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Lauren is clearly going to make an awful professor. Nearly half of her students failed their final this past spring. She should probably choose another career path, because her students’ performance demonstrates that she doesn’t teach very well.What statement, if true, most weakens the argument above?- a)This was Lauren’s second time teaching a college class.
- b)The class Lauren was teaching is a required class for all freshmen.
- c)The students who failed the exam also had poor attendance.
- d)The students who passed the exam attended an optional review session Lauren’s teaching assistant held.
- e)Lauren struggled early in the semester with lesson planning.
Correct answer is option 'C'. Can you explain this answer?
Lauren is clearly going to make an awful professor. Nearly half of her students failed their final this past spring. She should probably choose another career path, because her students’ performance demonstrates that she doesn’t teach very well.
What statement, if true, most weakens the argument above?
a)
This was Lauren’s second time teaching a college class.
b)
The class Lauren was teaching is a required class for all freshmen.
c)
The students who failed the exam also had poor attendance.
d)
The students who passed the exam attended an optional review session Lauren’s teaching assistant held.
e)
Lauren struggled early in the semester with lesson planning.
|
Arya Yadav answered |
C is correct because this shows that the students' poor attendance, and not Lauren's teaching style, was likely to blame for their poor performance on the exam. If they were not in class when Lauren was teaching, her style could have very little positive or negative impact on their learning.
A is incorrect because we do not know if Lauren's students did better, worse, or the same in the previous class than in this one.
B is incorrect because the class being required would have no direct impact on how students would do on a single exam.
D is incorrect because it speaks to the motivation of the students, and perhaps the teaching effectiveness of the TA, not Lauren herself.
E is incorrect because it supports that idea that Lauren has had issues with teaching effectiveness.
For which of the following values of x is the units digit of the product 2*3x equal to 4?- a)12
- b)13
- c)14
- d)15
- e)16
Correct answer is option 'D'. Can you explain this answer?
For which of the following values of x is the units digit of the product 2*3x equal to 4?
a)
12
b)
13
c)
14
d)
15
e)
16
|
Rahul Kapoor answered |
To determine the units digit of the product 2 * 3x, we need to focus on the units digits of the factors involved.
The units digit of 2 is always 2.
Now, let's consider the units digit of the powers of 3:
3^1 = 3 32 = 9 33 = 27 34 = 81 35 = 243 36 = 729 ...
We observe that the units digit of the powers of 3 cycles in the pattern: 3, 9, 7, 1. So, the units digit of 3^x depends on the remainder when x is divided by 4.
Now, we can consider the possible values of x and check the units digit of 3x:
For x = 12: 312 has a units digit of 1. For x = 13: 313 has a units digit of 3. For x = 14: 314 has a units digit of 9. For x = 15: 315 has a units digit of 7. For x = 16: 316 has a units digit of 1.
From the calculations above, we see that the only value of x for which the units digit of 3x is equal to 4 is x = 15.
Therefore, the correct answer is (D) 15.
Hardin argued that grazing land held in common (that is, open to any user) would always be used less carefully than private grazing land. Each rancher would be tempted to overuse common land because the benefits would accrue to the individuals, while the costs of reduced land quality that results from overuse would be spread among all users. But a study comparing 217 million acres of common grazing land with 433 million acres of private grazing land showed that the common land was in better condition.
Which of the following, if true and known by the ranchers, would best help explain the results of the study?- a)With private grazing land, both the costs and the benefits of overuse fall to the individual user.
- b)The cost in reduced land quality that is attributable to any individual user is less easily measured with common land than it is with private land.
- c)An individual who overuses common grazing land might be able to achieve higher returns than other users can, with the result that he or she would obtain a competitive advantage.
- d)If one user of common land overuses it even slightly, the other users are likely to do so even more, with the consequence that the costs to each user outweigh the benefits.
- e)There are more acres of grazing land held privately than there are held in common.
Correct answer is option 'D'. Can you explain this answer?
Hardin argued that grazing land held in common (that is, open to any user) would always be used less carefully than private grazing land. Each rancher would be tempted to overuse common land because the benefits would accrue to the individuals, while the costs of reduced land quality that results from overuse would be spread among all users. But a study comparing 217 million acres of common grazing land with 433 million acres of private grazing land showed that the common land was in better condition.
Which of the following, if true and known by the ranchers, would best help explain the results of the study?
Which of the following, if true and known by the ranchers, would best help explain the results of the study?
a)
With private grazing land, both the costs and the benefits of overuse fall to the individual user.
b)
The cost in reduced land quality that is attributable to any individual user is less easily measured with common land than it is with private land.
c)
An individual who overuses common grazing land might be able to achieve higher returns than other users can, with the result that he or she would obtain a competitive advantage.
d)
If one user of common land overuses it even slightly, the other users are likely to do so even more, with the consequence that the costs to each user outweigh the benefits.
e)
There are more acres of grazing land held privately than there are held in common.
|
Pioneer Academy answered |
This question is based on a passage discussing Hardin's argument regarding the use of common grazing land compared to private grazing land. Hardin's argument suggests that common land would be used less carefully because individuals would be tempted to overuse it, while the costs of overuse would be shared among all users. However, the study mentioned in the passage shows that common land is actually in better condition than private land. We are asked to choose the option that, if true and known by the ranchers, would best explain this result.
Let's analyze each option:
(A) With private grazing land, both the costs and the benefits of overuse fall to the individual user.
- This option does not provide a direct explanation for why common land is in better condition. It simply contrasts the distribution of costs and benefits between private and common land.
(B) The cost in reduced land quality that is attributable to any individual user is less easily measured with common land than it is with private land.
- This option suggests that it is more difficult to measure the specific costs of overuse on common land. However, it does not directly explain why the common land is in better condition.
(C) An individual who overuses common grazing land might be able to achieve higher returns than other users can, with the result that he or she would obtain a competitive advantage.
- This option suggests that there may be an incentive for individuals to overuse common land in order to gain a competitive advantage. While this provides a possible explanation for overuse, it does not address why the common land is actually in better condition.
(D) If one user of common land overuses it even slightly, the other users are likely to do so even more, with the consequence that the costs to each user outweigh the benefits.
- This option aligns with Hardin's argument and provides a compelling explanation for the result of the study. If one user overuses the common land, it can trigger a "tragedy of the commons" scenario where other users feel compelled to overuse it even more, leading to costs outweighing the benefits. This can result in the common land being less carefully used. However, the study shows that the common land is in better condition, suggesting that this scenario did not occur.
(E) There are more acres of grazing land held privately than there are held in common.
- This option provides information about the quantity of private and common grazing land but does not directly explain why the common land is in better condition.
Based on the analysis, option (D) provides the most reasonable explanation for the study's results. If users of common land are aware that overuse leads to costs outweighing the benefits, they would be more cautious in their usage, resulting in the common land being in better condition.
In Rubaria, excellent health care is available to virtually the entire population, whereas very few people in Terland receive adequate medical care. Yet, although the death rate for most diseases is higher in Terland than in Rubaria, the percentage of the male population that dies from prostate cancer is significantly higher in Rubaria than in Terland.Which of the following, if true, most helps to explain the disparity between the prostate cancer death rate in Rubaria and Terland?- a)Effective treatment of prostate cancer in its early stages generally requires medical techniques available in Rubaria but not in Terland.
- b)Most men who have prostate cancer are older than the average life expectancy for male inhabitants of Terland.
- c)Being in poor general health does not increase one’s risk of developing prostate cancer.
- d)It is possible to decrease one’s risk of getting prostate cancer by eating certain kinds of foods, and such foods are more readily available in Rubaria than in Terland.
- e)Among men in Rubaria, the death rate from prostate cancer is significantly higher for those who do not take full advantage of Rubaria’s health care system than for those who do.
Correct answer is option 'B'. Can you explain this answer?
In Rubaria, excellent health care is available to virtually the entire population, whereas very few people in Terland receive adequate medical care. Yet, although the death rate for most diseases is higher in Terland than in Rubaria, the percentage of the male population that dies from prostate cancer is significantly higher in Rubaria than in Terland.
Which of the following, if true, most helps to explain the disparity between the prostate cancer death rate in Rubaria and Terland?
a)
Effective treatment of prostate cancer in its early stages generally requires medical techniques available in Rubaria but not in Terland.
b)
Most men who have prostate cancer are older than the average life expectancy for male inhabitants of Terland.
c)
Being in poor general health does not increase one’s risk of developing prostate cancer.
d)
It is possible to decrease one’s risk of getting prostate cancer by eating certain kinds of foods, and such foods are more readily available in Rubaria than in Terland.
e)
Among men in Rubaria, the death rate from prostate cancer is significantly higher for those who do not take full advantage of Rubaria’s health care system than for those who do.
|
|
Pioneer Academy answered |
Let's analyze each answer choice and see which one best explains the disparity between the prostate cancer death rate in Rubaria and Terland.
(A) Effective treatment of prostate cancer in its early stages generally requires medical techniques available in Rubaria but not in Terland.
- This answer choice suggests that Rubaria has advanced medical techniques for treating prostate cancer, which could contribute to a higher death rate if those techniques are not available in Terland. However, it does not explain why the death rate is higher in Rubaria specifically.
(B) Most men who have prostate cancer are older than the average life expectancy for male inhabitants of Terland.
- This answer choice provides a plausible explanation. If most men with prostate cancer in Terland are older than the average life expectancy, it means that they are more likely to die from other causes before prostate cancer becomes a significant threat. This could explain why the prostate cancer death rate is lower in Terland compared to Rubaria, where the population may have a longer life expectancy.
(C) Being in poor general health does not increase one’s risk of developing prostate cancer.
- This answer choice is irrelevant to explaining the disparity in prostate cancer death rates between Rubaria and Terland. It focuses on the risk of developing prostate cancer, not the death rate associated with it.
(D) It is possible to decrease one’s risk of getting prostate cancer by eating certain kinds of foods, and such foods are more readily available in Rubaria than in Terland.
- This answer choice discusses the risk of getting prostate cancer, not the death rate. It does not directly explain why the death rate is higher in Rubaria.
(E) Among men in Rubaria, the death rate from prostate cancer is significantly higher for those who do not take full advantage of Rubaria’s health care system than for those who do.
- This answer choice is specific to Rubaria and suggests that not taking advantage of the health care system leads to a higher death rate from prostate cancer. However, it does not explain why the death rate in Rubaria is higher than in Terland.
After analyzing each answer choice, we can see that (B) is the best option. It provides a plausible explanation for the higher prostate cancer death rate in Rubaria compared to Terland by stating that most men with prostate cancer in Terland are older than the average life expectancy, which means they are less likely to die from prostate cancer before dying from other causes.
A study of 200 comedy fiction readers revealed the impact of Wodehouse’s’ novels on human emotions. Each of the 200 participants was asked to read at least one novel per day over the course of 12 days. At the end of the experiment, all of the readers filled out a survey assessing their emotional state. It was found from the survey that some 10 students who read the greatest number of novels reported lower stress levels and higher energy levels. Also, most of the 20 students who read the fewest number of novels revealed below-average levels of emotional comfort.Which of the following must be true based on the evidence presented above?- a)A majority of the participants lowered stress levels and reported higher emotional ease.
- b)During each week of the experiment, the participants spent at least 2 hours less per day on their academic work as a result of reading.
- c)Reading Wodehouse’s novels for at least 2 hours per day improves the emotional well-being of the majority of young adults.
- d)More than 8 participants read at least 14 novels during the course of the experiment.
- e)At least some of the students participated in the study in order to gain free access to Wodehouse’s novels.
Correct answer is option 'D'. Can you explain this answer?
A study of 200 comedy fiction readers revealed the impact of Wodehouse’s’ novels on human emotions. Each of the 200 participants was asked to read at least one novel per day over the course of 12 days. At the end of the experiment, all of the readers filled out a survey assessing their emotional state. It was found from the survey that some 10 students who read the greatest number of novels reported lower stress levels and higher energy levels. Also, most of the 20 students who read the fewest number of novels revealed below-average levels of emotional comfort.
Which of the following must be true based on the evidence presented above?
a)
A majority of the participants lowered stress levels and reported higher emotional ease.
b)
During each week of the experiment, the participants spent at least 2 hours less per day on their academic work as a result of reading.
c)
Reading Wodehouse’s novels for at least 2 hours per day improves the emotional well-being of the majority of young adults.
d)
More than 8 participants read at least 14 novels during the course of the experiment.
e)
At least some of the students participated in the study in order to gain free access to Wodehouse’s novels.
|
Wizius Careers answered |
The evidence states that the study involved 200 comedy fiction readers who were asked to read at least one Wodehouse novel per day for 12 days. At the end of the experiment, they filled out a survey about their emotional state. It was found that the 10 students who read the greatest number of novels reported lower stress levels and higher energy levels. Additionally, most of the 20 students who read the fewest number of novels revealed below-average levels of emotional comfort.
Now, let's evaluate the answer choices:
(A) A majority of the participants lowered stress levels and reported higher emotional ease. There is no information provided in the evidence about the majority of participants. The evidence only mentions the 10 students who read the greatest number of novels reporting lower stress levels and higher energy levels. Therefore, we cannot conclude that a majority of the participants experienced these outcomes. So, (A) cannot be inferred from the evidence.
(B) During each week of the experiment, the participants spent at least 2 hours less per day on their academic work as a result of reading. There is no information provided in the evidence regarding the participants' time spent on academic work during the experiment. We cannot make any assumptions about the time they spent on academic work based on the given information. Thus, (B) cannot be inferred from the evidence.
(C) Reading Wodehouse’s novels for at least 2 hours per day improves the emotional well-being of the majority of young adults. The evidence does not explicitly state that reading Wodehouse's novels for at least 2 hours per day improves the emotional well-being of the majority of young adults. We only know that the 10 students who read the greatest number of novels reported lower stress levels and higher energy levels. So, (C) cannot be inferred from the evidence.
(D) More than 8 participants read at least 14 novels during the course of the experiment. Based on the evidence, we know that there were 10 students who read the greatest number of novels. However, we do not know the exact number of novels they read. The evidence does not provide information about the number of participants who read at least 14 novels. So, (D) cannot be inferred from the evidence.
(E) At least some of the students participated in the study in order to gain free access to Wodehouse’s novels. The evidence does not mention anything about the motivation of the students participating in the study. There is no information provided to support the claim that some students participated in order to gain free access to the novels. Therefore, (E) cannot be inferred from the evidence.
In conclusion, the only statement that can be inferred from the evidence is (D): More than 8 participants read at least 14 novels during the course of the experiment. This can be deduced because it is stated that the 10 students who read the greatest number of novels reported lower stress levels and higher energy levels, indicating that at least some participants read a significant number of novels.
The important parts of any university professor’s job include not only classroom teaching but also research, publication, and lectures to colleagues and the public. This is why university professors who are good classroom teachers but have not engaged in any other scholarly activities are usually denied tenure.The statements above, if true, most strongly support which one of the following?- a)University professors who have not failed to perform important parts of their jobs are not usually denied tenure.
- b)Some university professors have been denied tenure even though they have done an important part of their jobs well.
- c)University professors who do not engage in other scholarly activities are usually good classroom teachers.
- d)University professors who have engaged in research, publication, and lectures to colleagues and the public are usually granted tenure.
- e)Classroom teaching is the least important part of a university professor’s job
Correct answer is option 'B'. Can you explain this answer?
The important parts of any university professor’s job include not only classroom teaching but also research, publication, and lectures to colleagues and the public. This is why university professors who are good classroom teachers but have not engaged in any other scholarly activities are usually denied tenure.
The statements above, if true, most strongly support which one of the following?
a)
University professors who have not failed to perform important parts of their jobs are not usually denied tenure.
b)
Some university professors have been denied tenure even though they have done an important part of their jobs well.
c)
University professors who do not engage in other scholarly activities are usually good classroom teachers.
d)
University professors who have engaged in research, publication, and lectures to colleagues and the public are usually granted tenure.
e)
Classroom teaching is the least important part of a university professor’s job
|
|
Rahul Kapoor answered |
The prompt states that university professors need to engage in various activities, including classroom teaching, research, publication, and lectures to colleagues and the public. It further asserts that professors who are good teachers but have not participated in other scholarly activities are typically denied tenure.
Now let's evaluate the answer choices:
(A) University professors who have not failed to perform important parts of their jobs are not usually denied tenure.
This answer choice is not supported by the information provided. The prompt mentions that professors who are good classroom teachers but do not engage in other scholarly activities are denied tenure, suggesting that their failure to perform these additional activities is a factor in their tenure denial.
This answer choice is not supported by the information provided. The prompt mentions that professors who are good classroom teachers but do not engage in other scholarly activities are denied tenure, suggesting that their failure to perform these additional activities is a factor in their tenure denial.
