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Problem Solving Butler: April 2025
April 27PS 1PS 2

________________________________
PS 1



On the number line, the shaded interval is represented by which of the following inequalities ?

A. |x – 10| > 25
B. |x – 10| < 25
C. |x + 5| < 10
D. |x + 5| > 10
E. |x + 10| < 25
________________________________
PS 2

If 2x < p – 10 and |p| < 6, which of the following cannot be a value of x ?

A. -9
B. -7
C. -5
D. -3
E. -2
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Critical Reasoning Butler: April 2025
April 27CR 1CR 2

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CR 1

In the absence of other physical factors, there are only two physical changes that can increase the pressure exerted by a solid object on a horizontal surface. These changes are an increase in the contact force of the object and a decrease in the contact area of the object. If the object is at rest, its contact force is equal to the object’s weight.

Assuming the statements above are accurate, it is true that for a solid object at rest on a horizontal surface

A. any increase in the pressure exerted on the surface by the object is due to a decrease in its contact area
B. if changes in the solid object’s contact force occur, there will be compensating changes to the object’s contact area with the surface
C. if there is a decrease in the object’s weight, then, other factors being equal, the pressure exerted on the surface by the object must increase
D. a solid object with a constant contact area always exerts constant pressure on the horizontal surface
E. if other physical factors are unchanged, increasing the object’s weight will lead to an increase in the pressure exerted by the object on the horizontal surface
__________________________
CR 2

A dairy cow’s milk production gradually increases over the first year of its calf’s life. On average, a healthy Jersey cow produces 10 gallons of milk per day, two months after its calf’s birth. Therefore, if a Jersey cow produces 9 gallons per day, two months after its calf’s birth, its rate of increase in milk production has been below average.

Which of the statements below indicates a flaw in this reasoning?

A. The volume of milk it produces is only one measure of the value of a dairy cow.
B. Some Jersey cows produce as much as 12 gallons of milk per day, two months after its calf’s birth.
C. The average increase in milk production is not synonymous with the average volume of milk produced.
D. “below average” does not necessarily connote insufficiency.
E. Some Jersey cows can produce 9 gallons of milk per day, immediately after the birth of its calf.
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Data Sufficiency Butler: April 2025
April 27DS 1DS 2

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DS 1

A neighborhood bakery owner selected some pastries to feature in a weekend display case. Was the number of selected pastries that were fruit-filled but not topped with glaze less than the number of selected pastries that were topped with glaze but not fruit-filled?

(1) Every selected pastry that was fruit-filled was also topped with glaze.

(2) Every selected pastry that was not fruit-filled was also not topped with glaze.
__________________________
DS 2

During lunch service, a snack kiosk sold bread rolls, wraps, bowls of soup, and salads. If the prices of one bread roll, one wrap, one bowl of soup, and one salad were in the ratio 3:6:5:4, respectively, what percent of the total revenue from the sale of these four items came from salads?

(1) The numbers of bread rolls, wraps, bowls of soup, and salads sold were in the ratio 5:2:1:4.

(2) The total revenue from the sale of all four items was $96.
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Problem Solving Butler: April 2025
April 28PS 1PS 2

___________________________
PS 1

The function f(n) for an integer n is defined by the number of prime factors of n. What is the value of f(f(210 x 143))?

A. 1
B. 2
C. 3
D. 4
E. 6

___________________________
PS 2

A function f(n) is defined as \(2^{\frac{(n-1)}{2}}\) when n is odd and 3n/2 when n is even. What is the value of f(f(f(3)))?

A. √2
B. 2
C. 3
D. 4
E. 9
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Critical Reasoning Butler: April 2025
April 28CR 1CR 2

____________________________
CR 1

Because the interstate highway has been closed due to storm damage, congestion on other roads leading to the capital has increased by thirty percent. To resolve this issue, priority on these roads must be given to smaller vehicles.

Which of the following, if true, casts the most doubt on the effectiveness of the solution proposed above?

A. After a small southern city allocated different priorities to vehicles of different sizes, congestion on those roads was reported to decrease by 50 percent.
B. Since the interstate highway was closed, the number of cars on the road has increased by thirty percent.
C. Over eighty percent of the traffic on the other roads leading to the capital consists of smaller vehicles.
D. The major cause of congestion on the roads leading to the capital is the lack of adherence to traffic laws.
E. Since the interstate highway was closed, the average amount of commuting time on roads leading into the capital has doubled.
_____________________________
CR 2

Investment in electronic goods can be conducted on the futures market. With positive news, such as an announcement of new electronic technology, prices of electronic goods likely to benefit from the news rise; if negative news about the arrival is predicted, prices fall. Earlier today, trade publications reported that Malus Industries is close to developing an improved voice recognition technology. As the introduction of this new technology will increase the utility and value of telecommunication devices, prices of telecommunication devices futures will rise today.

Which of the following, if true, most weakens the argument above?

A. The improved voice recognition system will not enhance the utility and value of telecommunication devices unless properly implemented.
B. Industry insiders announced today that Malus Industry’s employees have unionized and are planning a general strike that will go into effect any time.
C. The application of the improved voice recognition system extends far beyond telecommunication devices.
D. Futures prices for telecommunication devices have been fluctuating more dramatically this month than last month.
E. It is rare for most people who trade in electronic goods futures to personally use the technology they trade in.
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Data Sufficiency Butler: April 2025
April 28DS 1DS 2

_______________________________
DS 1

At a community center, a total of 31 people enrolled in at least one of three weekend workshops: pottery, photography, and creative writing. If 17 people enrolled in pottery, 13 enrolled in photography, and 12 enrolled in creative writing, how many people enrolled in all three workshops?

(1) 24 people enrolled in exactly one workshop.
(2) A total of 5 people were enrolled in both the pottery workshop and the photography workshop.
_______________________________
DS 2

At a museum, all visitors in a certain tour group were either students or teachers. Some visitors rented audio guides, and the rest did not. If 12 students did not rent audio guides, whereas 24 teachers did rent audio guides, how many teachers were in the tour group?

(1) The number of students who rented audio guides was twice the number of teachers who did not rent audio guides.
(2) The total number of visitors in the group who rented audio guides was twice the total number of visitors who did not rent audio guides.
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Reading Comprehension Butler: April 2025
March 28RC 1
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Problem Solving Butler: April 2025
April 29PS 1PS 2

__________________________________
PS 1

During a 24–hour period, the minute's arm of the clock covers how many more rotations than the hour's arm of the clock?

A. 11
B. 12
C. 22
D. 23
E. 24

__________________________________
PS 2

Working alone, machines A, B, and C can complete a task in 6, 12, and 18 hours respectively. All three machines were started together to complete the task but machine A was switched off after 2 hours and machine B was also switched off after another 1 hour. Machine C completed the remaining task. If the work was started at 1200 hrs, at what time did the work get over?

A. 1630 hrs
B. 1700 hrs
C. 1730 hrs
D. 1830 hrs
E. 1930 hrs
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