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This is an overlapping sets problem. What the question stem states is that each of 15 athletes either belongs to running events, field events or both. Now if we have number of athletes which belong to both we will still need number of athletes which belong only to field events, then we can sum these two and subtract from 15 to get the answer, however statement 1 does not do this hence insufficient
Statement 2 on the other hand directly provides the total number of people in field events and when we subtract this from 15 we will the the number of people which belong ONLY to running event. Hence this alone is sufficient

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Please someone share solution for 23 April DS 2
Ask me questions further if needed
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4X12/3(5X2) =?

Tell the answer.
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Problem Solving Butler: April 2025
April 21PS 1PS 2

_____________________________
PS 1

What is the smallest value of x such that 120x^2 is a cube of an integer?

A) 6
B) 10
C) 12
D) 15
E) 30
_____________________________
PS 2

If \(a\) and \(b\) are the greatest and the least product of 4 distinct integers, each of which has a value between -4 and 6, inclusive, then what is the value of \(a-b\)?

A) 960
B) 840
C) 720
D) 480
E) 360
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Critical Reasoning Butler: April 2025
April 21CR 1CR 2

_________________________________
CR 1

Which of the following most logically completes the passage?

For the past several years, cellular phone service has not been available in Volsinia, despite service being available in neighboring Rolisica. Recently two companies, Cyberdyne and Noratech, have each established the infrastructure necessary to provide cellular service to Volsinia residents. Although the services offered by the companies are similarly priced and are equally easy to use, Cyberdyneís product is likely to dominate the market, because .

(A) Cyberdyne has a much larger share of the international cellular service market than Noratech does.

(B) the number of Volsinia residents who will purchase cellular service is likely to double over the next few years.

(C) Noratechís infrastructure is better designed to accommodate population growth in Volsinia.

(D) both Cyberdyne and Noratech sell mobile phones in addition to cellular service.

(E) Cyberdyne is the only cellular service provider with a substantial presence in Rolisica, and many Volsinia residents frequently travel between the two countries.


_________________________________
CR 2

The sponsoring of bodies that govern sports by companies is a common practice. However, the introduction of commercial interests into a sport often leads to reforms in that sport such as changes to the design of uniforms, to the duration of games, and even to the actual rules. For this reason, traditional views are in opposition to the involvement of corporations in sports. Clearly, the objectors of corporate sponsoring have failed to consider the long-lasting subsistence of certain sports because __________.

(A) when the sponsoring corporation of a sport faces an important decision, it gratefully accepts suggestions put forward by fans

(B) many would probably have ceased to exist without the funding provided by corporations

(C) if they had not, they would have realized that sport does not need to be played at a commercial level to be enjoyed

(D) they are less concerned with a sport's character and more concerned with whether a sport will be played in 100 years time

(E) commercializing a game can remove its authentic appeal to spectators
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Data Sufficiency Butler: April 2025
April 21DS 1DS 2

__________________________________
DS 1
Tracy has 3 bags of marbles, each bag containing at least 1 blue marble, at least 1 red marble, and no marbles of another color. If Tracy selects 1 marble at random from each bag, what is the probability that all 3 marbles that she selects will be red?

(1) There is a total of 5 red marbles and 5 blue marbles in the 3 bags.
(2) The ratios of red to blue marbles in the 3 bags are 2: 1, 1: 1, and 1: 2.

__________________________________
DS 2

Trains A and B which were originally 420 miles apart began traveling towards one another on parallel adjacent tracks. How many miles from the point where train A began to travel will the trains meet?

(1) Train A is traveling at a constant speed of 94 miles per hour and train B is traveling at a constant speed of 47 miles per hour.