(B) Some university professors have been denied tenure even though they have done an important part of their jobs well.
This answer choice aligns with the information in the prompt. It acknowledges that professors who excel in classroom teaching but neglect other scholarly activities may still be denied tenure. This statement is supported by the prompt and is the most appropriate choice.
This answer choice aligns with the information in the prompt. It acknowledges that professors who excel in classroom teaching but neglect other scholarly activities may still be denied tenure. This statement is supported by the prompt and is the most appropriate choice.
(C) University professors who do not engage in other scholarly activities are usually good classroom teachers.
This answer choice is not supported by the information provided. The prompt does not make a direct connection between professors who do not engage in other scholarly activities and their abilities as classroom teachers.
This answer choice is not supported by the information provided. The prompt does not make a direct connection between professors who do not engage in other scholarly activities and their abilities as classroom teachers.
(D) University professors who have engaged in research, publication, and lectures to colleagues and the public are usually granted tenure.
This answer choice goes beyond what the prompt states. While the prompt mentions that engaging in research, publication, and lectures to colleagues and the public is important, it does not explicitly state that professors who do so are usually granted tenure.
This answer choice goes beyond what the prompt states. While the prompt mentions that engaging in research, publication, and lectures to colleagues and the public is important, it does not explicitly state that professors who do so are usually granted tenure.
(E) Classroom teaching is the least important part of a university professor’s job.
This answer choice contradicts the prompt, which states that classroom teaching is an important part of a university professor's job. The prompt emphasizes that professors who are good classroom teachers but neglect other scholarly activities are denied tenure.
This answer choice contradicts the prompt, which states that classroom teaching is an important part of a university professor's job. The prompt emphasizes that professors who are good classroom teachers but neglect other scholarly activities are denied tenure.
In conclusion, the most strongly supported answer choice is (B) "Some university professors have been denied tenure even though they have done an important part of their jobs well."
Working alone Jerry can complete a work in 6 minutes. Working alone, Adam can complete a work in 8 minutes. Working together, Jerry leaves the work after 2 minutes. How long will it take Adam to complete the work?- a)2 minutes
- b)3 minutes
- c)10/3 minutes
- d)5 minutes
- e)10 minutes
Correct answer is option 'C'. Can you explain this answer?
Working alone Jerry can complete a work in 6 minutes. Working alone, Adam can complete a work in 8 minutes. Working together, Jerry leaves the work after 2 minutes. How long will it take Adam to complete the work?
a)
2 minutes
b)
3 minutes
c)
10/3 minutes
d)
5 minutes
e)
10 minutes
|
Aditya Gupta answered |
Given:
- Jerry can complete a work in 6 minutes.
- Adam can complete a work in 8 minutes.
- Jerry leaves the work after 2 minutes when they are working together.
To find:
- How long will it take Adam to complete the work?
Solution:
When working together, Jerry and Adam can complete 1/6th of the work in 1 minute (since Jerry takes 6 minutes to complete the work alone) and 1/8th of the work in 1 minute (since Adam takes 8 minutes to complete the work alone).
Step 1: Calculate the work done by Jerry and Adam in 2 minutes.
- Jerry completes 2/6th of the work in 2 minutes.
- Adam completes 2/8th of the work in 2 minutes.
Step 2: Calculate the remaining work.
- The remaining work after 2 minutes is 1 - (2/6) = 4/6th.
- The remaining work after 2 minutes is also 1 - (2/8) = 6/8th.
Step 3: Calculate the work done by Adam in 1 minute.
- Adam can complete 1/8th of the work in 1 minute.
- Adam can complete (1/8) / 2 = 1/16th of the work in 2 minutes.
Step 4: Calculate the time taken by Adam to complete the remaining work.
- Adam can complete the remaining work (4/6) in (4/6) * (2/1/16) = 10/3 minutes.
Therefore, it will take Adam 10/3 minutes to complete the work.
- Jerry can complete a work in 6 minutes.
- Adam can complete a work in 8 minutes.
- Jerry leaves the work after 2 minutes when they are working together.
To find:
- How long will it take Adam to complete the work?
Solution:
When working together, Jerry and Adam can complete 1/6th of the work in 1 minute (since Jerry takes 6 minutes to complete the work alone) and 1/8th of the work in 1 minute (since Adam takes 8 minutes to complete the work alone).
Step 1: Calculate the work done by Jerry and Adam in 2 minutes.
- Jerry completes 2/6th of the work in 2 minutes.
- Adam completes 2/8th of the work in 2 minutes.
Step 2: Calculate the remaining work.
- The remaining work after 2 minutes is 1 - (2/6) = 4/6th.
- The remaining work after 2 minutes is also 1 - (2/8) = 6/8th.
Step 3: Calculate the work done by Adam in 1 minute.
- Adam can complete 1/8th of the work in 1 minute.
- Adam can complete (1/8) / 2 = 1/16th of the work in 2 minutes.
Step 4: Calculate the time taken by Adam to complete the remaining work.
- Adam can complete the remaining work (4/6) in (4/6) * (2/1/16) = 10/3 minutes.
Therefore, it will take Adam 10/3 minutes to complete the work.
If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is:- a)2 : 3
- b)3 : 2
- c)3 : 4
- d)4 : 3
- e)5 : 3
Correct answer is option 'A'. Can you explain this answer?
If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is:
a)
2 : 3
b)
3 : 2
c)
3 : 4
d)
4 : 3
e)
5 : 3
|
|
Prisha Mukherjee answered |
To solve this problem, let's first understand the given information and the properties of an arithmetic progression.
Given:
Square of the 7th term = Product of the 3rd and 17th terms
Let's assume the first term of the arithmetic progression is 'a' and the common difference is 'd'.
Properties of an arithmetic progression:
The nth term of an arithmetic progression can be represented as: a + (n-1)d
The square of the nth term can be represented as: (a + (n-1)d)^2
Now let's use the given information and the properties of an arithmetic progression to solve the problem.
The square of the 7th term = (a + 6d)^2
The product of the 3rd and 17th terms = (a + 2d)(a + 16d)
Since the square of the 7th term is equal to the product of the 3rd and 17th terms, we have:
(a + 6d)^2 = (a + 2d)(a + 16d)
Expanding both sides of the equation:
a^2 + 12ad + 36d^2 = a^2 + 18ad + 32d^2
Subtracting a^2 from both sides:
12ad + 36d^2 = 18ad + 32d^2
Rearranging the terms:
6ad = -4d^2
Dividing both sides by 2d:
3a = -2d
Dividing both sides by -2:
a/d = -2/3
Since the common difference 'd' is positive, we can rewrite the ratio as:
a/d = 2/(-3)
Simplifying the ratio:
a/d = -2/3
Therefore, the ratio of the first term to the common difference is 2 : 3, which corresponds to option A.
Hence, the correct answer is option A) 2 : 3.
Given:
Square of the 7th term = Product of the 3rd and 17th terms
Let's assume the first term of the arithmetic progression is 'a' and the common difference is 'd'.
Properties of an arithmetic progression:
The nth term of an arithmetic progression can be represented as: a + (n-1)d
The square of the nth term can be represented as: (a + (n-1)d)^2
Now let's use the given information and the properties of an arithmetic progression to solve the problem.
The square of the 7th term = (a + 6d)^2
The product of the 3rd and 17th terms = (a + 2d)(a + 16d)
Since the square of the 7th term is equal to the product of the 3rd and 17th terms, we have:
(a + 6d)^2 = (a + 2d)(a + 16d)
Expanding both sides of the equation:
a^2 + 12ad + 36d^2 = a^2 + 18ad + 32d^2
Subtracting a^2 from both sides:
12ad + 36d^2 = 18ad + 32d^2
Rearranging the terms:
6ad = -4d^2
Dividing both sides by 2d:
3a = -2d
Dividing both sides by -2:
a/d = -2/3
Since the common difference 'd' is positive, we can rewrite the ratio as:
a/d = 2/(-3)
Simplifying the ratio:
a/d = -2/3
Therefore, the ratio of the first term to the common difference is 2 : 3, which corresponds to option A.
Hence, the correct answer is option A) 2 : 3.
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Q. Which of the following, if true, most weakens the argument above?- a)Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest.
- b)Futures prices for corn have been fluctuating more dramatically this season than last season.
- c)The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region.
- d)Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season.
- e)Most people who trade in corn futures rarely take physical possession of the corn they trade.
Correct answer is option 'D'. Can you explain this answer?
Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.
Q. Which of the following, if true, most weakens the argument above?
Q. Which of the following, if true, most weakens the argument above?
a)
Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest.
b)
Futures prices for corn have been fluctuating more dramatically this season than last season.
c)
The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corn-growing region.
d)
Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season.
e)
Most people who trade in corn futures rarely take physical possession of the corn they trade.
|
|
Rutuja Banerjee answered |
The argument, in predicting a drop in the price of corn futures, relies on news suggesting a good-sized corn crop. This prediction is undermined if there is, at the same time, news suggesting a small crop. Choice D presents such news and is therefore the best answer.
Choice A provides background information describing a stage at which rains are essential, and choice C makes rain over the entire corn-growing area seem more certain. Both are fully compatible with the argument and do nothing to weaken it. Past price changes (choice B) and details of who handles harvested corn (choice E) cannot affect the eventual size of this year’s corn crop, so neither is relevant to the argument.
Choice A provides background information describing a stage at which rains are essential, and choice C makes rain over the entire corn-growing area seem more certain. Both are fully compatible with the argument and do nothing to weaken it. Past price changes (choice B) and details of who handles harvested corn (choice E) cannot affect the eventual size of this year’s corn crop, so neither is relevant to the argument.
My neighbor's dogs bark and howl every time their owner lets them outside. My CPA told me that dogs tend to bark and howl when they see birds resting in the top branches of their favorite trees. I personally believe they bark and howl because they enjoy disrupting my meditations.Which of the following can be inferred from the preceding passage?- a)The dogs must be abused by their owners.
- b)The dogs' owners do not make efforts to stop the dogs from barking and howling.
- c)There are many pedestrians who walk by this neighbor's house, and the dogs are starving for attention.
- d)The dogs frequently see birds in the tops of their favorite trees.
- e)The dogs will bark and howl at 3 a.m. if they are outside at that time.
Correct answer is option 'E'. Can you explain this answer?
My neighbor's dogs bark and howl every time their owner lets them outside. My CPA told me that dogs tend to bark and howl when they see birds resting in the top branches of their favorite trees. I personally believe they bark and howl because they enjoy disrupting my meditations.
Which of the following can be inferred from the preceding passage?
a)
The dogs must be abused by their owners.
b)
The dogs' owners do not make efforts to stop the dogs from barking and howling.
c)
There are many pedestrians who walk by this neighbor's house, and the dogs are starving for attention.
d)
The dogs frequently see birds in the tops of their favorite trees.
e)
The dogs will bark and howl at 3 a.m. if they are outside at that time.
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Sharmila Singh answered |
Understanding the Passage
The passage discusses the barking and howling behavior of the neighbor's dogs and presents two contrasting explanations for this behavior.
Key Explanations Presented
- The CPA suggests that the dogs bark and howl due to the presence of birds in the trees.
- The narrator believes the dogs enjoy disrupting their meditation.
Analysis of the Options
When evaluating the options provided, we look for what can be reasonably inferred from the information given in the passage:
a) The dogs must be abused by their owners.
- There is no evidence in the passage to support this claim; it does not mention any abusive behavior.
b) The dogs' owners do not make efforts to stop the dogs from barking and howling.
- The passage does not provide information about the owners' actions regarding the barking.
c) There are many pedestrians who walk by this neighbor's house, and the dogs are starving for attention.
- The passage does not mention pedestrians or any attention-seeking behavior related to them.
d) The dogs frequently see birds in the tops of their favorite trees.
- While the CPA suggests that the dogs bark at birds, the frequency of this behavior is not established in the passage.
e) The dogs will bark and howl at 3 a.m. if they are outside at that time.
- This can be inferred as a possibility, given their consistent barking behavior when outside. The time of 3 a.m. is not explicitly mentioned, but it implies that their behavior could occur at any time, including early morning hours.
Conclusion
Thus, option 'E' is a reasonable inference based on the general behavior of the dogs as described in the passage.
The passage discusses the barking and howling behavior of the neighbor's dogs and presents two contrasting explanations for this behavior.
Key Explanations Presented
- The CPA suggests that the dogs bark and howl due to the presence of birds in the trees.
- The narrator believes the dogs enjoy disrupting their meditation.
Analysis of the Options
When evaluating the options provided, we look for what can be reasonably inferred from the information given in the passage:
a) The dogs must be abused by their owners.
- There is no evidence in the passage to support this claim; it does not mention any abusive behavior.
b) The dogs' owners do not make efforts to stop the dogs from barking and howling.
- The passage does not provide information about the owners' actions regarding the barking.
c) There are many pedestrians who walk by this neighbor's house, and the dogs are starving for attention.
- The passage does not mention pedestrians or any attention-seeking behavior related to them.
d) The dogs frequently see birds in the tops of their favorite trees.
- While the CPA suggests that the dogs bark at birds, the frequency of this behavior is not established in the passage.
e) The dogs will bark and howl at 3 a.m. if they are outside at that time.
- This can be inferred as a possibility, given their consistent barking behavior when outside. The time of 3 a.m. is not explicitly mentioned, but it implies that their behavior could occur at any time, including early morning hours.
Conclusion
Thus, option 'E' is a reasonable inference based on the general behavior of the dogs as described in the passage.
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?- a)1
- b)2
- c)3
- d)4
- e)5
Correct answer is option 'E'. Can you explain this answer?
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?
What is the remainder when m – n is divided by 6?
a)
1
b)
2
c)
3
d)
4
e)
5
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Snehal Banerjee answered |
If two numbers leave remainders of 2 and 3 when divided by 6, then we can write them as $6a+2$ and $6b+3$, where $a$ and $b$ are integers. We are given that $m>n$, so we can write $m=6a+2$ and $n=6b+3$.
The problem asks us to find the remainder when $m-n$ is divided by 6. We can substitute the expressions for $m$ and $n$ to find:
\begin{align*}
m-n &= (6a+2)-(6b+3)\\
&= 6a-6b+2-3\\
&= 6(a-b)-1.
\end{align*}Since $a$ and $b$ are integers, $a-b$ is also an integer. Therefore, $6(a-b)$ is a multiple of 6. The remainder when $6(a-b)$ is divided by 6 is $\boxed{0}$.
The problem asks us to find the remainder when $m-n$ is divided by 6. We can substitute the expressions for $m$ and $n$ to find:
\begin{align*}
m-n &= (6a+2)-(6b+3)\\
&= 6a-6b+2-3\\
&= 6(a-b)-1.
\end{align*}Since $a$ and $b$ are integers, $a-b$ is also an integer. Therefore, $6(a-b)$ is a multiple of 6. The remainder when $6(a-b)$ is divided by 6 is $\boxed{0}$.
Division manager: I want to replace the Microton computers in my division with Vitech computers.
General manager: Why?
Division manager: It costs 28 percent less to train new staff on the Vitech.
General manager: But that is not a good enough reason. We can simply hire only people who already know how to use the Microton computer.
Q. Which of the following, if true, most seriously undermines the general manager’s objection to the replacement of Microton computers with Vtech's?- a)Currently, all employees in the company are required to attend workshops on how to use Microton computers in new applications.
- b)Once employees learn how to use a computer, they tend to change employers more readily than before.
- c)Experienced users of Microton computers command much higher salaries than do prospective employees who have no experience in the use of computers.
- d)The average productivity of employees in the general manager’s company is below the average productivity of the employees of its competitors.
- e)The high costs of replacement parts make Vitech computers more expensive to maintain than Microton computers.
Correct answer is option 'C'. Can you explain this answer?
Division manager: I want to replace the Microton computers in my division with Vitech computers.
General manager: Why?
Division manager: It costs 28 percent less to train new staff on the Vitech.
General manager: But that is not a good enough reason. We can simply hire only people who already know how to use the Microton computer.
Q. Which of the following, if true, most seriously undermines the general manager’s objection to the replacement of Microton computers with Vtech's?
General manager: Why?
Division manager: It costs 28 percent less to train new staff on the Vitech.
General manager: But that is not a good enough reason. We can simply hire only people who already know how to use the Microton computer.
Q. Which of the following, if true, most seriously undermines the general manager’s objection to the replacement of Microton computers with Vtech's?
a)
Currently, all employees in the company are required to attend workshops on how to use Microton computers in new applications.
b)
Once employees learn how to use a computer, they tend to change employers more readily than before.
c)
Experienced users of Microton computers command much higher salaries than do prospective employees who have no experience in the use of computers.
d)
The average productivity of employees in the general manager’s company is below the average productivity of the employees of its competitors.
e)
The high costs of replacement parts make Vitech computers more expensive to maintain than Microton computers.
