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Aboyhasnoname
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instead of subtraction...divide the both equations
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Can you please explain how did you arrive at the third line
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divide the first two equations

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mshiva0340
Beautifull. Thank you
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here after arriving R18 = 3*R17, i.e R18 = 27*R15. What is this equation R18*T18 = R15*T15 can you explain please
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Bunuel
Critical Reasoning Butler: June 2025
June 23CR 1CR 2

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CR 1

Company X sold more products last year than it ever had before. However, Company X’s profit last year was smaller than ever before.

Which of the following, if true, would most contribute to an explanation of the facts above?

A. The prices of the products sold by Company X last year were higher than ever before.

B. A new company, Company Y, entered the market and became a competitor of Company X.

C. Two years ago, Company X’s profit was double its profit from last year.

D. Last year, the expenses of Company X were much higher than ever before.

E. Two years ago, Company X sold fewer products than it did last year.

______________________________
CR 2

Consuming gluten, a protein composite found in foods processed from wheat and related grains, causes allergic reactions in some adults. Medical records indicate that the percentage of adults in our country who have seen a doctor for gluten allergies has increased significantly in the last four years. Either our adults have been exposed to more glutens, or they have developed a greater sensitivity to them.

Which of the following is an assumption on which the argument depends?

A. The number of doctors specializing in nutrition in our country has not decreased over the past four years.

B. Adults who are allergic to gluten are no more likely than other adults to have allergies to other food ingredients.

C. Adults who have allergic reactions to gluten are not more likely to be see a doctor for treatment now than they were four years ago.

D. In our country, either more gluten has been introduced into foods artificially, or adults have eaten more food naturally containing gluten.

E. The percentage of the population in our country of adult age has not changed relative to four years ago.
CR 1 answer is d
CR 2 answer is c.
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CR QUESTION 2 - Option Choice A is the correct answer for this.

A States that no of doctors hasn’t decreased over the past 4 years. If the number of doctors decreased then the percent of adults who have seen a doctor will go up. This is one of the strong assumptions. If this is negated then the conclusion will break that it is just due to decrease of doctors the % has gone up and not due to adults exposure or greater sensitivity
Shouldn’t CR 2 be E??
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Quote:

*jeffn sends image:*
E
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Problem Solving Butler: June 2025
June 24PS 1PS 2

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PS 1

There are three types of tickets available for a concert: orchestra, which cost $12 each; balcony, which cost $9 each; and box, which cost $25 each. There were P orchestra tickets, B balcony tickets, and R box tickets sold for the concert. Which of the following expressions gives the percentage of ticket proceeds due to the sale of orchestra tickets?

(A) 100*P/(P + B + R)
(B) 100*12P/(12P + 9B + 25R)
(C) 12P/(12P + 9B + 25R)
(D) 100*(9B + 25R)/(12P + 9B + 25R)
(E) 100*(12P + 9B + 25R)/(12P)

___________________________
PS 2

If a + b + c + d is a positive number, a minimum of x of the numbers a, b, c, and d must be positive where x is equal to

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
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Critical Reasoning Butler: June 2025
June 24CR 1CR 2

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CR 1

Edward Grieg: Your gallery is biased against my paintings. I have submitted twenty canvases in the last three years and you have not accepted any of them for display. You are punishing me because I won the Western Art award three years ago and your manager thought the award should have gone to his artist son.

Gallery owner: You are wrong! Our acceptance standards and display policies do not discriminate against you. Our staff covers the painters’ names, so the review board does not know who the artist is when it determines which pieces of art will be accepted for display and sale. The review board would not know which paintings you submitted.

Which one of the following assumptions does the gallery owner make in his reply?

(A) The gallery manager holds no bad feelings about Edward Grieg winning the Western Art award over his artist son.

(B) Many artists submit their work to galleries without having any pieces accepted for display.

(C) The review board cannot recognize Edward Grieg’s paintings without seeing his name on the canvases.

(D) The gallery accepts only nature studies, and Edward Grieg’s paintings frequently portray people and interior settings.

(E) The review board has tended to favor oil paintings over the last several years and Edward Grieg more typically paints water colors.
________________________________
CR 2

­A cancer drug that shows positive results in early laboratory tests can generate a great deal of interest from cancer patients. Because of this interest, and the desire to make a profit early in the development cycle, many pharmaceutical companies rush the new drug to market as quickly as possible. But positive early results are often misleading, meaning that the effort to bring the drug to market was largely wasted. Consequently, the strategy to maximize long-term profit from a new cancer drug is to bring the drug to market only after its positive effects are more thoroughly tested and established.

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

(A) The first is a consideration that has been raised to argue that a certain strategy is counterproductive; the second presents an alternative strategy.

(B) The first is a consideration raised to support the strategy that the argument recommends; the second presents that strategy.

(C) The first is a consideration raised to explain the appeal of a certain strategy; the second presents an alternative strategy.

(D) The first is an assumption, rejected by the argument, that has been used to justify a course of action; the second presents that course of action.

(E) The first is a consideration that has been used to justify pursuing a goal that the argument rejects; the second presents a course of action that has been adopted in pursuit of that goal.­
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Data Sufficiency Butler: June 2025
June 24DS 1DS 2

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DS 1

Students took a test and received either A’s, B’s, C’s, D’s, or F’s. If 30% of the class got A’s or B’s, and 50% got C’s or D’s, how many students got F’s?

(1) 10 students received B’s.
(2) There was a total of 40 students in the class.
_____________________________
DS 2

A paint shop sells spray cans at a flat charge of 50 cents per can. If a customer bought 10 cans and the owner decided to give that customer a special discount on the last two cans, what was the price of the two discounted cans?

(1) The customer paid four dollars and twenty cents total for the ten cans.
(2) The customer bought the ten cans for an average price of 42 cents per can.
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Anyone else want to give this question a try?
the-equation-x-1-1-2-x-1-1-2-4x-1-1-2-has-446812.html
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Anyone else want to give this question a try?
the-equation-x-1-1-2-x-1-1-2-4x-1-1-2-has-446812.html
What’s the answer? It showed Official Answer not provided
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