Graduate Record Examination GRE Dashboard

The probability that the sum of the integers on the chosen pieces of paper will be 21 is 01-Jun.

To calculate the probability that the sum of the integers on the chosen pieces of paper will be 21, we first note that the only possible integers are 9, 10, 11, and 12. The pairs that can be formed from these numbers do not yield a sum of 21, making the probability of this event occurring effectively zero.

A) 01-Jun

Option A is correct as it indicates a probability of zero, given that it represents the outcome where no pairs of numbers can yield a sum of 21. There are no possible combinations of the numbers 9, 10, 11, and 12 that add up to 21.

B) 01-May

Option B is incorrect because it suggests an alternative probability that does not pertain to the question's context. The combinations of numbers available do not support a sum of 21, so this option does not reflect the situation correctly.

C) 01-Mar

Option C is also incorrect as it presents a probability figure unrelated to the actual outcomes possible with the numbers provided. Given that no valid pairs exist to reach a sum of 21, this option is not applicable.

D) 02-May

Option D is incorrect. Like the previous options, this does not represent a valid probability for the scenario since no pairs from the integers 9 to 12 can yield a total of 21.

E) 01-Feb

Option E is incorrect for similar reasons. It does not correspond to the situation described, as the integers available cannot form a pair that sums to 21.

Conclusion

The correct answer is A, as it accurately reflects the impossibility of forming a sum of 21 with the given integers. All other options fail to represent any valid probability in this context, reinforcing that the only feasible outcome is zero. Therefore, A is the appropriate choice based on the circumstances presented in the question.

Although toy companies are making progress toward diversifying their depictions of merpeople, their offerings are still constrained by gender and racial conventions.

The passage highlights the emerging participation of diverse individuals in mermaiding while simultaneously demonstrating that traditional representations of merpeople, particularly mermen, remain limited. Despite some advancements in representation, such as the introduction of a merman doll, the lack of diversity in its design underscores the ongoing constraints imposed by gender and racial norms.

A) Differences in the ways that mermaids and mermen are represented are likely to become more pronounced as mermaiding becomes increasingly popular.

This option incorrectly suggests that the differences in representation will become more pronounced with growing popularity. The passage indicates that while participation is increasing, the existing representations are still limited and traditional, implying that popularity alone does not lead to significant change in representation.

B) Ultimately, the responsibility for increasing the visibility of mermen lies with individual artists rather than with toy companies.

This choice misplaces the responsibility for representation. The extract emphasizes the role of major companies in shaping representations of merpeople and highlights the lack of diversity in their offerings, suggesting that corporate responsibility is significant in this context, rather than solely that of individual artists.

C) Paradoxically, depictions of merpeople are becoming more narrowly traditional as increasingly diverse individuals are drawn to mermaiding.

While this option hints at a contradiction, it does not accurately reflect the passage's emphasis on the constraints of traditional representations. The growing diversity in participation does not translate to a narrowing of depictions; rather, it shows that traditional gender norms still dominate the portrayal of mermen.

D) Even if more men were to participate in mermaiding, it is unlikely that depictions of mermen in commercial and artistic circles would become more diverse.

This statement is partially correct but lacks nuance. The passage discusses the under-representation of mermen and suggests that even with increased male participation, the existing commercial and artistic representations are still influenced by traditional norms, yet it does not definitively state that depictions will not become more diverse.

E) Although toy companies are making progress toward diversifying their depictions of merpeople, their offerings are still constrained by gender and racial conventions.

This option accurately summarizes the key points made in the passage. It acknowledges the progress made by toy companies in introducing mermen but also highlights the significant limitations that still exist in terms of gender and racial diversity, aligning perfectly with the evidence presented.

Conclusion

The correct answer, E, encapsulates the tension between progress and limitation in the representation of merpeople as described in the passage. While there are developments toward more inclusive depictions, the constraints of traditional gender and racial norms persist, making this option the most accurate reflection of the passage's conclusions. All other options fail to capture the complexity of the situation as effectively as E does.

Quantity B is greater.

In this context, Quantity B, represented as \(y + 90\), is greater than Quantity A, which is \(z\). This conclusion is drawn based on the properties of the rectangle PQRS and the relationships defined in the problem.

A) Quantity A is greater.

This option suggests that \(z\) is greater than \(y + 90\). However, without any additional information or context that supports this relationship, we cannot conclude that \(z\) exceeds \(y + 90\). Thus, this option is incorrect.

B) Quantity B is greater.

This option correctly states that \(y + 90\) is greater than \(z\). Given the properties of the rectangle and the implications of the dimensions involved, this assertion aligns with the relationships defined in the problem, making it the correct choice.

C) The two quantities are equal.

This option posits that \(z\) and \(y + 90\) are equal. However, no information in the context indicates that these two quantities are equal. Therefore, this option is not valid.

D) The relationship cannot be determined from the information given.

This option implies uncertainty regarding the relationship between \(z\) and \(y + 90\). However, based on the information provided, we can ascertain that \(y + 90\) is indeed greater, so this option is incorrect.