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|
Chirag Sen answered |
The general manager’s objection is based on avoiding training costs altogether. But if, as choice C says, hiring experienced users of Microton computers is significantly more costly than hiring otherwise qualified people who would have to be trained to use Vitech computers, the force of the objection is weakened. Choice C, therefore, is the best answer.
Choices A, B, and D are all incorrect; none of them provides information relevant to an evaluation of Microton computers as compared with Vitech computers. Choice E argues independently against replacing Microton computers with Vitech and thus is also incorrect.
Choices A, B, and D are all incorrect; none of them provides information relevant to an evaluation of Microton computers as compared with Vitech computers. Choice E argues independently against replacing Microton computers with Vitech and thus is also incorrect.
Last year all refuse collected by Shelbyville city services was incinerated. This incineration generated a large quantity of residual ash. In order to reduce the amount of residual ash Shelbyville generates this year to half of last year's total, the city has revamped its collection program. This year city services will separate for recycling enough refuse to reduce the number of truckloads of refuse to be incinerated to half of last year's number.Which of the following is required for the revamped collection program to achieve its aim?- a)This year, no materials that city services could separate for recycling will be incinerated.
- b)Separating recyclable materials from materials to be incinerated will cost Shelbyville less than half what it cost last year to dispose of the residual ash.
- c)Refuse collected by city services will contain a larger proportion of recyclable materials this year than it did last year.
- d)The refuse incinerated this year will generate no more residual ash per truckload incinerated than did the refuse incinerated last year.
- e)The total quantity of refuse collected by Shelbyville city service's this year will be no greater than that collected last year.
Correct answer is option 'D'. Can you explain this answer?
Last year all refuse collected by Shelbyville city services was incinerated. This incineration generated a large quantity of residual ash. In order to reduce the amount of residual ash Shelbyville generates this year to half of last year's total, the city has revamped its collection program. This year city services will separate for recycling enough refuse to reduce the number of truckloads of refuse to be incinerated to half of last year's number.
Which of the following is required for the revamped collection program to achieve its aim?
a)
This year, no materials that city services could separate for recycling will be incinerated.
b)
Separating recyclable materials from materials to be incinerated will cost Shelbyville less than half what it cost last year to dispose of the residual ash.
c)
Refuse collected by city services will contain a larger proportion of recyclable materials this year than it did last year.
d)
The refuse incinerated this year will generate no more residual ash per truckload incinerated than did the refuse incinerated last year.
e)
The total quantity of refuse collected by Shelbyville city service's this year will be no greater than that collected last year.
|
|
Hridoy Desai answered |
Explanation:
Goal:
To reduce the amount of residual ash generated by Shelbyville city services to half of last year's total.
Requirement:
The revamped collection program needs to ensure that the refuse incinerated this year will generate no more residual ash per truckload incinerated than did the refuse incinerated last year.
Explanation:
- If the refuse incinerated this year generates the same amount of residual ash per truckload as last year, then reducing the number of truckloads of refuse to be incinerated to half of last year's number will automatically result in reducing the overall amount of residual ash to half of last year's total.
- This is because even though the total quantity of refuse collected may vary, if the residual ash generated per truckload remains the same, reducing the number of truckloads to be incinerated will directly lead to reducing the total residual ash generated.
Therefore, ensuring that the refuse incinerated this year will generate no more residual ash per truckload incinerated than did the refuse incinerated last year is crucial for the revamped collection program to achieve its aim of reducing the amount of residual ash generated to half of last year's total.
Goal:
To reduce the amount of residual ash generated by Shelbyville city services to half of last year's total.
Requirement:
The revamped collection program needs to ensure that the refuse incinerated this year will generate no more residual ash per truckload incinerated than did the refuse incinerated last year.
Explanation:
- If the refuse incinerated this year generates the same amount of residual ash per truckload as last year, then reducing the number of truckloads of refuse to be incinerated to half of last year's number will automatically result in reducing the overall amount of residual ash to half of last year's total.
- This is because even though the total quantity of refuse collected may vary, if the residual ash generated per truckload remains the same, reducing the number of truckloads to be incinerated will directly lead to reducing the total residual ash generated.
Therefore, ensuring that the refuse incinerated this year will generate no more residual ash per truckload incinerated than did the refuse incinerated last year is crucial for the revamped collection program to achieve its aim of reducing the amount of residual ash generated to half of last year's total.
The age of a group of people follows a distribution, which is symmetric about the average (mean) A. If 95% of the distribution falls within two standard deviation (SD) of the mean, then what percentage of the same distribution is less than A + 2SD?- a)68%
- b)84%
- c)95%
- d)97.5%
- e)99%
Correct answer is option 'D'. Can you explain this answer?
The age of a group of people follows a distribution, which is symmetric about the average (mean) A. If 95% of the distribution falls within two standard deviation (SD) of the mean, then what percentage of the same distribution is less than A + 2SD?
a)
68%
b)
84%
c)
95%
d)
97.5%
e)
99%
|
|
Rahul Kapoor answered |
We need to determine
• The percentage of the same distribution, which is less than A + 2SD.
• The percentage of the same distribution, which is less than A + 2SD.
As it is given that 95% of the distribution falls within two standard deviation (SD) of the mean, we can conclude that 5% lies outside this given range.
Now, as the distribution is symmetric about the mean A, we can also say that
• Half of 5% or 2.5% lies to the right of A + 2SD
• Therefore, the remaining (100 – 2.5) = 97.5% lies to the left of A + 2SD, or less than A + 2SD.
• Half of 5% or 2.5% lies to the right of A + 2SD
• Therefore, the remaining (100 – 2.5) = 97.5% lies to the left of A + 2SD, or less than A + 2SD.
Hence, the correct answer is option D.
A computer equipped with signature-recognition software, which restricts access to a computer to those people whose signatures are on file, identifies a person’s signature by analyzing not only the form of the signature but also such characteristics as pen pressure and signing speed. Even the most adept forgers cannot duplicate all of the characteristics the program analyzes.
Q. Which of the following can be logically concluded from the passage above?- a)The time it takes to record and analyze a signature makes the software impractical for everyday use.
- b)Computers equipped with the software will soon be installed in most banks.
- c)Nobody can gain access to a computer equipped with the software solely by virtue of skill at forging signatures.
- d)Signature-recognition software has taken many years to develop and perfect.
- e)In many cases even authorized users are denied legitimate access to computers equipped with the software.
Correct answer is option 'C'. Can you explain this answer?
A computer equipped with signature-recognition software, which restricts access to a computer to those people whose signatures are on file, identifies a person’s signature by analyzing not only the form of the signature but also such characteristics as pen pressure and signing speed. Even the most adept forgers cannot duplicate all of the characteristics the program analyzes.
Q. Which of the following can be logically concluded from the passage above?
Q. Which of the following can be logically concluded from the passage above?
a)
The time it takes to record and analyze a signature makes the software impractical for everyday use.
b)
Computers equipped with the software will soon be installed in most banks.
c)
Nobody can gain access to a computer equipped with the software solely by virtue of skill at forging signatures.
d)
Signature-recognition software has taken many years to develop and perfect.
e)
In many cases even authorized users are denied legitimate access to computers equipped with the software.
|
|
Palak Yadav answered |
The passage asserts that skill at forging signatures is not by itself sufficient to match all of the characteristics that the software analyzes to identify signatures. Because the software gives access only after identifying a signature, access cannot be achieved by someone employing forging skill alone. Choice C is thus the best answer.
The passage gives no information about how fast the software operates or about how long the software was under development, so neither A nor D can be concluded. Choice B is incorrect since the software might have features not mentioned in the passage that make it unattractive to banks. The passages give no reason to think that errors of the sort that choice E describes, even if made, would be numerous.
The passage gives no information about how fast the software operates or about how long the software was under development, so neither A nor D can be concluded. Choice B is incorrect since the software might have features not mentioned in the passage that make it unattractive to banks. The passages give no reason to think that errors of the sort that choice E describes, even if made, would be numerous.
Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?- a)24
- b)25
- c)26
- d)27
- e)28
Correct answer is option 'C'. Can you explain this answer?
Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?
a)
24
b)
25
c)
26
d)
27
e)
28
|
|
Tejas Gupta answered |
Understanding the Problem
Ben has 30 pencils of 5 different colors, with 6 pencils of each color. The goal is to find the minimum number of pencils he must select to ensure he has at least 2 of each color.
Analyzing Worst-Case Scenario
To determine the minimum number of pencils needed, consider the worst-case scenario in selection:
- Ben could potentially select the maximum number of pencils without getting 2 of each color.
Calculating Worst-Case Selections
1. Select 1 Pencil of Each Color:
- Ben can pick 1 pencil from each of the 5 colors.
- Total pencils selected so far: 5
2. Select 1 Pencil from Each Color Again:
- He can pick another pencil from each of the 5 colors (totaling 2 pencils of each color).
- Total pencils selected so far: 10 (5 from the first selection + 5 from the second selection)
3. Now, To Ensure 2 of Each Color:
- To avoid having 2 of any specific color, he can only select 1 pencil of each color until he has 5 colors represented.
- If he continues picking just 1 pencil of each color, he would need to pick 10 pencils (5 colors x 2).
Final Selections for Guarantee
To ensure that there are at least 2 pencils of each color:
- After selecting 10 pencils, if he picks any additional pencil (the 11th), it must be from one of the colors he already has, resulting in at least one color having 2 pencils.
Conclusion
Therefore, to guarantee at least 2 pencils of each color, Ben must select a minimum of:
- Total pencils needed = 10 + 2 = 12
However, since there are 6 pencils of each color, to ensure this condition is met with maximum efficiency, he would need to select at least 26 pencils to ensure he has 2 of each color.
Thus, the final answer is option C: 26.
Ben has 30 pencils of 5 different colors, with 6 pencils of each color. The goal is to find the minimum number of pencils he must select to ensure he has at least 2 of each color.
Analyzing Worst-Case Scenario
To determine the minimum number of pencils needed, consider the worst-case scenario in selection:
- Ben could potentially select the maximum number of pencils without getting 2 of each color.
Calculating Worst-Case Selections
1. Select 1 Pencil of Each Color:
- Ben can pick 1 pencil from each of the 5 colors.
- Total pencils selected so far: 5
2. Select 1 Pencil from Each Color Again:
- He can pick another pencil from each of the 5 colors (totaling 2 pencils of each color).
- Total pencils selected so far: 10 (5 from the first selection + 5 from the second selection)
3. Now, To Ensure 2 of Each Color:
- To avoid having 2 of any specific color, he can only select 1 pencil of each color until he has 5 colors represented.
- If he continues picking just 1 pencil of each color, he would need to pick 10 pencils (5 colors x 2).
Final Selections for Guarantee
To ensure that there are at least 2 pencils of each color:
- After selecting 10 pencils, if he picks any additional pencil (the 11th), it must be from one of the colors he already has, resulting in at least one color having 2 pencils.
Conclusion
Therefore, to guarantee at least 2 pencils of each color, Ben must select a minimum of:
- Total pencils needed = 10 + 2 = 12
However, since there are 6 pencils of each color, to ensure this condition is met with maximum efficiency, he would need to select at least 26 pencils to ensure he has 2 of each color.
Thus, the final answer is option C: 26.
Three years ago, Ron gave up eating anything with wheat in it. In that time, he lowered his cholesterol by 100 points and lost nearly 85 pounds. He says he feels better than he has in years. As a result, he is writing a book which says that everyone should stop eating wheat products. He says people are not made to eat wheat and that giving it up is the key to losing weight and being healthier.Which of the following, if true, most weakens the argument above?- a)Wheat is found in nearly all processed foods.
- b)Ron has a family history of celiac disease, which is an extreme sensitivity to wheat gluten.
- c)Some studies have shown that a lower carbohydrate diet can help people lose weight and feel better.
- d)Ron runs three miles every morning.
- e)Ron used to be a vegetarian but has resumed eating meat.
Correct answer is option 'B'. Can you explain this answer?
Three years ago, Ron gave up eating anything with wheat in it. In that time, he lowered his cholesterol by 100 points and lost nearly 85 pounds. He says he feels better than he has in years. As a result, he is writing a book which says that everyone should stop eating wheat products. He says people are not made to eat wheat and that giving it up is the key to losing weight and being healthier.
Which of the following, if true, most weakens the argument above?
a)
Wheat is found in nearly all processed foods.
b)
Ron has a family history of celiac disease, which is an extreme sensitivity to wheat gluten.
c)
Some studies have shown that a lower carbohydrate diet can help people lose weight and feel better.
d)
Ron runs three miles every morning.
e)
Ron used to be a vegetarian but has resumed eating meat.
|
|
Saumya Sharma answered |
Weakness in the Argument:
The argument claims that giving up wheat is the key to losing weight and being healthier, based on Ron's personal experience. To weaken this argument, we need to find a statement that challenges the assumption that everyone should stop eating wheat products.
Analysis of Options:
a) Wheat is found in nearly all processed foods.
This statement supports the argument by implying that wheat is present in most processed foods, reinforcing the idea that giving up wheat is beneficial. Therefore, option 'a' does not weaken the argument.
b) Ron has a family history of celiac disease, which is an extreme sensitivity to wheat gluten.
This statement weakens the argument by providing an alternative explanation for Ron's improved health. If Ron has celiac disease, then his improved health may be due to eliminating wheat because of his condition, rather than a general principle that applies to everyone. Therefore, option 'b' weakens the argument.
c) Some studies have shown that a lower carbohydrate diet can help people lose weight and feel better.
This statement is a general claim about the benefits of a lower carbohydrate diet, which does not directly address the argument about giving up wheat. While it suggests an alternative approach to improve health, it does not specifically weaken the argument. Therefore, option 'c' does not weaken the argument.
d) Ron runs three miles every morning.
This statement provides additional information about Ron's lifestyle but does not directly challenge the argument that giving up wheat is the key to losing weight and being healthier. It may contribute to Ron's overall health improvement but does not weaken the argument. Therefore, option 'd' does not weaken the argument.
e) Ron used to be a vegetarian but has resumed eating meat.
This statement is unrelated to the argument about giving up wheat. It may have implications for Ron's overall diet, but it does not directly address the claim that everyone should stop eating wheat products. Therefore, option 'e' does not weaken the argument.
Conclusion:
Among the given options, option 'b' weakens the argument by providing an alternative explanation for Ron's improved health, suggesting that his family history of celiac disease may be the primary reason for his positive outcomes.
The argument claims that giving up wheat is the key to losing weight and being healthier, based on Ron's personal experience. To weaken this argument, we need to find a statement that challenges the assumption that everyone should stop eating wheat products.
Analysis of Options:
a) Wheat is found in nearly all processed foods.
This statement supports the argument by implying that wheat is present in most processed foods, reinforcing the idea that giving up wheat is beneficial. Therefore, option 'a' does not weaken the argument.
b) Ron has a family history of celiac disease, which is an extreme sensitivity to wheat gluten.
This statement weakens the argument by providing an alternative explanation for Ron's improved health. If Ron has celiac disease, then his improved health may be due to eliminating wheat because of his condition, rather than a general principle that applies to everyone. Therefore, option 'b' weakens the argument.
c) Some studies have shown that a lower carbohydrate diet can help people lose weight and feel better.
This statement is a general claim about the benefits of a lower carbohydrate diet, which does not directly address the argument about giving up wheat. While it suggests an alternative approach to improve health, it does not specifically weaken the argument. Therefore, option 'c' does not weaken the argument.
d) Ron runs three miles every morning.
This statement provides additional information about Ron's lifestyle but does not directly challenge the argument that giving up wheat is the key to losing weight and being healthier. It may contribute to Ron's overall health improvement but does not weaken the argument. Therefore, option 'd' does not weaken the argument.
e) Ron used to be a vegetarian but has resumed eating meat.
This statement is unrelated to the argument about giving up wheat. It may have implications for Ron's overall diet, but it does not directly address the claim that everyone should stop eating wheat products. Therefore, option 'e' does not weaken the argument.
Conclusion:
Among the given options, option 'b' weakens the argument by providing an alternative explanation for Ron's improved health, suggesting that his family history of celiac disease may be the primary reason for his positive outcomes.
During the past 20 years, computer scientists focused increasingly on starting and running successful businesses. However, since businesses must be profitable, computer scientists must focus on developing products that generate profit. Consequently, computer science has lost its creative aspect.
Q. Which of the following assumptions is most necessary in order for the conclusion above to be drawn from the argument above?- a)All computer programs must lack creativity in order to be well received.
- b)Some computer scientists entirely disregarded creativity and chose instead to pursue profit.
- c)A program cannot be both creative and profitable.
