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Problem Solving Butler: March 2025
March 26PS 1PS 2

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PS 1

In the year 2010, the average age of children in a class of 20 was 12 years. In 2011, 10 more children joined and the average age of the children in the class became 14. What was the average age of these 10 children in the year 2015?

A. 15
B. 16
C. 17
D. 18
E. 20
_______________________
PS 2

The value of a stone is directly proportional to the cube of its weight. If the stone breaks into three small parts with the ratio of weights 1:1:2, what is the approximate percentage drop in the value of the stone?

A. 10%
B. 15%
C. 60%
D. 85%
E. 95%
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Critical Reasoning Butler: March 2025
March 26CR 1CR 2

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CR 1

Salesman: Four out of five automobile repair and service franchises use only Elaion engine oil. So, if you are looking for high-quality engine oil, Elaion is the one to go for.

Which of the following, if true, undermines the salesman’s argument to the greatest degree?

A. Many engine oil manufacturers increase product sales to automobile repair and service franchises by selling these products to the franchises at the lowest price the manufacturers can afford.
B. Many automobile repair and service franchises that do not usually use Elaion will do so for cars whose engines cannot handle the engine oil they normally use.
C. Some competing brands of engine oil are intended to be used in machinery other than car engines.
D. Unlike some of its competitors, Elaion can be freely purchased without proof of identification.
E. In product trials, Elaion has been found to be more effective than its competitors that have been on the market longer than it has.
_______________________
CR 2

The oldest surviving example of written narrative fiction, the Akkadian poem The Epic of Gilgamesh, dates from the seventh century BCE, but the fact that the text of the poem sometimes refers to King Gilgamesh as “Bilgamesh” suggests that the Akkadians heard the story of Gilgamesh at least five centuries before this poem was written. After all, the Akkadians adopted the legend of Gilgamesh from the Babylonians, and presumably, along with the basic story, they adopted the then-current Babylonian spelling of his name. Further, even though Babylonian writing was originally inconsistent regarding the spelling of the legendary king’s name, by the seventh century BCE, the Babylonians consistently spelled it as Gilgamesh and had been doing so for five hundred years.

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

(A) The first and the second each describe evidence that has been used to challenge the position that the argument seeks to establish.
(B) The first is evidence that forms the basis for an objection to the position that the argument seeks to establish; the second is that position.
(C) The first is evidence that forms the basis for an objection to the position that the argument seeks to establish; the second is a consideration that is introduced to counter the strength of that evidence.
(D) The first provides evidence in support of the position that the argument seeks to establish; the second is that position.
(E) The first and the second each provide evidence in support of the position that the argument seeks to establish.
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Data Sufficiency Butler: March 2025
March 26DS 1DS 2

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DS 1

At a company wellness fair, 41 employees signed up for at least one of the following: yoga classes, nutrition sessions, and meditation sessions. A total of 18 employees signed up for nutrition sessions, and 14 signed up for meditation sessions. How many employees signed up for all three?

(1) 9 employees signed up for both nutrition sessions and meditation sessions, of whom 2 also signed up for yoga classes.

(2) 27 employees signed up for yoga classes.

______________________
DS 2

At a community center, Nora and five other volunteers packed snack bags for an event. If altogether they packed 43 snack bags, and no two volunteers packed the same number of snack bags, did Nora pack more than 6 snack bags?

(1) Each volunteer packed at least 4 snack bags, and the greatest number of snack bags packed by a volunteer was greater than 12.
(2) Nora packed fewer snack bags than the median number of snack bags packed by the six volunteers.
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Problem Solving Butler: March 2025
March 27PS 1PS 2

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PS 1

13 students in a class had a median score of 10 and an average score of 15. If all scores were in integers and Mike scored higher than all other students in the quiz, what can be the lowest possible score of Mike?

A. More than 23
B. 23
C. 22
D. 21
E. 20

___________________________
PS 2

The list A consists of 10 consecutive even integers. If 19 is the median of the set, what is the sum of all integers in the set?

A. 175
B. 180
C. 185
D. 190
E. 195
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Critical Reasoning Butler: March 2025
March 27CR 1CR 2

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CR 1

Dolcenia Enterprises, an electronic devices company, has relied on an “auto-pilot strategy” of automated onboarding and computerized troubleshooting to eliminate the category of customer care officers serving corporate customers. The company now intends to employ the same concept in serving retail customers acquired in physical stores.

The plan of Dolcenia Enterprises assumes that

A) other electronic devices companies will not also be addressing customer troubleshooting in the same manner
B) computerized troubleshooting cannot be done without the use of automated onboarding
C) the same type of auto-pilot strategy will be used in Dolcenia Enterprises for helping both retail customers and corporate customers
D) personal service by customer care personnel is not necessary for addressing retail customer queries successfully
E) customer care officers are the only employees of Dolcenia Enterprises who could be assigned tasks related to onboarding

_________________________
CR 2

A newly built spider silk “bio-factory” in Michigan is a closely controlled artificial biome that is used for harvesting silk fibers from the golden orb web spider and produces on 1 acre of floor space what it takes 50 acres of fields to produce. However, expenses, particularly for the water needed to maintain the spiders’ biome, are high, and the silk fiber produced costs about three times as much as Connecticut bombyx mori (common silkworm) silk fibers, the silk fibers commonly sold throughout the United States.

