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Problem Solving Butler: July 2026
July 28PS 1PS 2

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PS 1

Mrs. Sharma has a few chocolate candies which she wants to distribute among her five grand-daughters. If she distributes the candies among them in the ratio of 1 : 4 : 5 : 7 : 9, then 1 candy is left out. If she distributes the candies in the ratio of 2 : 3 : 3 : 4 : 5, then 3 candies are left out. However, if she distributes the candies among them in the ratio of 1 : 2 : 3 : 7 : 8, then no candies are left over. What is the minimum number of candies that any of the five grand-daughters can receive in any of the three cases?

A. 3
B. 4
C. 5
D. 6
E. 12
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PS 2

An article, if sold at a discount of 30%, results in a loss of 35 dollars. However, there is a profit of 5 dollars if sold at a discount of 10%. What would be the profit or loss if it was sold without any discount?

A. 10%
B. 12.1%
C. 13.5%
D. 14.3%
E. 15.2%
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Critical Reasoning Butler: July 2026
July 28CR 1CR 2

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CR 1

Film critic: The documentary film The Decline of English Literature presents the view that contemporary British writers lack the basic narrative skills common among nineteenth-century British authors. The film's comparison is persuasive because it analyzes 20 popular, critically respected British novels, 10 from the nineteenth century and 10 from the past two decades, and demonstrates that the contemporary novels are not nearly as well-written as the nineteenth-century novels.

Which of the following, if true, casts the most doubt on the argument above?

(A) A film viewer who was not familiar with literary criticism may not be convinced by the film’s analysis of 20 novels.

(B) The film critic may favor nineteenth-century fiction and may therefore be biased in favor of the filmmaker’s view.

(C) The film’s title may predispose viewers to accept the film’s conclusion even before viewing the comparisons in the film.

(D) The filmmaker could have chosen to analyze only books that support the position she was trying to establish.

(E) The literary methods used by contemporary British authors could require less narrative skill than methods used by writers in other parts of the world.
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CR 2

It is inaccurate to say that a diet high in refined sugar cannot cause adult-onset diabetes, since a diet high in refined sugar can make a person overweight, and being overweight can predispose a person to adult-onset diabetes.

The argument above is most parallel, in its logical structure, to which of the following?

(A) It is inaccurate to say that being in cold air can cause a person to catch a cold, since colds are caused by viruses, and viruses flourish in warm, crowded places.

(B) It is accurate to say that no airline flies from Halifax to Washington. No single airline offers a direct flight, although some airlines have flights from Halifax to Boston and others have flights from Boston to Washington.

(C) It is correct to say that over-fertilization is the primary cause of lawn disease, since fertilizer causes lawn grass to grow rapidly and rapidly growing grass has little resistance to disease.

(D) It is incorrect to say that inferior motor oil cannot cause a car to get poorer gasoline mileage, since inferior motor oil can cause engine valve deterioration, and engine valve deterioration can lead to poorer gasoline mileage.

(E) It is inaccurate to say that Alexander the Great was a student of Plato; Alexander was a student of Aristotle, and Aristotle was a student of Plato.
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Data Sufficiency Butler: July 2026
July 28DS 1DS 2

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DS 1

­There are three times as many hot dogs as pizzas and five times as many brownies as hot dogs in "Junk Food 'R' Us" restaurant. The restaurant sells only whole products (you cannot buy half a pizza, for example). How many brownies are there in the restaurant?

(1) There are at least 10 pizzas in the restaurant

(2) There are 32 hot dogs at most in the restaurant
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DS 2

The number of cats in Libby’s house is twice the number of dogs and one third the number of fish. If cats, dogs and fish are the only pets in Libby’s house, what is the probability of randomly selecting two cats?

(1) The number of cats in Libby’s house is 12.
(2) The total number of pets in Libby’s house is 54.
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Problem Solving Butler: July 2026
July 29PS 1PS 2

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PS 1

Which of the following is a prime number?

I. 9! + 5
II. 11! + 15
III. 13! + 13

A) I only
B) II only
C) III only
D) II and III only
E) None

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PS 2

The total amount of Mark’s cell phone bill for the month of April was $120.75. The bill consisted of a fixed charge of $82.50 plus a charge of $0.025 per minute for data usage. For how many hours of data usage was Mark charged for the month of April?

A. 22
B. 22.5
C. 23
D. 24
E. 25.5
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Critical Reasoning Butler: July 2026
July 29CR 1CR 2

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CR 1

­Even the smallest amounts of chlorofluorocarbons contribute to the needless and rapid destruction of the Earth's protective ozone layer. The destruction of the ozone layer will lead to catastrophic global warming and greatly increased incidence of skin cancer. The loss of the ozone layer is unacceptable, so chlorofluorocarbons should not be used, especially since _________.

Which of the following best completes the passage?

A. most people live in areas where the ozone layer is thickest

B. users of chlorofluorocarbons are generally unaware of the risks involved

C. most chlorofluorocarbons are used in small amounts

D. safe and equally cheap replacements are readily available

E. the ozone layer serves to protect human life in a variety of ways

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CR 2

A large Southern state university has changed its teaching practices. Formerly, instructors without PhDs taught most introductory courses; now professors with PhDs will teach all introductory classes. That means the average class size will increase from 44 students per class to 600 per class, but overall the students’ learning experience should improve.

Which one of the following is an assumption required by this argument?

(A) Requiring professors with PhDs to teach all introductory classes will mean that the university must hire more faculty with doctorates.

(B) Students tend to participate in smaller classes more than they do in large lectures, even when the lectures are supplemented by weekly discussion sections.

(C) Major private universities already have implemented a format in which professors with PhDs teach all introductory classes as large lectures.

(D) A class taught by a PhD, even in a lecture format with hundreds of students, is a better learning environment than a smaller class taught by an instructor without a PhD.

(E) Services that rank colleges and universities usually consider the percentage of classes taught by PhDs when computing rank.
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Data Sufficiency Butler: July 2026
July 29DS 1DS 2

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DS 1

Paula has a collection of used books worth $104. How many are histories?

(1) Paula has only mysteries and histories; each mystery is worth $1, and each history is worth $25.
(2) Paula has exactly 4 mysteries in her collection that together are worth a total of $4.
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DS 2

­If company Y’s profits decreased $1.5 million from last year to this year, what was the percent decrease in profits?

(1) If the profits had decreased by $2 million, there would have been a 40 percent decrease.

(2) This year’s profits were $3.5 million
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jeffn
I got this till 6 different combinations i could not get till 60 because I forgot to factor B... :(
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then you should have made it 6 times 10
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