- d)Computer scientists are obsessed with the profitability of their work.
- e)Non-profit institutions use large amounts of software.
Correct answer is option 'C'. Can you explain this answer?
During the past 20 years, computer scientists focused increasingly on starting and running successful businesses. However, since businesses must be profitable, computer scientists must focus on developing products that generate profit. Consequently, computer science has lost its creative aspect.
Q. Which of the following assumptions is most necessary in order for the conclusion above to be drawn from the argument above?
Q. Which of the following assumptions is most necessary in order for the conclusion above to be drawn from the argument above?
a)
All computer programs must lack creativity in order to be well received.
b)
Some computer scientists entirely disregarded creativity and chose instead to pursue profit.
c)
A program cannot be both creative and profitable.
d)
Computer scientists are obsessed with the profitability of their work.
e)
Non-profit institutions use large amounts of software.
|
|
Niharika Sen answered |
The argument’s conclusion is: "computer science has lost its creative aspect"
The argument draws the false dichotomy that the writing of profitable programs requires forgoing the writing of creative applications. In other words, it assumes that profitable and creative programs are mutually exclusive. Further, it assumes that all computer scientists are pursuing writing profitable programs.
A. There is a difference between being well received and being profitable. The argument assumes that only non-creative programs can be profitable. However, this does not mean creative programs will not be well-received. It just means they will not be profitable.
B. Even if some computer scientists disregarded creativity, we cannot (as the original argument and this answer do) assume that creativity and profit are mutually exclusive.
C. This answer identifies a crucial assumption in the original argument. If writing creative and profitable programs were not mutually exclusive, then one could write profitable programs without "computer science [having] lost its creative aspect."
D. The extent to which a computer scientist is obsessed with the profitability of his work has no influence on whether profitability drives away creativity (as the original argument assumes).
E. The users of software have influence on whether software can be both profitable and creative.
B. Even if some computer scientists disregarded creativity, we cannot (as the original argument and this answer do) assume that creativity and profit are mutually exclusive.
C. This answer identifies a crucial assumption in the original argument. If writing creative and profitable programs were not mutually exclusive, then one could write profitable programs without "computer science [having] lost its creative aspect."
D. The extent to which a computer scientist is obsessed with the profitability of his work has no influence on whether profitability drives away creativity (as the original argument assumes).
E. The users of software have influence on whether software can be both profitable and creative.
In the past, most airline companies minimized aircraft weight to minimize fuel costs. The safest airline seats were heavy, and airlines equipped their planes with few of these seats. This year the seat that has sold best to airlines has been the safest one→a clear indication that airlines are assigning a higher priority to safe seating than to minimizing fuel costs.
Q. Which of the following, if true, most seriously weakens the argument above?- a)Last year’s best-selling airline seat was not the safest airline seat on the market.
- b)No airline company has announced that it would be making safe seating a higher priority this year.
- c)The price of fuel was higher this year than it had been in most of the years when the safest airline seats sold poorly.
- d)Because of increases in the cost of materials, all airline seats were more expensive to manufacture this year than in any previous year.
- e)Because of technological innovations, the safest airline seat on the market this year weighed less than most other airline seats on the market.
Correct answer is option 'E'. Can you explain this answer?
In the past, most airline companies minimized aircraft weight to minimize fuel costs. The safest airline seats were heavy, and airlines equipped their planes with few of these seats. This year the seat that has sold best to airlines has been the safest one→a clear indication that airlines are assigning a higher priority to safe seating than to minimizing fuel costs.
Q. Which of the following, if true, most seriously weakens the argument above?
Q. Which of the following, if true, most seriously weakens the argument above?
a)
Last year’s best-selling airline seat was not the safest airline seat on the market.
b)
No airline company has announced that it would be making safe seating a higher priority this year.
c)
The price of fuel was higher this year than it had been in most of the years when the safest airline seats sold poorly.
d)
Because of increases in the cost of materials, all airline seats were more expensive to manufacture this year than in any previous year.
e)
Because of technological innovations, the safest airline seat on the market this year weighed less than most other airline seats on the market.
|
|
Ruchi Pillai answered |
If the safest airline seats are now among the lightest, as choice E says, then buying them could be part of a strategy of minimizing fuel costs, rather than indicating a shift away from that goal. Choice E, therefore, is the best choice.
Choice A merely confirms that seat safety has improved, and thus does not weaken the argument. Many policy shifts take place without being publicly announced, so choice B does not weaken the argument. Choice C indicates that minimizing fuel costs remains a priority, but it is neutral on whether safety has become more important, so C is incorrect. Choice D does not distinguish between safe and unsafe seats, and is thus also incorrect.
Choice A merely confirms that seat safety has improved, and thus does not weaken the argument. Many policy shifts take place without being publicly announced, so choice B does not weaken the argument. Choice C indicates that minimizing fuel costs remains a priority, but it is neutral on whether safety has become more important, so C is incorrect. Choice D does not distinguish between safe and unsafe seats, and is thus also incorrect.
When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?- a)9
- b)10
- c)11
- d)12
- e)13
Correct answer is option 'E'. Can you explain this answer?
When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?
a)
9
b)
10
c)
11
d)
12
e)
13
|
|
Pallavi Choudhury answered |
Given:
- When y is divided by 7, the remainder is 2.
- When y is divided by 11, the remainder is 3.
To find:
- The sum of the digits of the smallest possible value that meets the definition for y.
Solution:
To find the smallest value of y, we need to find the least common multiple (LCM) of 7 and 11.
Finding the LCM:
To find the LCM of 7 and 11, we can find the product of the two numbers and then divide it by their greatest common divisor (GCD).
- The product of 7 and 11 is 77.
- The GCD of 7 and 11 is 1 (since they are prime numbers).
So, the LCM of 7 and 11 is 77.
Finding the smallest possible value of y:
Since the remainder when y is divided by 7 is 2, the smallest possible value of y that satisfies this condition is 2.
To find the smallest possible value of y that satisfies the condition when y is divided by 11, we need to find the smallest multiple of 77 that leaves a remainder of 3 when divided by 11.
Finding the smallest multiple of 77 that leaves a remainder of 3 when divided by 11:
To find this, we can start by finding the multiples of 77 and checking if they leave a remainder of 3 when divided by 11.
77 x 1 = 77 (remainder = 0 when divided by 11)
77 x 2 = 154 (remainder = 3 when divided by 11)
Therefore, the smallest multiple of 77 that leaves a remainder of 3 when divided by 11 is 154.
Calculating the sum of the digits:
To find the sum of the digits of 154, we add the individual digits together.
1 + 5 + 4 = 10
So, the sum of the digits of the smallest possible value that meets the definition for y is 10.
Therefore, the correct answer is option B) 10.
- When y is divided by 7, the remainder is 2.
- When y is divided by 11, the remainder is 3.
To find:
- The sum of the digits of the smallest possible value that meets the definition for y.
Solution:
To find the smallest value of y, we need to find the least common multiple (LCM) of 7 and 11.
Finding the LCM:
To find the LCM of 7 and 11, we can find the product of the two numbers and then divide it by their greatest common divisor (GCD).
- The product of 7 and 11 is 77.
- The GCD of 7 and 11 is 1 (since they are prime numbers).
So, the LCM of 7 and 11 is 77.
Finding the smallest possible value of y:
Since the remainder when y is divided by 7 is 2, the smallest possible value of y that satisfies this condition is 2.
To find the smallest possible value of y that satisfies the condition when y is divided by 11, we need to find the smallest multiple of 77 that leaves a remainder of 3 when divided by 11.
Finding the smallest multiple of 77 that leaves a remainder of 3 when divided by 11:
To find this, we can start by finding the multiples of 77 and checking if they leave a remainder of 3 when divided by 11.
77 x 1 = 77 (remainder = 0 when divided by 11)
77 x 2 = 154 (remainder = 3 when divided by 11)
Therefore, the smallest multiple of 77 that leaves a remainder of 3 when divided by 11 is 154.
Calculating the sum of the digits:
To find the sum of the digits of 154, we add the individual digits together.
1 + 5 + 4 = 10
So, the sum of the digits of the smallest possible value that meets the definition for y is 10.
Therefore, the correct answer is option B) 10.
Working alone at its constant rate, Machine A can produce 1,050 electrical components in 5 hours. Machine B, working alone, can produce 1,050 electrical components in 15/2 hours. If the two machine work simultaneously for T hours and produce 1,050 electrical components, how many electrical components has Machine B produced at the end of T hours?- a)140
- b)210
- c)420
- d)525
- e)630
Correct answer is option 'C'. Can you explain this answer?
Working alone at its constant rate, Machine A can produce 1,050 electrical components in 5 hours. Machine B, working alone, can produce 1,050 electrical components in 15/2 hours. If the two machine work simultaneously for T hours and produce 1,050 electrical components, how many electrical components has Machine B produced at the end of T hours?
a)
140
b)
210
c)
420
d)
525
e)
630
|
|
Aditya Gupta answered |
To solve this problem, let's first find the individual rates of production for each machine.
Machine A produces 1,050 electrical components in 5 hours, so its rate of production is 1,050/5 = 210 components per hour.
Machine B produces 1,050 electrical components in 15/2 hours, which is equivalent to 7.5 hours. Therefore, its rate of production is 1,050/7.5 = 140 components per hour.
Now, let's determine the combined rate of production when both machines work simultaneously for T hours.
Since we want to find the number of electrical components produced by Machine B at the end of T hours, let's assume Machine B works for T hours while Machine A continues to work for 5 hours.
The rate of production for Machine A is 210 components per hour, so in 5 hours it produces 210 * 5 = 1050 components.
Therefore, the combined rate of production for Machines A and B is 210 + 140 = 350 components per hour.
Now, let's find the number of electrical components produced by Machine B at the end of T hours.
Since the combined rate of production is 350 components per hour, in T hours the combined production is 350 * T.
From the question, we know that the combined production is 1,050 components, so we can set up the equation 350 * T = 1,050.
Dividing both sides of the equation by 350, we find T = 3.
Therefore, Machine B has produced 140 components per hour * 3 hours = 420 components at the end of T hours.
Hence, the correct answer is option C) 420.
Machine A produces 1,050 electrical components in 5 hours, so its rate of production is 1,050/5 = 210 components per hour.
Machine B produces 1,050 electrical components in 15/2 hours, which is equivalent to 7.5 hours. Therefore, its rate of production is 1,050/7.5 = 140 components per hour.
Now, let's determine the combined rate of production when both machines work simultaneously for T hours.
Since we want to find the number of electrical components produced by Machine B at the end of T hours, let's assume Machine B works for T hours while Machine A continues to work for 5 hours.
The rate of production for Machine A is 210 components per hour, so in 5 hours it produces 210 * 5 = 1050 components.
Therefore, the combined rate of production for Machines A and B is 210 + 140 = 350 components per hour.
Now, let's find the number of electrical components produced by Machine B at the end of T hours.
Since the combined rate of production is 350 components per hour, in T hours the combined production is 350 * T.
From the question, we know that the combined production is 1,050 components, so we can set up the equation 350 * T = 1,050.
Dividing both sides of the equation by 350, we find T = 3.
Therefore, Machine B has produced 140 components per hour * 3 hours = 420 components at the end of T hours.
Hence, the correct answer is option C) 420.
Ben is stocking milk at the local JumboMart. The milk cooler holds 780 cartons of milk and is completely full when Ben starts his shift. The store sells 75 percent of the milk during the first hour that Ben works and then sells another 20 percent of the remaining milk during the second hour. If there are 1000 cartons of milk in the back room, how many of them will Ben not need in order to restock the milk cooler?- a)259
- b)376
- c)585
- d)624
- e)741
Correct answer is option 'B'. Can you explain this answer?
Ben is stocking milk at the local JumboMart. The milk cooler holds 780 cartons of milk and is completely full when Ben starts his shift. The store sells 75 percent of the milk during the first hour that Ben works and then sells another 20 percent of the remaining milk during the second hour. If there are 1000 cartons of milk in the back room, how many of them will Ben not need in order to restock the milk cooler?
a)
259
b)
376
c)
585
d)
624
e)
741
|
|
Rahul Kapoor answered |
Let's calculate the number of cartons of milk that will be sold during Ben's shift.
During the first hour, 75% of the milk is sold. This means 75/100 * 780 = 585 cartons of milk are sold.
After the first hour, there are 780 - 585 = 195 cartons of milk remaining.
During the second hour, 20% of the remaining milk is sold. This means 20/100 * 195 = 39 cartons of milk are sold.
After the second hour, there are 195 - 39 = 156 cartons of milk remaining.
Now, let's calculate how many cartons of milk Ben will need to restock the milk cooler.
The milk cooler originally holds 780 cartons of milk, and there are currently 156 cartons remaining. Therefore, Ben will need to restock the cooler with 780 - 156 = 624 cartons of milk.
Since there are 1000 cartons of milk in the back room, Ben will not need 1000 - 624 = 376 cartons of milk.
Therefore, the correct answer is B) 376.
Tammy bikes the course of a race at 30 miles per hour, then returns home along the same route at 10 miles per hour. If the total time it takes her to travel the course and return home is 2 hours, and if the time spent turning around is negligible, what is the length, in miles, of the race course?
- a)25
- b)20
- c)15
- d)30
- e)35
Correct answer is option 'C'. Can you explain this answer?
Tammy bikes the course of a race at 30 miles per hour, then returns home along the same route at 10 miles per hour. If the total time it takes her to travel the course and return home is 2 hours, and if the time spent turning around is negligible, what is the length, in miles, of the race course?
a)
25
b)
20
c)
15
d)
30
e)
35
|
|
Aditya Gupta answered |
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's assume the length of the race course is 'x' miles.
Biking to the race:
Time taken = Distance / Speed = x / 30
Returning home:
Time taken = Distance / Speed = x / 10
Total time taken = Time to the race + Time to return home
2 = x / 30 + x / 10
To solve this equation, we can multiply through by the least common multiple (LCM) of 30 and 10, which is 30.
2 * 30 = x + 3x
60 = 4x
x = 15
Therefore, the length of the race course is 15 miles.
So, the correct answer is option C.
Time = Distance / Speed
Let's assume the length of the race course is 'x' miles.
Biking to the race:
Time taken = Distance / Speed = x / 30
Returning home:
Time taken = Distance / Speed = x / 10
Total time taken = Time to the race + Time to return home
2 = x / 30 + x / 10
To solve this equation, we can multiply through by the least common multiple (LCM) of 30 and 10, which is 30.
2 * 30 = x + 3x
60 = 4x
x = 15
Therefore, the length of the race course is 15 miles.
So, the correct answer is option C.
In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter’s age squared. How old is Janice?- a)18
- b)36
- c)40
- d)42
- e)45
Correct answer is option 'D'. Can you explain this answer?
In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter’s age squared. How old is Janice?
a)
18
b)
36
c)
40
d)
42
e)
45
|
|
Parth Singh answered |
's age minus 10. How old is Janice's daughter now?
Let's represent Janice's current age as J and her daughter's current age as D.
According to the problem, in three years, Janice will be three times as old as her daughter, so we can write the equation:
J + 3 = 3(D + 3) [Equation 1]
Six years ago, Janice's age was her daughter's age minus 10, which can be written as:
J - 6 = D - 6 - 10 [Equation 2]
Simplifying Equation 2, we get:
J - 6 = D - 16 [Equation 3]
To solve the system of equations, we can substitute Equation 3 into Equation 1:
D - 16 + 3 = 3(D + 3)
Simplifying the equation further, we get:
D - 13 = 3D + 9
Combining like terms, we have:
3D - D = -13 - 9
2D = -22
Dividing both sides by 2, we find:
D = -11
Since the daughter's age cannot be negative, there seems to be an error in the problem statement or in the calculations. Please double-check the information provided.
Let's represent Janice's current age as J and her daughter's current age as D.
According to the problem, in three years, Janice will be three times as old as her daughter, so we can write the equation:
J + 3 = 3(D + 3) [Equation 1]
Six years ago, Janice's age was her daughter's age minus 10, which can be written as:
J - 6 = D - 6 - 10 [Equation 2]
Simplifying Equation 2, we get:
J - 6 = D - 16 [Equation 3]
To solve the system of equations, we can substitute Equation 3 into Equation 1:
D - 16 + 3 = 3(D + 3)
Simplifying the equation further, we get:
D - 13 = 3D + 9
Combining like terms, we have:
3D - D = -13 - 9
2D = -22
Dividing both sides by 2, we find:
D = -11
Since the daughter's age cannot be negative, there seems to be an error in the problem statement or in the calculations. Please double-check the information provided.
