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Data Sufficiency Butler: May 2026
May 27DS 1DS 2

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DS 1

At a community center’s weekend open house, 360 registered visitors had access to two optional sessions: a gardening workshop and a budgeting seminar. How many of the registered visitors attended both sessions?

(1) Of the 360 registered visitors, 140 attended the gardening workshop, and 180 attended the budgeting seminar.

(2) The number of registered visitors who attended neither session was 40 greater than the number who attended both sessions.
______________________
DS 2

At a music audition, judges assigned scores to 9 applicants. Among the applicants, 3 tied for the lowest score of 14 points, and 2 tied for the highest score of 65 points. If the median score of the 9 applicants was 50 points, what was the average (arithmetic mean) score of the 9 applicants?

(1) If the applicants who received 14 points or 65 points are not considered, the median score of the remaining applicants is 56 points.

(2) If the applicants who received 14 points or 65 points are not considered, the range of the remaining scores is 12 points.
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shouldn’t the equation be y-z=6 ?
How I came to the equation was : I know x.zy > x.yz, by that z>y. For the 100th term it should be y+10 -z =4. For the 10th term, you would get the equation z-1 - y =5. From both the equations, z=y+6. So, based on the options, z can only be 6.
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Problem Solving Butler: May 2026
May 28PS 1PS 2

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PS 1

Ida had five cards with matching envelopes – same in design, different in color. She removed the cards from all envelopes and randomly put them back. What is the probability that exactly one card got into the matching envelope?

A. 3/16
B. 5/8
C. 3/8
D. 1/4
E. 1/2

_______________________
PS 2

A set has ten positive integers – six even and four odd. Two integers are picked randomly and multiplied. What is the probability that the product is even?

A. 2/15
B. 7/15
C. 8/15
D. 2/5
E. 13/15
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Critical Reasoning Butler: April 2026
May 28CR 1CR 2

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CR 1

Archaeological examination of the ancient city of Helike, located in Achaea, revealed a pattern of geological damage and collapsed buildings that resembles the pattern formed after tsunamis level down settlements. Thus, archaeologists have theorized that the destruction was caused by a well-documented tsunami that struck Acahea in 373 BCE.

Which of the following, if true, most strongly supports the archaeologists' hypothesis?

A. Ceramic funeral urns that are often found in graves dating from years before and after 373 BCE were also found in several graves near Helike.
B. Inscriptions utilizing a form of the Hellenic alphabet that was certainly used in Achaea after 373 BCE were found in Hellike.
C. Most contemporary accounts of Achaean history mention that a severe tsunami struck the region in 373 BCE.
D. Several coins minted in styles current in Achaea in the century between 350 BCE and 200 BCE were found in Helike.
E. Excavation in Helike found fragments of pottery created before 373 BCE in abundance but did not find any fragments of pottery created after 373 BCE.
_____________________
CR 2

Opioid painkillers, such as oxycodone, are administered intravenously, meaning they are injected directly into the bloodstream. Such painkillers must be injected intravenously because if taken by any other method, the opioids will be processed by the liver before the opioids enter the bloodstream, rendering them useless by the time they reach their target cells. Certain non-opioid painkillers, however, contain chemical agents that are not processed by the liver. Therefore, such non-opioid painkillers can be administered in several different ways.

The statements above most strongly support a claim that the research accomplishment of which of the following would be beneficial to the users of opioid painkillers?

A. Determining, in a systematic way, what chemicals are naturally found in the human bloodstream and whether they tend to be processed by the liver.
B. Chemically altering, by procedures that work in the laboratory, the non-opioid painkillers that are not processed by the liver into opioids.
C. Permanently rendering the liver incapable of processing painkillers.
D. Combining oxycodone with compounds that prevent oxycodone from being processed by the liver but do not affect how target cells react to oxycodone.
E. Determining the amount of time each non-opioid painkiller takes to reach its target cells.
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Data Sufficiency Butler: May 2026
May 28DS 1DS 2

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DS 1

A delivery van traveled from Westport Depot to Lakeview Market in 7 hours. If the trip consisted of a 4-hour first leg at one constant speed and a 3-hour second leg at a different constant speed, what was the van’s average (arithmetic mean) speed for the entire trip?

(1) If the van had traveled for 8 hours at its first-leg speed and for 6 hours at its second-leg speed, it would have traveled 700 kilometers.
(2) If the van had traveled for 1 hour at each of those two speeds, it would have traveled 110 kilometers.
________________________
DS 2

A juice bar mixed apple juice and berry concentrate to make 6 liters of a fruit drink. If apple juice cost $4 per liter, and berry concentrate cost $10 per liter, was the volume of apple juice used greater than the volume of berry concentrate used?