Which of the following, if true, best supports a projection that the spider-silk facility in Michigan will be profitable?

A. Unlike bombyx mori (common silkworm) silk fibers, the silk fibers harvested from spiders are gathered without harming the insects and thus will sell at exceptionally high prices to customers concerned with animal cruelty.
B. It is virtually impossible to reduce the cost of Connecticut bombyx mori (common silkworm) silk fibers any further.
C. Once the facility operators gain experience, it will be possible to cut operating expenses by about 20 percent.
D. Since silk fibers ship relatively well, the market for the spider silk fibers is no more limited to Michigan than the market for Connecticut bombyx mori (common silkworm) silk fibers is to Connecticut.
E. A second spider silk facility is being built in Greenland, taking advantage of cheap water supplies and high demand for cold-resistant fabrics.
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Data Sufficiency Butler: March 2025
March 27DS 1DS 2

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DS 1

In a bakery display case, a chocolate tart and a lemon tart were arranged in a single row with the other desserts. Including those two tarts, are there more than 12 desserts in the row?

(1) Counting from the left end of the row, the chocolate tart is the 7th dessert, and counting from the right end of the row, the lemon tart is the 5th dessert.
(2) Exactly 1 dessert is between the chocolate tart and the lemon tart.

______________________
DS 2

A school bookstore sold only two kinds of planners during orientation week: a basic planner for 8 euros and a deluxe planner for 11 euros. How many planners did the bookstore sell in total?

(1) The average (arithmetic mean) selling price per planner was 9 euros.

(2) The number of basic planners sold was twice the number of deluxe planners sold.
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Problem Solving Butler: March 2025
March 30PS 1PS 2

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PS 1

If \(\frac{x }{ (x – 2)(x + 1) ≤ 0}\), which of the following specifies all the possible values of x ?

A. x < –1
B. 0 ≤ x < 2
C. x ≤ –1 and 0 ≤ x < 2
D. x < –1 and 0 ≤ x < 2
E. x ≤ –1 and x ≥ 2
_________________________
PS 2

A set of 19 integers has a median of 31 and a range of 51. What is the lowest possible value of the smallest integer in the set?

A. 30
B. 6
C. 5
D. -20
E. -21
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Critical Reasoning Butler: March 2025
March 30CR 1CR 2

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CR 1

The caretakers at the Schwimmer-Rock Zoo have failed to detect numerous preventable diseases in the zoo’s animals before they became serious. Several other zoos in the country have managed to reduce the mortality rate from preventable diseases among their animals by 15 to 30 percent by instituting mandatory, monthly full-body checkups of each animal. To detect preventable diseases early, thereby reducing animal mortality rates, the Schwimmer-Rock Zoo will institute the same policy.

Which of the following, if true, may potentially be a drawback in the policy of instituting checkups of each animal?

A. In zoos without monthly, full-body checkups, the animal mortality rate is 30 percent above the average mortality rate in all zoos in the country.
B. The zoo’s owners prefer that checkup schedules be set so as to minimize the amount of time that the animals will not be on display.
C. There are more animals in the Schwimmer-Rock Zoo than there are in the zoos that have instituted mandatory, monthly full-body checkups.
D. Newly hired caretakers would find it difficult to conduct so many checkups so often, unless they were provided with additional training.
E. Frequent full-body checkups of all animals would require significant additional expenses and increase pressure on the zoo’s stringent budget.

______________________
CR 2

Which of the following most logically completes the argument?

The classic Greco-Roman style of sculpture most closely associated with ancient Greco-Roman art was widely practiced until the third century. Accounts from Asian travelers describe these sculptures as being painted in bright primary colors. However, all surviving examples of art made in this style have no paint whatsoever, famously being stark-white marble. Nonetheless, it does not follow that the Asian accounts are therefore inaccurate regarding the painting of sculptures, as __________.

A. some accounts from Asian travelers also describe ancient Greco-Roman sculptures produced in other styles as being painted in bright primary colors
B. sculptures produced in this style are far more common in the erstwhile Roman empire than in Asia
C. only one other style of sculpture practiced today uses paints in the same manner as the Asian accounts described the Greco-Roman sculptures as having used
D. the Asian travelers’ accounts of ancient Greco-Roman statuary were written well before the third century
E. the paint used is made of plant pigments that begin to dissolve after a few centuries
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Data Sufficiency Butler: March 2025
March 30DS 1DS 2

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DS 1

At a professional training conference, 44 attendees signed up for the data analytics workshop and 31 signed up for the public speaking workshop. Were at least 60 attendees at the conference?

(1) At least 16 attendees signed up for neither workshop.

(2) 1/4 of the attendees signed up for both workshops.

________________________
DS 2

A stationery store received a shipment of notebooks. When the manager packs the notebooks into cartons that hold 8 notebooks each, 5 notebooks are left unpacked. If the same shipment is packed into cartons that hold 12 notebooks each, how many notebooks will be left unpacked?

(1) If the notebooks are packed into cartons that hold 6 notebooks each, 5 notebooks are left unpacked.

(2) If the notebooks are packed into cartons that hold 10 notebooks each, 5 notebooks are left unpacked.
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