If <n> is the greatest integer less than or equal to n, what is the value of (<-2.1>)*(<2.1>)*(<2.9>) ?- a)2
- b)0
- c)-8
- d)-12
- e)-18
Correct answer is option 'D'. Can you explain this answer?
If <n> is the greatest integer less than or equal to n, what is the value of (<-2.1>)*(<2.1>)*(<2.9>) ?
a)
2
b)
0
c)
-8
d)
-12
e)
-18
|
|
Rahul Kapoor answered |
To find the value of (<-2.1>)(<2.1>)(<2.9>), we need to evaluate the greatest integer less than or equal to each of the given numbers.
The greatest integer less than or equal to -2.1 is -3. The greatest integer less than or equal to 2.1 is 2. The greatest integer less than or equal to 2.9 is 2.
Therefore, the expression becomes: (-3)(2)(2).
Multiplying these values, we get: -3 * 2 * 2 = -12.
Hence, the correct answer is D) -12.
If the flowers Drew received today had been sent by someone who knows Drew well, that person would have known that Drew preferes violets to roses. Yet Drew received roses. On the other hand, if the flowers had been sent by someone who does not know Drew well, then that person would have sent a signed card with the flowers. Yet Drew received no card. Therefore, the florist must made some sort of mistake: either Drew was supposed to receive violets, or a card, or these flowers were intended for someone else.Which of the following statements, if true, most weakens the argument?- a)Most people send roses when they send flowers
- b)Some people send flowers for a reason other than the desire to please
- c)Someone who does not know Drew well would be unlikely to send Drew flowers
- d)The florist has never delivered the wrong flowers to Drew before
- e)Some people who know Drew well have sent Drew cards along with flowers
Correct answer is option 'B'. Can you explain this answer?
If the flowers Drew received today had been sent by someone who knows Drew well, that person would have known that Drew preferes violets to roses. Yet Drew received roses. On the other hand, if the flowers had been sent by someone who does not know Drew well, then that person would have sent a signed card with the flowers. Yet Drew received no card. Therefore, the florist must made some sort of mistake: either Drew was supposed to receive violets, or a card, or these flowers were intended for someone else.
Which of the following statements, if true, most weakens the argument?
a)
Most people send roses when they send flowers
b)
Some people send flowers for a reason other than the desire to please
c)
Someone who does not know Drew well would be unlikely to send Drew flowers
d)
The florist has never delivered the wrong flowers to Drew before
e)
Some people who know Drew well have sent Drew cards along with flowers
|
|
Rahul Kapoor answered |
The argument states that Drew received roses instead of violets, which Drew prefers, and there was no card included with the flowers. The conclusion drawn from this is that the florist made a mistake, either by sending the wrong flowers or by intending the flowers for someone else.
(A) Most people send roses when they send flowers.
- This statement is irrelevant to the argument because it doesn't address the specific situation regarding Drew's preference for violets and the absence of a card. It doesn't weaken or strengthen the argument.
(B) Some people send flowers for a reason other than the desire to please.
- This statement weakens the argument because it suggests that there could be a reason other than knowing Drew's preferences for why roses were sent instead of violets. The sender may have had a different intention, such as conveying sympathy or expressing gratitude. Therefore, the florist's choice of roses may not necessarily be a mistake.
(C) Someone who does not know Drew well would be unlikely to send Drew flowers.
- This statement is also irrelevant to the argument. It doesn't address the issue of the florist's mistake or the absence of a card. It doesn't weaken or strengthen the argument.
(D) The florist has never delivered the wrong flowers to Drew before.
- This statement strengthens the argument by implying that the florist is usually reliable and doesn't make mistakes in delivering flowers. It supports the conclusion that the florist might have made a mistake this time.
(E) Some people who know Drew well have sent Drew cards along with flowers.
- This statement is also irrelevant to the argument. It doesn't address the issue of the florist's mistake or the absence of a card. It doesn't weaken or strengthen the argument.
Among the answer choices, (B) weakens the argument the most by suggesting an alternative reason for sending roses instead of violets. It introduces the possibility that the flowers were sent for a different purpose, not solely to please Drew. Therefore, option (B) is the correct answer.
There are 7 keys in a key ring. If two more keys are to be added in the ring at random, what is the probability that two keys will be adjacent?- a)1/8
- b)1/6
- c)1/5
- d)1/4
- e)1/3
Correct answer is option 'D'. Can you explain this answer?
There are 7 keys in a key ring. If two more keys are to be added in the ring at random, what is the probability that two keys will be adjacent?
a)
1/8
b)
1/6
c)
1/5
d)
1/4
e)
1/3
|
|
Prashanth Chawla answered |
Understanding the Problem
We have a key ring with 7 keys, and we want to add 2 more keys at random. We need to find the probability that these two new keys will be adjacent.
Possible Arrangements
- The total number of keys after adding the 2 new keys will be 9.
- When arranging these keys in a circle, the number of distinct arrangements is given by (n-1)!, where n is the total number of keys.
- Therefore, the number of arrangements for 9 keys is 8!.
Adjacent Keys Calculation
- To count the arrangements where the two new keys are adjacent, we can treat the two new keys as a single unit or block.
- This creates a new scenario with 8 units (the block of 2 keys + 7 original keys).
- The number of distinct arrangements for these 8 units in a circle is 7!.
Probability Calculation
- The probability that the two new keys are adjacent is the ratio of the number of arrangements with adjacent keys to the total arrangements.
- Probability = (Number of adjacent arrangements) / (Total arrangements) = 7! / 8! = 7 / 8.
Final Step
- However, since there are 2 ways to arrange the 2 new keys within their block (Key A next to Key B or Key B next to Key A), we multiply the adjacent arrangements by 2.
- Therefore, the effective number of adjacent arrangements becomes 2 * 7!.
- Now, the probability becomes (2 * 7!) / 8! = 2 / 8 = 1 / 4.
Thus, the correct probability that the two keys will be adjacent is 1/4 (option D).
We have a key ring with 7 keys, and we want to add 2 more keys at random. We need to find the probability that these two new keys will be adjacent.
Possible Arrangements
- The total number of keys after adding the 2 new keys will be 9.
- When arranging these keys in a circle, the number of distinct arrangements is given by (n-1)!, where n is the total number of keys.
- Therefore, the number of arrangements for 9 keys is 8!.
Adjacent Keys Calculation
- To count the arrangements where the two new keys are adjacent, we can treat the two new keys as a single unit or block.
- This creates a new scenario with 8 units (the block of 2 keys + 7 original keys).
- The number of distinct arrangements for these 8 units in a circle is 7!.
Probability Calculation
- The probability that the two new keys are adjacent is the ratio of the number of arrangements with adjacent keys to the total arrangements.
- Probability = (Number of adjacent arrangements) / (Total arrangements) = 7! / 8! = 7 / 8.
Final Step
- However, since there are 2 ways to arrange the 2 new keys within their block (Key A next to Key B or Key B next to Key A), we multiply the adjacent arrangements by 2.
- Therefore, the effective number of adjacent arrangements becomes 2 * 7!.
- Now, the probability becomes (2 * 7!) / 8! = 2 / 8 = 1 / 4.
Thus, the correct probability that the two keys will be adjacent is 1/4 (option D).
Blood banks will shortly start to screen all donors for NANB hepatitis. Although the new screening tests are estimated to disqualify up to 5 percent of all prospective blood donors, they will still miss two-thirds of donors carrying NANB hepatitis. Therefore, about 10 percent of actual donors will still supply NANB-contaminated blood.Which of the following inferences about the consequences of instituting the new tests is best supported by the passage above?- a)The incidence of new cases of NANB hepatitis is likely to go up by 10 percent.
- b)Donations made by patients specifically for their own use are likely to become less frequent.
- c)The demand for blood from blood banks is likely to fluctuate more strongly.
- d)The blood supplies available from blood banks are likely to go down.
- e)The number of prospective first-time donors is likely to go up by 5 percent.
Correct answer is option 'D'. Can you explain this answer?
Blood banks will shortly start to screen all donors for NANB hepatitis. Although the new screening tests are estimated to disqualify up to 5 percent of all prospective blood donors, they will still miss two-thirds of donors carrying NANB hepatitis. Therefore, about 10 percent of actual donors will still supply NANB-contaminated blood.
Which of the following inferences about the consequences of instituting the new tests is best supported by the passage above?
a)
The incidence of new cases of NANB hepatitis is likely to go up by 10 percent.
b)
Donations made by patients specifically for their own use are likely to become less frequent.
c)
The demand for blood from blood banks is likely to fluctuate more strongly.
d)
The blood supplies available from blood banks are likely to go down.
e)
The number of prospective first-time donors is likely to go up by 5 percent.
|
|
Rahul Kapoor answered |
(A) The incidence of new cases of NANB hepatitis is likely to go up by 10 percent:
- The passage does not provide any information about the incidence of new cases of NANB hepatitis. It only mentions the potential percentage of actual donors supplying contaminated blood, which does not directly imply an increase in new cases.
(B) Donations made by patients specifically for their own use are likely to become less frequent:
- The passage does not mention anything about donations made by patients for their own use. It focuses on blood donors and the potential contamination of blood supplies.
(C) The demand for blood from blood banks is likely to fluctuate more strongly:
- The passage does not provide any information about the potential fluctuation in demand for blood. It mainly discusses the screening tests and their impact on the supply of contaminated blood.
(D) The blood supplies available from blood banks are likely to go down:
- This is the best-supported inference based on the passage, as explained above.
(E) The number of prospective first-time donors is likely to go up by 5 percent:
- The passage does not mention anything about the number of prospective first-time donors. It only discusses the potential disqualification of donors and the contamination of blood supplies.
In summary, the best-supported inference is that the blood supplies available from blood banks are likely to go down (option D).
An airplane engine manufacturer developed a new engine model with safety features lacking in the earlier model, which was still being manufactured. During the first year that both were sold, the earlier model far outsold the new model; the manufacturer thus concluded that safety was not the customers’ primary consideration.
Q. Which of the following, if true, would most seriously weaken the manufacturer’s conclusion?- a)Both private plane owners and commercial airlines buy engines from this airplane engine manufacturer.
- b)Many customers consider earlier engine models better safety risks than new engine models, since more is usually known about the safety of the earlier models.
- c)Many customers of this airplane engine manufacturer also bought airplane engines from manufacturers who did not provide additional safety features in their newer models.
- d)The newer engine model can be used in all planes in which the earlier engine model can be used.
- e)There was no significant difference in price between the newer engine model and the earlier engine model.
Correct answer is option 'B'. Can you explain this answer?
An airplane engine manufacturer developed a new engine model with safety features lacking in the earlier model, which was still being manufactured. During the first year that both were sold, the earlier model far outsold the new model; the manufacturer thus concluded that safety was not the customers’ primary consideration.
Q. Which of the following, if true, would most seriously weaken the manufacturer’s conclusion?
Q. Which of the following, if true, would most seriously weaken the manufacturer’s conclusion?
a)
Both private plane owners and commercial airlines buy engines from this airplane engine manufacturer.
b)
Many customers consider earlier engine models better safety risks than new engine models, since more is usually known about the safety of the earlier models.
c)
Many customers of this airplane engine manufacturer also bought airplane engines from manufacturers who did not provide additional safety features in their newer models.
d)
The newer engine model can be used in all planes in which the earlier engine model can be used.
e)
There was no significant difference in price between the newer engine model and the earlier engine model.
|
|
Tanishq Yadav answered |
The manufacturers’ conclusion would be weakened if it could be argued that, in the opinion of customers, safety considerations favor the earlier model. Choice B supports such an argument and is the best answer.
The groups mentioned in choice A would both expected to consider safety important, so their failing to buy the new model would be striking, without casting doubt on the conclusion; thus, choice A is incorrect. Choice C might support the conclusion, because customers bought other engine support the conclusion, because customers bought other engine models that might not include the newer safety features. Choice D and E suggest that usability and price, respectively, were not the customers’ primary consideration in favoring the earlier model, but neither choice weakens the conclusion that safety was not their primary consideration.
The groups mentioned in choice A would both expected to consider safety important, so their failing to buy the new model would be striking, without casting doubt on the conclusion; thus, choice A is incorrect. Choice C might support the conclusion, because customers bought other engine support the conclusion, because customers bought other engine models that might not include the newer safety features. Choice D and E suggest that usability and price, respectively, were not the customers’ primary consideration in favoring the earlier model, but neither choice weakens the conclusion that safety was not their primary consideration.
Opponents of laws that require automobile drivers and passengers to wear seat belts argue that in a free society people have the right to take risks as long as people do not harm others as a result of taking the risks. As a result, they conclude that it should be each person’s decision whether or not to wear a seat belt.Which of the following, if true, most seriously weakens the conclusion drawn above?- a)Many new cars are built with seat belts that automatically fasten when someone sits in the front seat.
- b)Automobile insurance rates for all automobile owners are higher because of the need to pay for the increased injuries or deaths of people not wearing seat belts.
- c)Passengers in airplanes are required to wear seat belts during takeoffs and landings.
- d)The rate of automobile fatalities in states that do not have mandatory seat belt laws is greater than the rate of fatalities in states that do have such laws.
- e)In automobile accidents, a greater number of passengers who do not wear seat belts are injured than are passengers who do wear seat belts.
Correct answer is option 'B'. Can you explain this answer?
Opponents of laws that require automobile drivers and passengers to wear seat belts argue that in a free society people have the right to take risks as long as people do not harm others as a result of taking the risks. As a result, they conclude that it should be each person’s decision whether or not to wear a seat belt.
Which of the following, if true, most seriously weakens the conclusion drawn above?
a)
Many new cars are built with seat belts that automatically fasten when someone sits in the front seat.
b)
Automobile insurance rates for all automobile owners are higher because of the need to pay for the increased injuries or deaths of people not wearing seat belts.
c)
Passengers in airplanes are required to wear seat belts during takeoffs and landings.
d)
The rate of automobile fatalities in states that do not have mandatory seat belt laws is greater than the rate of fatalities in states that do have such laws.
e)
In automobile accidents, a greater number of passengers who do not wear seat belts are injured than are passengers who do wear seat belts.
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Rahul Kapoor answered |
The argument's conclusion is that it should be each person's decision whether or not to wear a seat belt, based on the premise that people have the right to take risks as long as they do not harm others.
Let's evaluate each answer choice:
(A) Many new cars are built with seat belts that automatically fasten when someone sits in the front seat.
- This answer choice provides information about a feature in new cars but does not directly address the conclusion. It does not weaken the argument.
(B) Automobile insurance rates for all automobile owners are higher because of the need to pay for the increased injuries or deaths of people not wearing seat belts.
This answer choice introduces the concept of increased insurance rates due to injuries or deaths of individuals not wearing seat belts. This information directly weakens the argument because it shows that not wearing seat belts can have financial consequences for others, thus harming them indirectly.
(C) Passengers in airplanes are required to wear seat belts during takeoffs and landings.
- This answer choice introduces a comparison between seat belt requirements in airplanes and cars. However, it does not directly address the conclusion about individual rights and does not provide any information that weakens the argument.
(D) The rate of automobile fatalities in states that do not have mandatory seat belt laws is greater than the rate of fatalities in states that do have such laws.
- This answer choice directly weakens the argument by providing evidence that states with mandatory seat belt laws have lower fatality rates. This suggests that wearing seat belts can significantly reduce the risk of fatalities and contradicts the argument's premise that individuals should have the right to take risks without causing harm to others.
(E) In automobile accidents, a greater number of passengers who do not wear seat belts are injured than passengers who do wear seat belts.
- This answer choice provides information about the likelihood of injury in automobile accidents based on seat belt usage. Although it suggests a correlation between seat belt usage and reduced injuries, it does not directly address the conclusion about individual rights and does not weaken the argument.
After evaluating each answer choice, it becomes clear that option (B) weakens the conclusion most effectively. It demonstrates that not wearing seat belts can lead to increased financial burdens on others through higher insurance rates. Therefore, (B) is the correct answer.
Four female friends & four male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with men & women alternating. How many possible arrangements may she chose?- a)40320
- b)1680
- c)1152
- d)576
- e)70
Correct answer is option 'C'. Can you explain this answer?
Four female friends & four male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with men & women alternating. How many possible arrangements may she chose?
a)
40320
b)
1680
c)
1152
d)
576
e)
70
|
EduRev GMAT answered |
Now any of the alternate 4 places can be filled by 4 male or female in 4!
Similarily,
other 4 alternate places can be filled in 4!
Hence required probability= 2*4!*4!=1152
Similarily,
other 4 alternate places can be filled in 4!
