bicycles rented was at least 7 percent higher than the number rented on the corresponding day in Week 1.
(2) The number of bicycles rented on Sunday in Week 2 was greater than 76 percent of the number rented on Sunday in Week 1.
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April 15th Verbal Question of the Day



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Problem Solving Butler: April 2025
April 16PS 1PS 2

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PS 1

John takes x minutes to wrap y articles. How many hours will he take to wrap m bundles of articles if each bundle contains 100 articles?

A. 100mx / y
B. 100my / x
C. 5my / (3x)
D. 5mx / (3y)
E. 5mxy / 3
_____________________
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20 men take 30 minutes to decorate 100 articles. How long will it take 40 children and 20 women to decorate 200 articles if children are 25% less productive and women are 50% more productive than men?

A. 24 minute
B. 20 minute
C. 16 minute
D. 32 minute
E. 48 minute
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Critical Reasoning Butler: April 2025
April 16CR 1CR 2

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CR 1

People with health insurance are drastically more likely to seek a second opinion, after being examined by a qualified physician. Proportionally, more people in the 40-60 year age range have health insurance than in the 20-40 year range. Yet, oddly enough, the latest records show that people in the 40-60 year age range are no more likely to seek a second opinion than are those in the 20-40 age range.

Of the following, which, if true, best resolves the paradox seen above?

A. People with no health insurance were more likely to buy health insurance if they were over the age of 40 than if they were under that age.
B. Some people in the 20-40 age range have health insurance that covers more ailments than do some people in the 40-60 age range.
C. People generally do not seek a second opinion, unless it is from a physician more qualified than the one who first examined them.
D. Among all people with health insurance, the proportion of adults who sought second opinions declined in the last few years.
E. People who believe they are too young to acquire health issues are more likely than others to seek a second opinion.

______________________
CR 2

Looking to increase profits during a prolonged period of stagnated sales, the largest garment manufacturer in Britain has downsized the production staff of its factories. Although this strategy is inconsistent with the normal relationship between manpower and productivity, the manufacturer is confident that it will succeed.

The manufacturers' plan to increase profit margins relies on which of the following assumptions?

A. Garment manufacturers, out of necessity, reduce production staff whenever they do not have any new products to make.
B. The smaller garment manufacturers will continue taking away a large percentage of the largest manufacturer’s business.
C. Lower prices and more durable materials will attract many price-conscious consumers.
D. It will not be overly expensive for the manufacturer to install new factory safety regulations that will soon become mandatory for the garment industry.
E. The expenses saved by reducing the production staff will more than compensate for any decline in profit caused by lowered productivity.
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Data Sufficiency Butler: April 2025
April 16DS 1DS 2

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DS 1

At the start of a data-conversion job, two servers, Alpha and Beta, were assigned to process the same batch of files. Both servers began processing at the same time, but Alpha was taken offline after 3 hours. Was the number of additional hours that Beta continued processing by itself before the entire batch was completed more than 3 hours?

(1) During the 3 hours that Alpha was running, it processed 1/3 of the batch.
(2) Beta would need 9 hours to process the entire batch by itself.

_______________________
DS 2

At a warehouse, the daily output of Machine Orion is two-thirds of the daily output of Machine Vega. What is the daily output of Machine Orion, in units per day?

(1) If each machine produced 12 more units per day, then Machine Orion’s output would be three-fourths of Machine Vega’s output.
(2) If each machine produced 12 fewer units per day, then Machine Orion’s output would be one-half of Machine Vega’s output.
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April 16th Verbal Question of the Day



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Problem Solving Butler: April 2025
April 17PS 1PS 2

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PS 1

If p, q are each greater than 0 but less than 1, which of the following may be true?

I. p / q > 1
II. pq > 1
III. q – p > 1

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

_____________________
PS 2

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

A. x < 0
B. x < 2
C. –2 < x < 0
D. –1 < x < 2
E. 0 < x < 2
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Critical Reasoning Butler: April 2025
April 17CR 1CR 2

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CR 1

Since 2010, the proportion of mosquito infestations in Cervances resistant to the household insecticide proustein has increased considerably. Mosquitoes can rapidly become resistant to a household insecticide when it is used indiscriminately or when people fail to administer it as instructed. As proustein has not been used indiscriminately, public health officials theorize that the increase in proustein resistant mosquitoes is primarily a result of people failing to administer it as instructed.

Which of the following, if true of Cervances, provides most support for the health officials' theory?

A. The mosquitos’ resistance to several other commonly used household insecticides has not increased since 2010 in Cervances.
B. Proustein emanates an unpleasant smell that most people require a few days to get accustomed to.
C. At the time it was introduced, proustein was much more effective in eliminating mosquito infestations than any other household insecticides used for such infestations at the time.
D. A large number of Cervancians never seek help from pest control experts when they have a mosquito infestation.
E. Cervancian health clinics provide household insecticides to their patients without generating any profits from their sale.
_______________________
CR 2

Advertisement: According to a report by the Centre for Cybersecurity, the Buckland Anti-Virus Suite prevents more data loss in case of a virus infection than does any other anti-virus program in its class. This shows that the Buckland Anti-Virus Suite is the most reliable anti-virus program available.

Which of the following, if true, most seriously weakens the argument in the advertisement?

A. Anti-virus programs in the Buckland Anti-Virus Suite’s class are more likely to fail to prevent virus infections than are other varieties of anti-virus programs.
B. In the last few years, the Buckland Anti-Virus Suite has outsold all other anti-virus software in its class.
C. The Centre for Cybersecurity has listed many other anti-virus programs in other classes that saw more data loss in the event of a virus infection than did the Buckland Anti-Virus Suite.
D. The contrast between the amount of data lost per virus infection for the Buckland Anti-Virus Suite and that for other anti-virus programs in its class is very stark.
E. The Centre for Cybersecurity reports are only published on an annual basis.
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Data Sufficiency Butler: April 2025
April 17DS 1DS 2

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DS 1

A reseller bought a vintage floor lamp at a weekend flea market and later sold it online. What was the reseller’s profit percentage?

(1) If the reseller had sold the lamp for $24 more than the actual selling price, the profit would have been 100% greater than the actual profit

(2) If the reseller had sold the lamp for three times the actual selling price, the profit would have been 300% greater than the actual profit.
________________________
DS 2

At a farmers’ market, Mia, Leo, and Owen each bought some oranges. If the total number of oranges they bought is 36, what is the median number of oranges bought by the three people?

(1) The ratio of the number of oranges Mia bought to the number of oranges Owen bought was 7:12.

(2) Owen bought 12 oranges.
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