(1) Less than 4 liters of berry concentrate were used.

(2) The total cost of the apple juice and berry concentrate used to make the 6 liters of fruit drink was less than $39.
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Quote:

*Bunuel writes:*
Data Sufficiency Butler: May 2026

May 28
a-delivery-van-traveled-from-westport-depot-to-lakeview-market-in-458174.html
a-juice-bar-mixed-apple-juice-and-berry-concentrate-to-make-6-liters-458173.html



________________________
a-delivery-van-traveled-from-westport-depot-to-lakeview-market-in-458174.html

A delivery van traveled from Westport Depot to Lakeview Market in 7 hours. If the trip consisted of a 4-hour first leg at one constant speed and a 3-hour second leg at a different constant speed, what was the van’s average (arithmetic mean) speed for the entire trip?

(1) If the van had traveled for 8 hours at its first-leg speed and for 6 hours at its second-leg speed, it would have traveled 700 kilometers.
(2) If the van had traveled for 1 hour at each of those two speeds, it would have traveled 110 kilometers.
________________________
a-juice-bar-mixed-apple-juice-and-berry-concentrate-to-make-6-liters-458173.html

A juice bar mixed apple juice and berry concentrate to make 6 liters of a fruit drink. If apple juice cost $4 per liter, and berry concentrate cost $10 per liter, was the volume of apple juice used greater than the volume of berry concentrate used?

(1) Less than 4 liters of berry concentrate were used.

(2) The total cost of the apple juice and berry concentrate used to make the 6 liters of fruit drink was less than $39.
Hi for juice question answer should be B right.
And delivery van question it shoudn be C

Can some one confirm
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Quote:

Can some one confirm
yes correct
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*jeffn sends image:*
B
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Problem Solving Butler: May 2026
May 29PS 1PS 2

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PS 1

If |2x – 7| < x + 1, which of the following may be a value of x?

I. 1
II. 5
III. 14

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
______________________
PS 2

Sequence S contains the squares of positive even multiples of 3 in increasing order. What is the sum of the first 6 terms in S ?

A. 818
B. 1092
C. 1638
D. 3276
E. 6552
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Critical Reasoning Butler: May 2026
May 29CR 1CR 2

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CR 1

Demand for gold has been stagnant for five years now. However, despite the fact that prices and production amounts have also been steady during the last five years, gold mines experienced a twelve percent increase in profits this year.

Any of the following statements, if true about last year, helps to explain the rise in profits EXCEPT:

A. Many smaller gold mines were acquired by a larger mining conglomerate, prompting a fall in the price of mining supplies as the number of potential buyers reduced.
B. Gold mines have reduced labor costs by switching from paying miners an hourly wage to paying them by the amount of ore mined.
C. The price of cyanide, a vital component of the chemical process used to extract pure gold from its ore, dropped over twenty-five percent.
D. Many nations that consume large amounts of gold increased their production of electronics, which require the use of gold as a conductor, yet their overall use of gold decreased.
E. Taxes on mining activities in gold producing regions were lowered.
_______________________
CR 2

News anchor: The average resident of the state’s four major cities drives 150 miles per month, and most of the state’s residents live in these four cities. Moreover, the average distance driven by the residents of the state tends to remain stable from one month to the next. Therefore, most of the state’s residents drive at least 100 miles each month.

The argument presented by the news anchor is most susceptible to which of the following criticisms?

A. It reaches a conclusion for the entire state on the basis of data from just four cities.
B. It fails to consider the possibility that even if, on average, a certain distance is driven by the people within a certain group, many of those in the group may not drive at all.
C. It confuses a claim that would necessarily lead to the argument’s conclusion about the state’s residents with a claim that would only be highly likely to follow from the argument’s conclusion regarding the state’s residents.
D. It ignores the possibility that the residents of the cities may be driving outside of city limits.
E. It fails to consider the possibility that even if most residents of the state drive at least 100 miles each month, any given resident may not drive at all in some months.
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Data Sufficiency Butler: May 2026
May 29DS 1DS 2

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DS 1

A school used several buses for a field trip. If each bus carried a different number of students, was the median number of students per bus an integer?

(1) Each bus carried an odd number of students.
(2) The number of buses used for the field trip was odd.
_______________________
DS 2

A small theater sold only adult tickets and student tickets for one afternoon show. Each adult ticket cost $18, and each student ticket cost $10. If the theater sold 45 tickets for the show, how many adult tickets were sold?

(1) The average (arithmetic mean) ticket price was greater than $14.50 but less than $15.00.

(2) The total revenue from ticket sales was greater than $655 but less than $663.
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