Hence required probability= 2*4!*4!=1152
A history book written hundreds of years ago contains several inconsistencies. Some scholars argue that because the book contains inconsistencies, the author must have been getting information from more than one source.The conclusion cited does not follow unless- a)authors generally try to reconcile discrepancies between sources
- b)the inconsistencies would be apparent to the average reader of the history book at the present time
- c)the history book’s author used no source that contained inconsistencies repeated in the history book
- d)the author of the history book was aware of the kinds of inconsistencies that can arise when multiple sources are consulted
- e)the author of the history book was familiar with all of the available source material that was relevant to the history book
Correct answer is option 'C'. Can you explain this answer?
A history book written hundreds of years ago contains several inconsistencies. Some scholars argue that because the book contains inconsistencies, the author must have been getting information from more than one source.
The conclusion cited does not follow unless
a)
authors generally try to reconcile discrepancies between sources
b)
the inconsistencies would be apparent to the average reader of the history book at the present time
c)
the history book’s author used no source that contained inconsistencies repeated in the history book
d)
the author of the history book was aware of the kinds of inconsistencies that can arise when multiple sources are consulted
e)
the author of the history book was familiar with all of the available source material that was relevant to the history book
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|
Rahul Kapoor answered |
The argument states that because a history book written hundreds of years ago contains inconsistencies, the author must have been getting information from more than one source. The conclusion drawn is that the author used multiple sources.
To identify the flaw, we need to find an answer choice that shows the conclusion does not necessarily follow from the premises. Let's analyze each answer choice:
(A) authors generally try to reconcile discrepancies between sources
- This answer choice is irrelevant to the argument. It discusses authors' attempts to reconcile discrepancies between sources but does not address the claim that the author used multiple sources. It does not explain why the book contains inconsistencies.
(B) the inconsistencies would be apparent to the average reader of the history book at the present time
- This answer choice is also irrelevant to the argument. It discusses whether the average reader can identify the inconsistencies but does not address the claim that the author used multiple sources.
(C) the history book’s author used no source that contained inconsistencies repeated in the history book
- This answer choice correctly identifies the flaw in the argument. It suggests that the author may have used multiple sources, but those sources may have contained inconsistencies that are not repeated in the history book. Therefore, the presence of inconsistencies does not necessarily indicate the use of multiple sources.
(D) the author of the history book was aware of the kinds of inconsistencies that can arise when multiple sources are consulted
- This answer choice is also irrelevant to the argument. It discusses the author's awareness of inconsistencies that can arise when multiple sources are consulted but does not address whether the author actually used multiple sources.
(E) the author of the history book was familiar with all of the available source material that was relevant to the history book
- This answer choice is also irrelevant to the argument. It discusses the author's familiarity with all available source material but does not address whether the author actually used multiple sources.
Therefore, the correct answer is (C) because it identifies the flaw in the argument by suggesting that the author may have used multiple sources without repeating the inconsistencies found in those sources.
Between 1975 and 1985, nursing-home occupancy rates averaged 87 percent of capacity, while admission rates remained constant, at an average of 95 admissions per 1,000 beds per year. Between 1985 and 1988, however, occupancy rates rose to an average of 92 percent of capacity, while admission rates declined to 81 per 1,000 beds per year.
Q. If the statements above are true, which of the following conclusions can be most properly drawn?- a)The average length of time nursing-home residents stayed in nursing homes increased between 1985 and 1988.
- b)The proportion of older people living in nursing homes was greater in 1988 than in 1975.
- c)Nursing home admission rates tend to decline whenever occupancy rates rise.
- d)Nursing homes built prior to 1985 generally had fewer beds than did nursing homes built between 1985 and 1988.
- e)The more beds a nursing home has, the higher its occupancy rate is likely to be.
Correct answer is option 'A'. Can you explain this answer?
Between 1975 and 1985, nursing-home occupancy rates averaged 87 percent of capacity, while admission rates remained constant, at an average of 95 admissions per 1,000 beds per year. Between 1985 and 1988, however, occupancy rates rose to an average of 92 percent of capacity, while admission rates declined to 81 per 1,000 beds per year.
Q. If the statements above are true, which of the following conclusions can be most properly drawn?
Q. If the statements above are true, which of the following conclusions can be most properly drawn?
a)
The average length of time nursing-home residents stayed in nursing homes increased between 1985 and 1988.
b)
The proportion of older people living in nursing homes was greater in 1988 than in 1975.
c)
Nursing home admission rates tend to decline whenever occupancy rates rise.
d)
Nursing homes built prior to 1985 generally had fewer beds than did nursing homes built between 1985 and 1988.
e)
The more beds a nursing home has, the higher its occupancy rate is likely to be.
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Manasa Kulkarni answered |
Between 1985 and 1988, nursing home occupancy rates rose although admission rates declined. Choice A receives support from these facts since it would be a basis fro an adequate account of how they arose. Because it is the only choice that receives support, A is therefore the best answer.
Without information about the population of older people, nothing can be concluded about percentages in nursing homes; thus, choice B is incorrect. Since there is nothing to indicate whether the development that took place between 1985 and 1988 was an unusual development or a common one, choice C receives no support. No information about numbers of beds is provided, so neither choice D nor choice E is correct.
Without information about the population of older people, nothing can be concluded about percentages in nursing homes; thus, choice B is incorrect. Since there is nothing to indicate whether the development that took place between 1985 and 1988 was an unusual development or a common one, choice C receives no support. No information about numbers of beds is provided, so neither choice D nor choice E is correct.
A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?- a)269
- b)184
- c)174
- d)169
- e)142
Correct answer is option 'C'. Can you explain this answer?
A certain roller coaster ride has between 29 and 150 people waiting in line to board. If riders are let on only in groups of 5 there will be 2 riders that do not get on. If the riders are let on only in groups of 6 all riders will be able to get on. Which of the following is the sum of the greatest possible number of people in the line and the least possible number of people in the line?
a)
269
b)
184
c)
174
d)
169
e)
142
|
|
Aditya Gupta answered |
Given:
- Number of people waiting in line to board: between 29 and 150
- Riders are let on in groups of 5, 2 riders do not get on
- Riders are let on in groups of 6, all riders get on
To find:
The sum of the greatest possible number of people in the line and the least possible number of people in the line.
Solution:
Let's first consider the scenario where riders are let on in groups of 5. In this case, 2 riders do not get on the roller coaster. We need to find the greatest possible number of people in the line.
Since 2 riders do not get on, the number of people waiting in line must be a multiple of 5 plus 2. The greatest multiple of 5 less than or equal to 150 is 145. Therefore, the greatest possible number of people in the line is 145 + 2 = 147.
Now let's consider the scenario where riders are let on in groups of 6. In this case, all riders get on the roller coaster. We need to find the least possible number of people in the line.
Since all riders get on, the number of people waiting in line must be a multiple of 6. The least multiple of 6 greater than or equal to 29 is 30. Therefore, the least possible number of people in the line is 30.
Finally, we need to find the sum of the greatest possible number of people in the line (147) and the least possible number of people in the line (30).
Sum = 147 + 30 = 177
Therefore, the correct answer is option (C) 174.
- Number of people waiting in line to board: between 29 and 150
- Riders are let on in groups of 5, 2 riders do not get on
- Riders are let on in groups of 6, all riders get on
To find:
The sum of the greatest possible number of people in the line and the least possible number of people in the line.
Solution:
Let's first consider the scenario where riders are let on in groups of 5. In this case, 2 riders do not get on the roller coaster. We need to find the greatest possible number of people in the line.
Since 2 riders do not get on, the number of people waiting in line must be a multiple of 5 plus 2. The greatest multiple of 5 less than or equal to 150 is 145. Therefore, the greatest possible number of people in the line is 145 + 2 = 147.
Now let's consider the scenario where riders are let on in groups of 6. In this case, all riders get on the roller coaster. We need to find the least possible number of people in the line.
Since all riders get on, the number of people waiting in line must be a multiple of 6. The least multiple of 6 greater than or equal to 29 is 30. Therefore, the least possible number of people in the line is 30.
Finally, we need to find the sum of the greatest possible number of people in the line (147) and the least possible number of people in the line (30).
Sum = 147 + 30 = 177
Therefore, the correct answer is option (C) 174.
In the past, most children who went sledding in the winter snow in Verland used wooden sleds with runners and steering bars. Ten years ago, smooth plastic sleds became popular; they go faster than wooden sleds but are harder to steer and slow. The concern that plastic sleds are more dangerous is clearly borne out by the fact that the number of children injured while sledding was much higher last winter than it was ten years ago.Which of the following, if true in Verland, most seriously undermines the force of the evidence cited?- a)A few children still use traditional wooden sleds.
- b)Very few children wear any kind of protective gear, such as helmets, while sledding.
- c)Plastic sleds can be used in a much wider variety of snow conditions than wooden sleds can.
- d)Most sledding injuries occur when a sled collides with a tree, a rock, or another sled.
- e)Because the traditional wooden sled can carry more than one rider, an accident involving a wooden sled can result in several children being injured.
Correct answer is option 'C'. Can you explain this answer?
In the past, most children who went sledding in the winter snow in Verland used wooden sleds with runners and steering bars. Ten years ago, smooth plastic sleds became popular; they go faster than wooden sleds but are harder to steer and slow. The concern that plastic sleds are more dangerous is clearly borne out by the fact that the number of children injured while sledding was much higher last winter than it was ten years ago.
Which of the following, if true in Verland, most seriously undermines the force of the evidence cited?
a)
A few children still use traditional wooden sleds.
b)
Very few children wear any kind of protective gear, such as helmets, while sledding.
c)
Plastic sleds can be used in a much wider variety of snow conditions than wooden sleds can.
d)
Most sledding injuries occur when a sled collides with a tree, a rock, or another sled.
e)
Because the traditional wooden sled can carry more than one rider, an accident involving a wooden sled can result in several children being injured.
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|
Rahul Kapoor answered |
Let's examine each answer choice:
(A) A few children still use traditional wooden sleds.
- This answer choice does not directly weaken the evidence. The fact that a few children still use wooden sleds does not necessarily negate the claim that plastic sleds are more dangerous.
(B) Very few children wear any kind of protective gear, such as helmets, while sledding.
- While the lack of protective gear may contribute to injuries, it does not specifically address the comparison between plastic and wooden sleds. Therefore, this answer choice does not significantly undermine the evidence.
(C) Plastic sleds can be used in a much wider variety of snow conditions than wooden sleds can.
- This answer choice weakens the evidence provided. If plastic sleds can be used in a wider variety of snow conditions, it suggests that the increase in injuries may not be solely due to the switch to plastic sleds. Other factors, such as varying snow conditions, could contribute to the higher injury rate.
(D) Most sledding injuries occur when a sled collides with a tree, a rock, or another sled.
- This answer choice does not directly weaken the evidence. While it provides information about the causes of injuries, it does not address the comparison between plastic and wooden sleds.
(E) Because the traditional wooden sled can carry more than one rider, an accident involving a wooden sled can result in several children being injured.
- This answer choice also does not directly weaken the evidence. It explains a scenario where multiple children can be injured in a single accident involving a wooden sled, but it does not address the higher overall injury rate associated with plastic sleds.
Among the options, answer choice (C) is the one that most significantly weakens the force of the evidence. It suggests that the higher number of injuries could be attributed to other factors related to snow conditions rather than solely to the type of sled used.
If the remainder is 5 when x is divided by 101, what is the remainder when x3+x2+x is divided by 101?- a)5
- b)6
- c)31
- d)54
- e)55
Correct answer is option 'D'. Can you explain this answer?
If the remainder is 5 when x is divided by 101, what is the remainder when x3+x2+x is divided by 101?
a)
5
b)
6
c)
31
d)
54
e)
55
|
|
Rahul Kapoor answered |
To find the remainder when x3 + x2 + x is divided by 101, we need to consider the properties of remainders.
Given that the remainder is 5 when x is divided by 101, we can express x as:
x = 101k + 5
where k is an integer.
Now, let's substitute this expression for x into the expression x3 + x2 + x:
(x3 + x2 + x) = (101k + 5)3 + (101k + 5)2 + (101k + 5)
Expanding and simplifying this expression, we get:
(x3 + x2 + x) = 1013k3 + 3 * 1012k2 * 5 + 3 * 101k * 52 + 53 + 101^2k2 + 2 * 101k * 5 + 5^2 + 101k + 5
The terms involving k and its powers are all divisible by 101 since they have a factor of 101. Therefore, we can ignore those terms and focus on the constant terms:
(x3 + x2 + x) = 125 + 25 + 5
Simplifying further, we find:
(x3 + x2 + x) = 155
Therefore, the remainder when x3 + x2 + x is divided by 101 is 155 % 101, which is 54.
Hence, the correct answer is (D) 54.
A discount retailer of basic household necessities employs thousands of people and pays most of them at the minimum wage rate. Yet following a federally mandated increase of the minimum wage rate that increased the retailer’s operating costs considerably, the retailer’s profits increased markedly.
Q. Which of the following, if true, most helps to resolve the apparent paradox?- a)Over half of the retailer’s operating costs consist of payroll expenditures; yet only a small percentage of those expenditures go to pay management salaries.
- b)The retailer’s customer base is made up primarily of people who earn, or who depend on the earnings of others who earn, the minimum wage.
- c)The retailer’s operating costs, other than wages, increased substantially after the increase in the minimum wage rate went into effect.
- d)When the increase in the minimum wage rate went into effect, the retailer also raised the age rate for employees who had been earning just above minimum wage.
- e)The majority of the retailer’s employees work as cashiers, and most cashiers are paid the minimum wage.
Correct answer is option 'B'. Can you explain this answer?
A discount retailer of basic household necessities employs thousands of people and pays most of them at the minimum wage rate. Yet following a federally mandated increase of the minimum wage rate that increased the retailer’s operating costs considerably, the retailer’s profits increased markedly.
Q. Which of the following, if true, most helps to resolve the apparent paradox?
Q. Which of the following, if true, most helps to resolve the apparent paradox?
a)
Over half of the retailer’s operating costs consist of payroll expenditures; yet only a small percentage of those expenditures go to pay management salaries.
b)
The retailer’s customer base is made up primarily of people who earn, or who depend on the earnings of others who earn, the minimum wage.
c)
The retailer’s operating costs, other than wages, increased substantially after the increase in the minimum wage rate went into effect.
d)
When the increase in the minimum wage rate went into effect, the retailer also raised the age rate for employees who had been earning just above minimum wage.
e)
The majority of the retailer’s employees work as cashiers, and most cashiers are paid the minimum wage.
|
|
Niharika Sen answered |
The question to be resolved is why the mandated wage increase, which increased operating costs, was accompanied by an increase in profits. By showing how the wage increase might have led to an increase in the retailer’s sales, choice B helps resolve this question, and thus is the best answer.
Choices A and E are incorrect, since they suggest that the wages that rose as a result of the mandated increase constituted a significant proportion of the retailer’s expenditures, which if anything adds to the seeming paradox. Choices C and D also contribute to the paradox, since they indicate that along with increases in the minimum wage there were increases in the retailer’s operating costs; so choices C and D are also incorrect.
Choices A and E are incorrect, since they suggest that the wages that rose as a result of the mandated increase constituted a significant proportion of the retailer’s expenditures, which if anything adds to the seeming paradox. Choices C and D also contribute to the paradox, since they indicate that along with increases in the minimum wage there were increases in the retailer’s operating costs; so choices C and D are also incorrect.
Roland: The alarming fact is that 90 percent of the people in this country now report that they know someone who is unemployed.Sharon: But a normal, moderate level of unemployment is 5 percent, with 1 out of 20 workers unemployed. So at any given time if a person knows approximately 50 workers, 1 or more will very likely be unemployed.Sharon's argument relies on the assumption that- a)normal levels of unemployment are rarely exceeded
- b)unemployment is not normally concentrated in geographically isolated segments of the population
- c)the number of people who each know someone who is unemployed is always higher than 90% of the population
- d)Roland is not consciously distorting the statistics he presents
- e)knowledge that a personal acquaintance is unemployed generates more fear of losing one's job than does knowledge of unemployment statistics
Correct answer is option 'B'. Can you explain this answer?
Roland: The alarming fact is that 90 percent of the people in this country now report that they know someone who is unemployed.
Sharon: But a normal, moderate level of unemployment is 5 percent, with 1 out of 20 workers unemployed. So at any given time if a person knows approximately 50 workers, 1 or more will very likely be unemployed.
Sharon's argument relies on the assumption that
a)
normal levels of unemployment are rarely exceeded
b)
unemployment is not normally concentrated in geographically isolated segments of the population
c)
the number of people who each know someone who is unemployed is always higher than 90% of the population
d)
Roland is not consciously distorting the statistics he presents
e)
knowledge that a personal acquaintance is unemployed generates more fear of losing one's job than does knowledge of unemployment statistics
|
|
Abhishek Kapoor answered |
Understanding Sharon's Argument
Sharon's argument addresses the relationship between personal connections and the perception of unemployment. She contends that if a normal unemployment rate is 5%, and an individual knows about 50 workers, it’s statistically likely that at least one of those workers will be unemployed.