Conclusion

The conclusion that Quantity B is greater than Quantity A is supported by the analysis of the relationships described. All other options fail because they either misinterpret the relationship or lack sufficient evidence to support their claims. Thus, the analysis confirms that \(y + 90\) exceeds \(z\).

The rate of erosion per unit surface area is greater in the Huang's basin than in the Ganges'.

If the Huang's drainage basin covers a smaller surface area than the Ganges', then the amount of sediment it carries annually would indicate a higher rate of erosion per unit area compared to the Ganges, supporting the conclusion drawn.

A) Certain soil-conservation measures successful in the Huang basin have never been tried in the Ganges basin.

This option does not provide relevant information regarding the surface area of the drainage basins or their respective sediment transport. While it might suggest differences in management practices, it does not directly support the conclusion about erosion rates per unit area.

B) Many farming practices improve short-term productivity but increase erosion.

While this statement might imply factors that contribute to erosion, it does not address the comparative sizes of the Huang and Ganges basins. Thus, it fails to provide the necessary context needed to validate the conclusion regarding erosion rates per unit surface area.

C) More logging has recently been done along the Huang.

This choice suggests a potential increase in erosion due to logging activities, but it does not clarify the relationship between the sizes of the basins or provide a basis for comparing erosion rates per unit surface area. Therefore, it does not support the conclusion effectively.

D) The Huang's drainage basin covers a smaller surface area than the Ganges'.

This fact directly supports the conclusion. If the Huang has a smaller drainage area but carries more sediment, it logically follows that the erosion rate per unit area must be greater than that of the Ganges, thus validating the conclusion.

Conclusion

The correct answer is D, as it provides the necessary context to understand the relationship between the sediment carried by the rivers and the surface area of their respective drainage basins. Options A, B, and C lack the pertinent information needed to substantiate the conclusion regarding erosion rates, making them insufficient in this context.

Yingyang was receptive to arguments from a health perspective.

Yingyang acknowledged various ailments associated with meat consumption, indicating that he was open to considering health-related arguments for vegetarianism.

A) wary of

This option suggests a cautious or distrustful attitude, which does not align with Yingyang's openness to health arguments. He did not reject these arguments outright but rather acknowledged them, showing a willingness to engage with the perspective.

B) circumspect about

Being circumspect implies a careful or hesitant approach. While Yingyang may have been thoughtful in his consideration, the term does not accurately capture his receptiveness to health-related arguments, which indicates a more open stance.

C) receptive to

This choice accurately describes Yingyang's attitude towards health arguments related to vegetarianism. He was willing to listen to and consider the implications of meat consumption on health, showing an openness to integrate these ideas into his advocacy for vegetarianism.

D) disconcerted by

If Yingyang were disconcerted by health arguments, it would suggest that they caused him confusion or anxiety, which contradicts the notion that he acknowledged these arguments. He was not troubled by them but rather engaged with them.

E) ardent about

Being ardent implies a passionate or intense commitment, which does not reflect Yingyang's approach to health arguments. He recognized their validity but did not express fervent support for them in the same way he did for traditional and scriptural justifications.

F) amenable to

While "amenable" suggests a willingness to agree or be influenced, it lacks the explicit connotation of receptiveness that "receptive to" conveys. Yingyang's engagement with health arguments was more active and open than merely being agreeable.

Conclusion

Yingyang's receptiveness to health arguments highlights his comprehensive approach to advocating vegetarianism, considering both traditional beliefs and modern health perspectives. Other options either misrepresent his attitude or suggest a level of disengagement that does not align with his acknowledgment of health-related issues associated with meat consumption.

The charity must raise $65,000 total.

To achieve a total of $65,000, the charity must take into account the matching contributions from the company. The company contributes $3 for every $1 raised up to $9,000, and then $1 for every $1 raised thereafter.

A) $38

Raising $38 would yield a company contribution of $9,000 (the maximum it can match) plus the $38 raised by the charity, totaling $9,038. This is significantly below the target of $65,000, making this option incorrect.

B) $40

Raising $40 would again result in $9,000 from the company and $40 from the charity, totaling $9,040. This amount is still far from the target of $65,000, indicating that this option is also incorrect.

C) $42

If the charity raises $42, it would receive $9,000 from the company, bringing the total to $9,042. This is still not close to the required amount of $65,000, confirming this option is incorrect.

D) $49

Raising $49 would yield the maximum company contribution of $9,000, resulting in a total of $9,049. This amount is still far from the target of $65,000, thus this option is incorrect as well.

E) [No Option]

[No explanation needed as there is no content for this option.]

F) [No Option]

[No explanation needed as there is no content for this option.]

G) [No Option]

[No explanation needed as there is no content for this option.]

Conclusion

None of the provided options A, B, C, D, or G adequately address the amount the charity needs to raise to reach the target of $65,000. All calculations show that the charity's fundraising must significantly exceed $40 to meet the goal, which none of the options achieve.

There are 20 people in front of Ellie in the line.

To determine the number of people in front of Ellie, we can analyze their positions in line. If there are 12 people behind James, and there are 4 people between James and Ellie, then Ellie is positioned after James in the line.