(2) Train A is traveling at a constant speed that is twice the constant speed of train B.
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5,000 cats live in a certain town. Of these cats, x are white, y are black, and z are black and white. How many cats are neither white nor black?
A. 5,000 - x + z
3. 5,000 - z
с. 5,000 - х - у
D. 5,000 - x - y + z
E. 5,000 - x -У - z
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5,000 cats live in a certain town. Of these cats, x are white, y are black, and z are black and white. How many cats are neither white nor black?
A. 5,000 - x + z
3. 5,000 - z
с. 5,000 - х - у
D. 5,000 - x - y + z
E. 5,000 - x -У - z

This is a reworded OG question: https://gmatclub.com/forum/a-certain-hi ... 07387.html
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Def not 10 & 25. 8 I am getting (sqrt(2) - 4)/(-51) so I would say just 1, but not sure I did that right
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if x = 8, expression becomes Sqrt((sqrt2)-4)/something. Now sqrt of negative is not defined. so I cannot be an answer

if x = 10, : 16/4(x-10)is not defined, Division by zero is not defined.. so II cannot be an answer

if x = 25, 3x-75 = 0
Division by zero is not defined. so III cannot be an answer

None of the above .
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Hello everyone :)! Here is today’s (April 24) DI Butler Question: the-pineal-gland-produces-melatonin-a-hormone-that-regulates-sleep-r-444255.html#p3561007
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Data Sufficiency Butler: April 2025
April 25DS 1DS 2

_______________________________
DS 1

How many hours were Fran and Fred away from home?

(1) They left at 9.30 am on Monday and returned at 9.30pm on Friday.
(2) Their home was empty for exactly four days.
_______________________________
DS 2

In a class, there are 170 students, each plays at least one out of 3 outdoor sports: Hockey, Tennis or Cricket. Of these students, 55 play exactly one sport. Is there any student in the class who plays Tennis and Cricket but not Hockey?

(1) 25 students play all the three types of sports.
(2) 35 students play Hockey and exactly one of the other two sports.
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Critical Reasoning Butler: April 2025
April 25CR 1CR 2

_______________________________
CR 1

A soccer league is divided into a junior and a senior division, separated not by age but by a player’s skill level. This year, to determine the division for which an aspirant is best qualified, the league held a week-long trial, after which coach A and coach B selected players. Coach A nominated sixteen of the forty players for the senior league. Amongst Coach B’s nominations for the senior division were four players not nominated by Coach A. Therefore, there will be twenty players in the senior division.

Which of the following, if true, provides the strongest basis for the conclusion above to be warranted?

(A) To be selected for the senior division, a player need only be nominated by one of the two coaches.

(B) Of the sixteen players nominated by the coach A, coach B nominated more than half to play in the senior division.

(C) All of the players not assigned to the senior division by both coaches were assigned to the junior division.

(D) Of those chosen by both coaches to play in the senior division all will end up playing in the senior league.

(E) The four players that Coach B but not Coach A selected for the senior division played the previous year in that division.

_______________________________
CR 2

The lobbyist accused of offering a large cash bribe to the senator defended himself: "When I left the house that day, I was carrying no money with me, so I could not possibly have had anything to offer to the senator. Moreover, immediately before I met with the senator, I spent all my cash on lunch with a colleague at an upscale restaurant, which also explains why I was not in a position to offer the senator a bribe."

This argument is most vulnerable to what criticism?

(A) It offers a conclusion that is no more than a paraphrase of one piece of the pieces of information provided in its support.

(B) It presents as evidence in support of a claim information that is inconsistent with other evidence presented in support of the same claim.

(C) It does not preserve the proper time relationship between cause and effect.

(D) It presents two pieces of evidence that do not support the same conclusion.

(E) It confuses basic financial information with legal claims.
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Problem Solving Butler: April 2025
April 25PS 1PS 2

_________________________________
PS 1

A ration shop had a stock of 200 packets of 1/2 Kg each premium sugar, and 300 packets of 1kg each regular sugar. The premium sugar is procured at Rs 30 per kg, while the regular sugar is procured at Rs 20 per kg. If the owner mixes the stock and sold them at the price of premium sugar what is the percentage profit of the shopkeeper?

A. 20
B. 28.57
C. 33.33
D. 40
E. 42.86
_________________________________
PS 2

John and Jack are among 10 students who write an examination. John scored 80 marks. The average score of the 8 students other than them is 72.5. The average score of all the 10 students is one more than the average score of the 9 students other than John. The score of Jack is

A. 40
B. 45
C. 50
D. 55
E. 60
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