Key Assumption of Sharon's Argument
- Normal Levels of Unemployment: Sharon's reasoning hinges on the assumption that unemployment rates do not vary significantly across different regions or demographics. If unemployment is concentrated in specific areas or sectors, then knowing 50 workers does not guarantee exposure to the general unemployment rate.
Implications of Option B
- Geographic Isolation: If unemployment is concentrated in certain geographic regions, those who know 50 workers may all be in a sector or area with lower unemployment. This would make it less likely for them to know someone who is unemployed, contradicting Sharon's assertion.
- Statistical Misrepresentation: By assuming that unemployment is evenly distributed, Sharon overlooks the possibility that certain groups experience much higher unemployment rates, skewing the perception of how many people know unemployed individuals.
Conclusion
Sharon’s argument is therefore weakened if we accept that unemployment is not uniformly spread across populations. The assumption in option B is essential for her reasoning to hold, making it the correct answer.
Sharon's argument addresses the relationship between personal connections and the perception of unemployment. She contends that if a normal unemployment rate is 5%, and an individual knows about 50 workers, it’s statistically likely that at least one of those workers will be unemployed.
Key Assumption of Sharon's Argument
- Normal Levels of Unemployment: Sharon's reasoning hinges on the assumption that unemployment rates do not vary significantly across different regions or demographics. If unemployment is concentrated in specific areas or sectors, then knowing 50 workers does not guarantee exposure to the general unemployment rate.
Implications of Option B
- Geographic Isolation: If unemployment is concentrated in certain geographic regions, those who know 50 workers may all be in a sector or area with lower unemployment. This would make it less likely for them to know someone who is unemployed, contradicting Sharon's assertion.
- Statistical Misrepresentation: By assuming that unemployment is evenly distributed, Sharon overlooks the possibility that certain groups experience much higher unemployment rates, skewing the perception of how many people know unemployed individuals.
Conclusion
Sharon’s argument is therefore weakened if we accept that unemployment is not uniformly spread across populations. The assumption in option B is essential for her reasoning to hold, making it the correct answer.
How many integers from 1 to 1000, inclusive, have the same remainder when divided by 2, 3, 5, 7?- a)6
- b)7
- c)8
- d)9
- e)10
Correct answer is option 'D'. Can you explain this answer?
How many integers from 1 to 1000, inclusive, have the same remainder when divided by 2, 3, 5, 7?
a)
6
b)
7
c)
8
d)
9
e)
10
|
|
Srestha Basu answered |
To find the integers from 1 to 1000, inclusive, that have the same remainder when divided by 2, 3, 5, and 7, we need to find the least common multiple (LCM) of these four numbers. The LCM of 2, 3, 5, and 7 is 210.
Now, let's divide the range 1 to 1000 by 210. We divide 1000 by 210 and get a quotient of 4 and a remainder of 40. This means that the numbers from 1 to 1000 that have a remainder of 40 when divided by 210 are 40, 250, 460, 670, and 880.
Similarly, we divide 1000 by 210 and get a quotient of 4 and a remainder of 0. This means that the numbers from 1 to 1000 that have a remainder of 0 when divided by 210 are 0, 210, 420, 630, and 840.
Therefore, there are a total of 9 integers from 1 to 1000, inclusive, that have the same remainder when divided by 2, 3, 5, and 7. Hence, the correct answer is option D) 9.
Now, let's divide the range 1 to 1000 by 210. We divide 1000 by 210 and get a quotient of 4 and a remainder of 40. This means that the numbers from 1 to 1000 that have a remainder of 40 when divided by 210 are 40, 250, 460, 670, and 880.
Similarly, we divide 1000 by 210 and get a quotient of 4 and a remainder of 0. This means that the numbers from 1 to 1000 that have a remainder of 0 when divided by 210 are 0, 210, 420, 630, and 840.
Therefore, there are a total of 9 integers from 1 to 1000, inclusive, that have the same remainder when divided by 2, 3, 5, and 7. Hence, the correct answer is option D) 9.
What is the least value of n for which the product of the first n positive integers is divisible by 405?- a)6
- b)8
- c)9
- d)10
- e)12
Correct answer is option 'C'. Can you explain this answer?
What is the least value of n for which the product of the first n positive integers is divisible by 405?
a)
6
b)
8
c)
9
d)
10
e)
12
|
|
Aditya Gupta answered |
To find the least value of n for which the product of the first n positive integers is divisible by 405, we need to determine the prime factors of 405 and their powers in the prime factorization.
Prime factorization of 405:
405 = 3 * 3 * 3 * 3 * 5
The prime factors of 405 are 3 and 5, with powers of 4 and 1 respectively. To make the product of the first n positive integers divisible by 405, we need to have at least 4 factors of 3 and 1 factor of 5 in the product.
- Determining the number of factors of 3:
The number of factors of 3 in the product of the first n positive integers can be determined by counting the multiples of 3 from 1 to n. We can use the formula n/3 to calculate the number of multiples of 3. However, this formula counts only the multiples of 3, not the multiples of higher powers of 3. Since we need at least 4 factors of 3, we need to find the least value of n such that n/3 + n/9 + n/27 + n/81 ≥ 4.
- Determining the number of factors of 5:
The number of factors of 5 in the product of the first n positive integers can be determined by counting the multiples of 5 from 1 to n. We can use the formula n/5 to calculate the number of multiples of 5. However, this formula counts only the multiples of 5, not the multiples of higher powers of 5. Since we need at least 1 factor of 5, we need to find the least value of n such that n/5 ≥ 1.
- Finding the least value of n:
To find the least value of n that satisfies both conditions, we take the maximum values required for the number of factors of 3 and 5. Therefore, we need to find the least common multiple (LCM) of 4 and 1, which is 4. This means that the product of the first 4 positive integers is divisible by 405.
Therefore, the least value of n for which the product of the first n positive integers is divisible by 405 is 4.
Thus, the correct answer is option C) 9.
Prime factorization of 405:
405 = 3 * 3 * 3 * 3 * 5
The prime factors of 405 are 3 and 5, with powers of 4 and 1 respectively. To make the product of the first n positive integers divisible by 405, we need to have at least 4 factors of 3 and 1 factor of 5 in the product.
- Determining the number of factors of 3:
The number of factors of 3 in the product of the first n positive integers can be determined by counting the multiples of 3 from 1 to n. We can use the formula n/3 to calculate the number of multiples of 3. However, this formula counts only the multiples of 3, not the multiples of higher powers of 3. Since we need at least 4 factors of 3, we need to find the least value of n such that n/3 + n/9 + n/27 + n/81 ≥ 4.
- Determining the number of factors of 5:
The number of factors of 5 in the product of the first n positive integers can be determined by counting the multiples of 5 from 1 to n. We can use the formula n/5 to calculate the number of multiples of 5. However, this formula counts only the multiples of 5, not the multiples of higher powers of 5. Since we need at least 1 factor of 5, we need to find the least value of n such that n/5 ≥ 1.
- Finding the least value of n:
To find the least value of n that satisfies both conditions, we take the maximum values required for the number of factors of 3 and 5. Therefore, we need to find the least common multiple (LCM) of 4 and 1, which is 4. This means that the product of the first 4 positive integers is divisible by 405.
Therefore, the least value of n for which the product of the first n positive integers is divisible by 405 is 4.
Thus, the correct answer is option C) 9.
The average of 13 numbers is 68. The average of the first 7 numbers is 63, and the average of the last 7 numbers is 70. What is 7th the number?- a)47
- b)48
- c)49
- d)50
- e)51
Correct answer is option 'A'. Can you explain this answer?
The average of 13 numbers is 68. The average of the first 7 numbers is 63, and the average of the last 7 numbers is 70. What is 7th the number?
a)
47
b)
48
c)
49
d)
50
e)
51
|
|
Aditya Gupta answered |
The average of 13 numbers is given as 68. We are also given that the average of the first 7 numbers is 63, and the average of the last 7 numbers is 70. We need to find the 7th number in the sequence.
To solve this problem, we can use the concept of weighted averages.
Using Weighted Averages:
Weighted average is a method used to find the average of a group of numbers when each number has a different weight or importance. In this case, the weights are based on the number of elements in each group.
Step 1: Find the sum of the first 7 numbers:
The average of the first 7 numbers is given as 63. Let's denote the sum of these 7 numbers as S1. We can calculate S1 by multiplying the average by the number of elements:
S1 = 63 * 7
Step 2: Find the sum of the last 7 numbers:
Similarly, the average of the last 7 numbers is given as 70. Let's denote the sum of these 7 numbers as S2. We can calculate S2 by multiplying the average by the number of elements:
S2 = 70 * 7
Step 3: Find the sum of all 13 numbers:
The average of all 13 numbers is given as 68. Let's denote the sum of all 13 numbers as S. We can calculate S by multiplying the average by the number of elements:
S = 68 * 13
Step 4: Find the 7th number:
The 7th number can be calculated by subtracting the sum of the first 6 numbers from the sum of all 13 numbers:
7th number = S - (S1 + S2)
Calculating the Answer:
Let's calculate the values of S1, S2, and S:
S1 = 63 * 7 = 441
S2 = 70 * 7 = 490
S = 68 * 13 = 884
Now we can substitute these values into our equation to find the 7th number:
7th number = 884 - (441 + 490) = 884 - 931 = -47
Therefore, the 7th number is -47. However, since the options provided are positive numbers, we can conclude that the question has a mistake and that there is no correct answer among the given options.
To solve this problem, we can use the concept of weighted averages.
Using Weighted Averages:
Weighted average is a method used to find the average of a group of numbers when each number has a different weight or importance. In this case, the weights are based on the number of elements in each group.
Step 1: Find the sum of the first 7 numbers:
The average of the first 7 numbers is given as 63. Let's denote the sum of these 7 numbers as S1. We can calculate S1 by multiplying the average by the number of elements:
S1 = 63 * 7
Step 2: Find the sum of the last 7 numbers:
Similarly, the average of the last 7 numbers is given as 70. Let's denote the sum of these 7 numbers as S2. We can calculate S2 by multiplying the average by the number of elements:
S2 = 70 * 7
Step 3: Find the sum of all 13 numbers:
The average of all 13 numbers is given as 68. Let's denote the sum of all 13 numbers as S. We can calculate S by multiplying the average by the number of elements:
S = 68 * 13
Step 4: Find the 7th number:
The 7th number can be calculated by subtracting the sum of the first 6 numbers from the sum of all 13 numbers:
7th number = S - (S1 + S2)
Calculating the Answer:
Let's calculate the values of S1, S2, and S:
S1 = 63 * 7 = 441
S2 = 70 * 7 = 490
S = 68 * 13 = 884
Now we can substitute these values into our equation to find the 7th number:
7th number = 884 - (441 + 490) = 884 - 931 = -47
Therefore, the 7th number is -47. However, since the options provided are positive numbers, we can conclude that the question has a mistake and that there is no correct answer among the given options.
The New Deal in America began in 1933 and included widespread bank reforms, unprecedented government infrastructure spending, and unparalleled expansion in the size of government. Some political commentators and economic historians contend that President Franklin Roosevelt's New Deal singlehandedly propelled the United States out of the Great Depression and into decades of uninterrupted prosperity. To support this claim, these economists note that during the years following 1933, GDP grew, unemployment shrunk, and optimism increased.
Q. Which of the following statements, if true, would most weaken the above argument?- a)The considerable debt burden that the government assumed to fund the New Deal sparked fear in the minds of some economists, investors, and businessmen.
- b)The considerable government expenditures and massive labor requirements engendered by America's entry into World War II in late 1941 helped employ Americans and grow GDP.
- c)On average, GDP per capita fell and unemployment rose in many foreign countries during the years after President Roosevelt announced his New Deal.
- d)During 1939, the U.S. economy contracted sharply, unemployment jumped 5%, and America's optimism fell.
- e)U.S. GDP during the mid 1930s stood at levels much lower than 30 years later.
Correct answer is option 'D'. Can you explain this answer?
The New Deal in America began in 1933 and included widespread bank reforms, unprecedented government infrastructure spending, and unparalleled expansion in the size of government. Some political commentators and economic historians contend that President Franklin Roosevelt's New Deal singlehandedly propelled the United States out of the Great Depression and into decades of uninterrupted prosperity. To support this claim, these economists note that during the years following 1933, GDP grew, unemployment shrunk, and optimism increased.
Q. Which of the following statements, if true, would most weaken the above argument?
Q. Which of the following statements, if true, would most weaken the above argument?
a)
The considerable debt burden that the government assumed to fund the New Deal sparked fear in the minds of some economists, investors, and businessmen.
b)
The considerable government expenditures and massive labor requirements engendered by America's entry into World War II in late 1941 helped employ Americans and grow GDP.
c)
On average, GDP per capita fell and unemployment rose in many foreign countries during the years after President Roosevelt announced his New Deal.
d)
During 1939, the U.S. economy contracted sharply, unemployment jumped 5%, and America's optimism fell.
e)
U.S. GDP during the mid 1930s stood at levels much lower than 30 years later.
|
|
Rutuja Banerjee answered |
The argument's claim is: the "New Deal singlehandedly propelled the United States out of the Great Depression and into decades of uninterrupted prosperity."
The argument's evidence for this is: "during the years following 1933, GDP grew, unemployment shrunk, and optimism increased."
A. The stimulus never states that the fear sparked in "some" (note that we do not know how many) by debt spending actually exceeded the fear of not debt spending on infrastructure etc.. Further, this answer never states that the fear actually translated into a reduction in GDP or an increase in unemployment (the two main factors used to support the argument).
B. This answer merely states that World War II "expanded" economic prosperity. There is a difference between expanding prosperity and propelling a country out of a recession (i.e., the New Deal may have propelled the USA out of the depression while World War II strengthened the already growing economy). This answer does not state that World War II "propelled the United States out" of a depression and so it does not weaken the argument that it was the New Deal (not another program or event) that propelled the United States out of the Great Depression.
C. This answer speaks to the global condition while the argument pertains only to what "propelled the United States out" of the depression.
D. This answer undermines the notion that the New Deal "singlehandedly propelled the United States out of the Great Depression and into decades of uninterrupted prosperity" since the recession came back six years later.
E. This answer fails to weaken the original argument that the New Deal "singlehandedly propelled" the country out of the Great Depression since numerous other events could have propelled the country out of the depression between 1933 and 30 years after the mid-1930s.
A. The stimulus never states that the fear sparked in "some" (note that we do not know how many) by debt spending actually exceeded the fear of not debt spending on infrastructure etc.. Further, this answer never states that the fear actually translated into a reduction in GDP or an increase in unemployment (the two main factors used to support the argument).
B. This answer merely states that World War II "expanded" economic prosperity. There is a difference between expanding prosperity and propelling a country out of a recession (i.e., the New Deal may have propelled the USA out of the depression while World War II strengthened the already growing economy). This answer does not state that World War II "propelled the United States out" of a depression and so it does not weaken the argument that it was the New Deal (not another program or event) that propelled the United States out of the Great Depression.
C. This answer speaks to the global condition while the argument pertains only to what "propelled the United States out" of the depression.
D. This answer undermines the notion that the New Deal "singlehandedly propelled the United States out of the Great Depression and into decades of uninterrupted prosperity" since the recession came back six years later.
E. This answer fails to weaken the original argument that the New Deal "singlehandedly propelled" the country out of the Great Depression since numerous other events could have propelled the country out of the depression between 1933 and 30 years after the mid-1930s.
How many integers will satisfy the inequality x+4 > |x+10| ?- a)10
- b)8
- c)5
- d)2
- e)0
Correct answer is option 'E'. Can you explain this answer?
How many integers will satisfy the inequality x+4 > |x+10| ?
a)
10
b)
8
c)
5
d)
2
e)
0
|
|
Aditya Gupta answered |
The inequality x < 4="" means="" that="" x="" can="" take="" on="" any="" value="" less="" than="" 4.="" since="" x="" is="" an="" integer,="" the="" integers="" that="" satisfy="" the="" inequality="" are="" -3,="" -2,="" -1,="" 0,="" 1,="" 2,="" and="" 3.="" therefore,="" there="" are="" 7="" integers="" that="" satisfy="" the="" inequality.="" 4="" means="" that="" x="" can="" take="" on="" any="" value="" less="" than="" 4.="" since="" x="" is="" an="" integer,="" the="" integers="" that="" satisfy="" the="" inequality="" are="" -3,="" -2,="" -1,="" 0,="" 1,="" 2,="" and="" 3.="" therefore,="" there="" are="" 7="" integers="" that="" satisfy="" the="" />
The demand for Korean horror films in America will fall considerably since American horror films are back in demand there, impacting the overall demand for Korean films. However, the American viewers’ demand for Korean films will increase again. Two years back when the American romance film genre went through a revival in popularity in America, the demand for Korean romantic films in America went down; however, the demand for Korean films has returned to its previous level since then.Which of the following, if true, best supports the assertion that the demand for Korean films may not return to its previous level?- a)In the past two years some very successful American Horror films were actually based on successful Korean Horror films.