A) 16

Option A is incorrect because if there were 16 people in front of Ellie, that would imply that Ellie is the 17th person in line. Given the positions, this does not account for the correct number of individuals behind James and between him and Ellie.

B) 20

Option B is correct. If there are 12 people behind James and 4 people between James and Ellie, then James is the 8th person in line (since 12 behind him means he's 13th from the end). Thus, Ellie, being 4 places behind James, is the 12th person in line. Consequently, there are 20 people in front of her (32 total - 12 = 20).

C) 22

Option C is incorrect because if there were 22 people in front of Ellie, she would need to be the 23rd person in line. However, with the established gaps and total number of people, this positioning does not match the context provided.

D) 23

Option D is incorrect as it suggests that there are 23 people in front of Ellie, which would place her as the 24th person in line. This contradicts the established positions of James and the number of individuals behind him.

E) 24

Option E is incorrect. If there were 24 people in front of Ellie, she would be the 25th person in line. However, the calculations show that based on James's position and the total number of individuals, Ellie cannot occupy this position.

Conclusion

The analysis shows that Option B is definitively correct with 20 people in front of Ellie, accurately reflecting the distribution based on James's placement and the individuals behind him. All other options fail to account for the established positions and logical deductions based on the scenario provided.

The relationship cannot be determined from the information given.

Without additional information about the dimensions of triangle ABC or the radius of the circle, it is impossible to definitively compare the areas of the triangle and the circular region.

A) Quantity A is greater.

This option asserts that five times the area of triangle ABC exceeds the area of the circular region. However, without knowing the specific dimensions or angles of triangle ABC, it is impossible to calculate its area in relation to the circle's area.

B) Quantity B is greater.

This option claims that the area of the circular region is larger than five times the area of triangle ABC. Similar to option A, without specific measurements or ratios, we cannot determine if the circle's area surpasses that of the triangle multiplied by five.

C) The two quantities are equal.

This option suggests that five times the area of triangle ABC is equal to the area of the circular region. Again, without specific values for the triangle's area or the circle's radius, this equality cannot be established.

D) The relationship cannot be determined from the information given.

This option acknowledges the lack of sufficient information to make a definitive comparison between the two quantities. Without knowing dimensions or relationships between the triangle and the circle, determining the relationship is indeed impossible.

Conclusion

The correct answer is that the relationship cannot be determined due to insufficient information about the dimensions of triangle ABC and the circle. All other options make assumptions about the areas without concrete data, making them invalid. The core concept revolves around the inability to compare areas without relevant measurements.

The relationship cannot be determined from the information given.

The relationship between the area of triangle ABC and the area of the circle cannot be conclusively determined with the information provided. Factors such as the size of the triangle and the radius of the circle are not specified, making it impossible to compare the two quantities directly.

A) Quantity A is greater.

This option suggests that the area of triangle ABC multiplied by five exceeds the area of the circle. Without knowing specific dimensions of the triangle or the circle, we cannot assert that this is true, as the triangle could be small relative to the circle.

B) Quantity B is greater.

This option posits that the area of the circular region is larger than five times the area of triangle ABC. Similar to Option A, this cannot be determined without specific measurements, as the triangle could be large enough to make Quantity A greater.

C) The two quantities are equal.

This option claims that five times the area of triangle ABC is equal to the area of the circle. However, without any numerical values or ratios, there is no basis to establish equality between the two areas.

D) The relationship cannot be determined from the information given.

This option correctly identifies that the necessary information to compare the two quantities is lacking. The areas depend on the dimensions of triangle ABC and the radius of the circle, which are not provided.

Conclusion

The correct answer is D, as the lack of specific information about the sizes of triangle ABC and the circle prevents any definitive comparison between the two areas. Options A, B, and C all make assumptions that cannot be validated without additional data. Thus, the relationship between Quantity A and Quantity B remains indeterminate.

The area of the rectangular region is approximately 300 percent of the area of the circular region.

The relationship between the areas indicates that the area of the rectangular region is significantly larger compared to the area of the circular region, specifically around 300 percent.

A) 33%

This option is incorrect as it underestimates the area of the rectangular region relative to the circular region. Since the shaded region is considerably larger, the ratio cannot be as low as 33%.

B) 75%

This choice also fails to accurately reflect the size of the rectangular region in relation to the circular region. A percentage of 75% suggests a closer proximity in size, which is not supported by the given information.

C) 100%

While this option suggests that the areas are equal, it does not account for the stated relationship where the area of the rectangular region is much larger than that of the circular region. Therefore, this option is incorrect.

D) 150%

Although this option implies that the rectangular region is larger than the circular region, it still falls short of the actual percentage. The difference in area is more substantial than 150%, making this choice incorrect.

E) 300%

This option is correct as it accurately represents the substantial difference in area between the rectangular and circular regions. Given that the area of the circular region is only about 50 percent of the shaded region, and the rectangular region is larger, 300 percent is the most reasonable estimate.

Conclusion

The correct answer, 300%, reflects the significant size difference between the rectangular and circular regions. All other options underestimate the area of the rectangular region, failing to recognize the true proportional relationship established in the question. Thus, option E is the only accurate choice based on the context provided.