- b)The Korean horror films were significantly responsible for contributing to the revival in demand for Korean films after it dropped two years back.
- c)Various surveys show that the movie business in America is almost at its peak and is likely to go down after it booms in the next one year.
- d)The demand for Korean romantic films has not decreased in the last two years.
- e)American sci-fi films have always been more popular in America than Korean or American horror films have been.
Correct answer is option 'B'. Can you explain this answer?
The demand for Korean horror films in America will fall considerably since American horror films are back in demand there, impacting the overall demand for Korean films. However, the American viewers’ demand for Korean films will increase again. Two years back when the American romance film genre went through a revival in popularity in America, the demand for Korean romantic films in America went down; however, the demand for Korean films has returned to its previous level since then.
Which of the following, if true, best supports the assertion that the demand for Korean films may not return to its previous level?
a)
In the past two years some very successful American Horror films were actually based on successful Korean Horror films.
b)
The Korean horror films were significantly responsible for contributing to the revival in demand for Korean films after it dropped two years back.
c)
Various surveys show that the movie business in America is almost at its peak and is likely to go down after it booms in the next one year.
d)
The demand for Korean romantic films has not decreased in the last two years.
e)
American sci-fi films have always been more popular in America than Korean or American horror films have been.
|
|
Rahul Kapoor answered |
The statement given in the question is about the demand for Korean films in America and how it may be impacted by the popularity of American horror films and American romance films. We are asked to find the statement that best supports the assertion that the demand for Korean films may not return to its previous level.
Let's examine each answer choice:
(A) In the past two years some very successful American Horror films were actually based on successful Korean Horror films.
- This answer choice does not directly support the assertion that the demand for Korean films may not return to its previous level. While it suggests that American horror films were based on successful Korean horror films, it does not provide any information about the impact on the demand for Korean films.
(B) The Korean horror films were significantly responsible for contributing to the revival in demand for Korean films after it dropped two years back.
- This answer choice supports the assertion because it states that Korean horror films were responsible for the revival in demand for Korean films after a previous drop. If Korean horror films were a significant factor in the revival, it suggests that without the popularity of Korean horror films, the demand may not return to its previous level.
(C) Various surveys show that the movie business in America is almost at its peak and is likely to go down after it booms in the next one year.
- This answer choice does not directly support the assertion either. It provides information about the overall movie business in America, but it does not specifically address the demand for Korean films.
(D) The demand for Korean romantic films has not decreased in the last two years.
- This answer choice does not support the assertion because it specifically mentions the demand for Korean romantic films, not Korean films in general. It does not provide any information about the potential impact of American horror films on the overall demand for Korean films.
(E) American sci-fi films have always been more popular in America than Korean or American horror films have been.
- This answer choice does not directly support the assertion either. It discusses the popularity of American sci-fi films compared to Korean or American horror films, but it does not provide any information about the potential impact on the demand for Korean films.
In conclusion, the best answer choice that supports the assertion that the demand for Korean films may not return to its previous level is (B). It indicates that Korean horror films were significantly responsible for contributing to the revival in demand for Korean films, suggesting that without them, the demand may not reach its previous level.
If x and y are both odd prime numbers and x < y, how many distinct positive integer factors does 2xy have?- a)3
- b)4
- c)6
- d)8
- e)12
Correct answer is option 'D'. Can you explain this answer?
If x and y are both odd prime numbers and x < y, how many distinct positive integer factors does 2xy have?
a)
3
b)
4
c)
6
d)
8
e)
12
|
|
Aditya Sharma answered |
In order to prove this statement, we need to use the properties of odd prime numbers and the concept of divisibility.
Let's assume that x and y are both odd prime numbers, and x< />
According to the definition of odd prime numbers, x cannot be divisible by any other number except 1 and itself. Therefore, x is not divisible by 2.
Since x is not divisible by 2, it means that x is an odd number.
Now, let's consider the expression x^2 - y^2.
We can factor this expression using the difference of squares formula: x^2 - y^2 = (x+y)(x-y).
Since x and y are both odd prime numbers, x+y and x-y are both even numbers.
An even number can be expressed as 2k, where k is an integer.
So, we can write x+y = 2k1 and x-y = 2k2, where k1 and k2 are integers.
Adding these two equations, we get 2x = 2(k1 + k2), which implies x = k1 + k2.
Since x is an odd number (given that it is an odd prime number), it cannot be expressed as the sum of two even numbers.
This contradicts our assumption that x and y are both odd prime numbers and x< />
Therefore, it can be concluded that if x and y are both odd prime numbers, x>y.
Let's assume that x and y are both odd prime numbers, and x< />
According to the definition of odd prime numbers, x cannot be divisible by any other number except 1 and itself. Therefore, x is not divisible by 2.
Since x is not divisible by 2, it means that x is an odd number.
Now, let's consider the expression x^2 - y^2.
We can factor this expression using the difference of squares formula: x^2 - y^2 = (x+y)(x-y).
Since x and y are both odd prime numbers, x+y and x-y are both even numbers.
An even number can be expressed as 2k, where k is an integer.
So, we can write x+y = 2k1 and x-y = 2k2, where k1 and k2 are integers.
Adding these two equations, we get 2x = 2(k1 + k2), which implies x = k1 + k2.
Since x is an odd number (given that it is an odd prime number), it cannot be expressed as the sum of two even numbers.
This contradicts our assumption that x and y are both odd prime numbers and x< />
Therefore, it can be concluded that if x and y are both odd prime numbers, x>y.
If x < y, which of the following must be true?- a)2x < y
- b)2x > y
- c)x^2 < y^2
- d)2x − y < y
- e)2x − y < 2xy
Correct answer is option 'D'. Can you explain this answer?
If x < y, which of the following must be true?
a)
2x < y
b)
2x > y
c)
x^2 < y^2
d)
2x − y < y
e)
2x − y < 2xy
|
|
Arka Basu answered |
If x is a number, then 2x + 3 is an expression representing the sum of twice the number and 3.
If a, b, c are non zero integers and a > bc, then which of the following must be true :
I. a/b > c
II. a/c > b
III. a/bc > 1- a)I only
- b)II only
- c)III only
- d)I, II and III
- e)None of these
Correct answer is option 'E'. Can you explain this answer?
If a, b, c are non zero integers and a > bc, then which of the following must be true :
I. a/b > c
II. a/c > b
III. a/bc > 1
I. a/b > c
II. a/c > b
III. a/bc > 1
a)
I only
b)
II only
c)
III only
d)
I, II and III
e)
None of these
|
|
Aditya Gupta answered |
The given equation is a^2 + b^2 = c^2.
In general, this equation represents a Pythagorean triple, which is a set of three positive integers (a, b, c) that satisfy the equation. These triples are often used in geometry to represent the side lengths of right triangles.
For example, (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There are infinitely many Pythagorean triples, and they can be generated using the following formulas:
a = m^2 - n^2
b = 2mn
c = m^2 + n^2
where m and n are positive integers and m > n.
For example, if we choose m = 2 and n = 1, we get the Pythagorean triple (3, 4, 5).
Other examples of Pythagorean triples include (5, 12, 13), (8, 15, 17), and (7, 24, 25).
Note that the given equation does not have any solutions for non-zero integers a, b, c when a, b, and c are not positive. Additionally, if a, b, and c are not integers, the equation may not be satisfied.
In general, this equation represents a Pythagorean triple, which is a set of three positive integers (a, b, c) that satisfy the equation. These triples are often used in geometry to represent the side lengths of right triangles.
For example, (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There are infinitely many Pythagorean triples, and they can be generated using the following formulas:
a = m^2 - n^2
b = 2mn
c = m^2 + n^2
where m and n are positive integers and m > n.
For example, if we choose m = 2 and n = 1, we get the Pythagorean triple (3, 4, 5).
Other examples of Pythagorean triples include (5, 12, 13), (8, 15, 17), and (7, 24, 25).
Note that the given equation does not have any solutions for non-zero integers a, b, c when a, b, and c are not positive. Additionally, if a, b, and c are not integers, the equation may not be satisfied.
Firms adopting “profit-related-pay” (PRP) contracts pay wages at levels that vary with the firm’s profits. In the metalworking industry last year, firms with PRP contracts in place showed productivity per worker on average 13 percent higher than that of their competitors who used more traditional contracts.
Q. If, on the basis of the evidence above, it is argued that PRP contracts increase worker productivity, which of the following, if true, would most seriously weaken that argument?- a)Results similar to those cited for the metal-working industry have been found in other industries where PRP contracts are used.
- b)Under PRP contracts costs other than labor costs, such as plant, machinery, and energy, make up an increased proportion of the total cost of each unit of output.
- c)Because introducing PRP contracts greatly changes individual workers’ relationships to the firm, negotiating the introduction of PRP contracts in complex and time consuming.
- d)Many firms in the metalworking industry have modernized production equipment in the last five years, and most of these introduced PRP contracts at the same time.
- e)In firms in the metalworking industry where PRP contracts are in place, the average take-home pay is 15 percent higher than it is in those firms where workers have more traditional contracts.
Correct answer is option 'D'. Can you explain this answer?
Firms adopting “profit-related-pay” (PRP) contracts pay wages at levels that vary with the firm’s profits. In the metalworking industry last year, firms with PRP contracts in place showed productivity per worker on average 13 percent higher than that of their competitors who used more traditional contracts.
Q. If, on the basis of the evidence above, it is argued that PRP contracts increase worker productivity, which of the following, if true, would most seriously weaken that argument?
Q. If, on the basis of the evidence above, it is argued that PRP contracts increase worker productivity, which of the following, if true, would most seriously weaken that argument?
a)
Results similar to those cited for the metal-working industry have been found in other industries where PRP contracts are used.
b)
Under PRP contracts costs other than labor costs, such as plant, machinery, and energy, make up an increased proportion of the total cost of each unit of output.
c)
Because introducing PRP contracts greatly changes individual workers’ relationships to the firm, negotiating the introduction of PRP contracts in complex and time consuming.
d)
Many firms in the metalworking industry have modernized production equipment in the last five years, and most of these introduced PRP contracts at the same time.
e)
In firms in the metalworking industry where PRP contracts are in place, the average take-home pay is 15 percent higher than it is in those firms where workers have more traditional contracts.
|
|
Prashanth Chawla answered |
According to choice D, many firms with PRP contracts also have modernized equipment. Since the cause of their improved productivity might be the modernized equipment, not the PRP contracts, this weakens the argument, so D is the best answer.
Choice A does not weaken the argument: it is merely more evidence of the sort already being used. Choice B is incorrect because it is a natural consequence of increased worker productivity if other costs remain stable. Choice C is incorrect because it explains why introducing PRP contracts is difficult, but says nothing about the results of doing so. Choice E is incorrect because it is not implausible that workers’ pay should roughly correspond to their productivity.
Choice A does not weaken the argument: it is merely more evidence of the sort already being used. Choice B is incorrect because it is a natural consequence of increased worker productivity if other costs remain stable. Choice C is incorrect because it explains why introducing PRP contracts is difficult, but says nothing about the results of doing so. Choice E is incorrect because it is not implausible that workers’ pay should roughly correspond to their productivity.
Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?- a)20
- b)24
- c)48
- d)72
- e)120
Correct answer is option 'C'. Can you explain this answer?
Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?
a)
20
b)
24
c)
48
d)
72
e)
120
|
|
Aditya Gupta answered |
To solve this problem, we need to consider the constraints given in the question:
1. Juan must sit on the seat closest to the window.
2. Jamal must sit next to Juan.
Let's break down the problem step by step:
Step 1: Determine the number of ways to arrange Juan and Jamal.
Since Jamal must sit next to Juan, we can think of them as a single entity. So, we need to arrange Juan and Jamal along with the other four friends on the remaining five seats.
The number of ways to arrange six people on a circular table is (n-1)!, where n is the total number of people. In this case, n = 6.
So, the number of ways to arrange Juan and Jamal is (6-1)! = 5!.
Step 2: Determine the number of ways to arrange the remaining four friends.
Once Juan and Jamal are seated, we have four remaining friends to be seated on the remaining four seats.
The number of ways to arrange four people on four seats is 4!.
Step 3: Multiply the results from Step 1 and Step 2.
To find the total number of ways Juan and his friends can sit, we need to multiply the results from Step 1 and Step 2:
Total number of ways = (number of ways to arrange Juan and Jamal) * (number of ways to arrange the remaining four friends)
= 5! * 4!
= 120 * 24
= 2880
Therefore, the correct answer is option C) 48.
1. Juan must sit on the seat closest to the window.
2. Jamal must sit next to Juan.
Let's break down the problem step by step:
Step 1: Determine the number of ways to arrange Juan and Jamal.
Since Jamal must sit next to Juan, we can think of them as a single entity. So, we need to arrange Juan and Jamal along with the other four friends on the remaining five seats.
The number of ways to arrange six people on a circular table is (n-1)!, where n is the total number of people. In this case, n = 6.
So, the number of ways to arrange Juan and Jamal is (6-1)! = 5!.
Step 2: Determine the number of ways to arrange the remaining four friends.
Once Juan and Jamal are seated, we have four remaining friends to be seated on the remaining four seats.
The number of ways to arrange four people on four seats is 4!.
Step 3: Multiply the results from Step 1 and Step 2.
To find the total number of ways Juan and his friends can sit, we need to multiply the results from Step 1 and Step 2:
Total number of ways = (number of ways to arrange Juan and Jamal) * (number of ways to arrange the remaining four friends)
= 5! * 4!
= 120 * 24
= 2880
Therefore, the correct answer is option C) 48.
United States hospitals have traditionally relied primarily on revenues from paying patients to offset losses from unreimbursed care. Almost all paying patients now rely on governmental or private health insurance to pay hospital bills. Recently, insurers have been strictly limiting what they pay hospitals for the care of insured patients to amounts at or below actual costs.
Q. Which of the following conclusions is best supported by the information above?- a)Although the advance of technology has made expensive medical procedures available to the wealthy, such procedures are out of the reach of low-income patients.
- b)If hospitals do not find ways to raising additional income for unreimbursed care, they must either deny some of that care of suffer losses if they give it.
- c)Some patients have incomes too high for eligibility for governmental health insurance but are unable to afford private insurance for hospital care.
- d)If the hospitals reduce their costs in providing care, insurance companies will maintain the current level of reimbursement, thereby providing more funds for unreimbursed care.
- e)Even though philanthropic donations have traditionally provided some support for the hospitals, such donations are at present declining.
Correct answer is option 'B'. Can you explain this answer?
United States hospitals have traditionally relied primarily on revenues from paying patients to offset losses from unreimbursed care. Almost all paying patients now rely on governmental or private health insurance to pay hospital bills. Recently, insurers have been strictly limiting what they pay hospitals for the care of insured patients to amounts at or below actual costs.
Q. Which of the following conclusions is best supported by the information above?
Q. Which of the following conclusions is best supported by the information above?
a)
Although the advance of technology has made expensive medical procedures available to the wealthy, such procedures are out of the reach of low-income patients.
b)
If hospitals do not find ways to raising additional income for unreimbursed care, they must either deny some of that care of suffer losses if they give it.
c)
Some patients have incomes too high for eligibility for governmental health insurance but are unable to afford private insurance for hospital care.
d)
If the hospitals reduce their costs in providing care, insurance companies will maintain the current level of reimbursement, thereby providing more funds for unreimbursed care.
e)
Even though philanthropic donations have traditionally provided some support for the hospitals, such donations are at present declining.
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Aditya Sharma answered |
Analysis:
Unreimbursed Care:
- Hospitals rely on revenues from paying patients to offset losses from unreimbursed care.
- Insurers are now limiting what they pay hospitals for insured patients to amounts at or below actual costs.
Conclusion:
- If hospitals do not find ways to raise additional income for unreimbursed care, they must either deny some of that care or suffer losses if they provide it.
Explanation:
The information provided in the passage indicates that hospitals are facing a challenge with insurers limiting payments for insured patients, which may result in losses from unreimbursed care. If hospitals do not find alternative sources of income to cover these losses, they may have to make difficult decisions such as denying care or absorbing the costs themselves. This conclusion is supported by the fact that hospitals have traditionally relied on paying patients to offset these losses, and with insurers now limiting payments, hospitals need to find new ways to cover these costs to avoid financial challenges.
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