The following information about student enrollment in a certain small college.
DISTRIBUTION OF ENROLLMENT
BY CLASS AND SEX
(Total enrollment: 1,400)
PERCENT OF TOTAL ENROLLMENT MAJORING IN EACH OF THE FOLLOWING ACADEMIC AREAS
(No student is majoring in more than one area.)
The ratio of the number of male freshmen to the number of female sophomores is approximately
Show Hint
- 2 to 1
- 3 to 1
- 3 to 2
- 4 to 1
- 5 to 3
The Correct Option is B
Solution and Explanation
This question asks for an approximate ratio between two values found in the "DISTRIBUTION OF ENROLLMENT" table.
Step 2: Detailed Explanation:
1. Find the required values from the table. - Number of male freshmen: Look at the row for "Freshmen" and the column for "Males". The value is 303. - Number of female sophomores: Look at the row for "Sophomores" and the column for "Females". The value is 109.
2. Form the ratio and approximate. - The ratio is 303 to 109, or \(\frac{303}{109}\). - To approximate this, we can round the numbers. 303 is very close to 300, and 109 is very close to 100. - The ratio is approximately \(\frac{300}{100} = 3\). - This corresponds to a ratio of 3 to 1. - For a more precise check, \(303 \div 109 \approx 2.78\). This value is much closer to 3 than to 2, 1.5, 4, or 1.67.
Step 3: Final Answer:
The ratio is approximately 3 to 1.
How many of the enrolled students are not majoring in humanities, social sciences, or physical sciences?
Show Hint
- 87
- 122
- 182
- 230
- 322
The Correct Option is C
Solution and Explanation
This question requires us to use the second table ("PERCENT OF TOTAL ENROLLMENT") to find the number of students who fall outside the listed categories. These could be students with undeclared majors or majors in other fields not listed.
Step 2: Detailed Explanation:
1. Find the total percentage of students in the listed majors. - Humanities: 33% - Social Sciences: 30% - Physical Sciences: 24% - Total percentage in these majors = \(33% + 30% + 24% = 87%\).
2. Find the percentage of students NOT in these majors. - The total of all students is 100%. - Percentage not in these majors = \(100% - 87% = 13%\).
3. Calculate the number of students corresponding to this percentage. - The total enrollment is given as 1,400 students. - Number of students not in these majors = 13% of 1,400. \[ 0.13 \times 1400 = 13 \times \frac{1400}{100} = 13 \times 14 \] \[ 13 \times 14 = 13 \times (10 + 4) = 130 + 52 = 182 \] Step 3: Final Answer:
There are 182 students who are not majoring in one of the three listed academic areas.
Which of the following can be inferred from the tables?
I. The number of males majoring in physical sciences is greater than the number of females majoring in that area.
II. Students majoring in either social sciences or physical sciences constitute more than 50 percent of the total enrollment.
III. The ratio of the number of males to the number of females in the senior class is less than 2 to 1.
I. The number of males majoring in physical sciences is greater than the number of females majoring in that area.
II. Students majoring in either social sciences or physical sciences constitute more than 50 percent of the total enrollment.
III. The ratio of the number of males to the number of females in the senior class is less than 2 to 1.
Show Hint
- I only
- II only
- I and II
- I and III
- II and III
The Correct Option is
Solution and Explanation
This is an inference question. We must evaluate each statement to see if it can be proven true using only the data provided in the two tables.
Step 2: Detailed Explanation:
Statement I: The number of males majoring in physical sciences is greater than the number of females majoring in that area.
- Total physical science majors = 24% of 1400 = \(0.24 \times 1400 = 336\) students. - Total males = 860; Total females = 540. - The tables do not provide a breakdown of majors by sex. We cannot determine how the 336 physical science majors are split between males and females. It's possible that all 336 are male, or that all 336 are female (since 336 \textless 540). Since we cannot prove it, the statement cannot be inferred. - Therefore, Statement I is not necessarily true.
Statement II: Students majoring in either social sciences or physical sciences constitute more than 50 percent of the total enrollment.
- Percentage of social science majors = 30%. - Percentage of physical science majors = 24%. - Total percentage = \(30% + 24% = 54%\). - Since \(54% \textgreater 50%\), this statement is true. - Therefore, Statement II can be inferred.
Statement III: The ratio of the number of males to the number of females in the senior class is less than 2 to 1.
- From the first table, number of senior males = 160. - From the first table, number of senior females = 84. - The ratio is \(\frac{160}{84}\). - A ratio of 2 to 1 is equivalent to \(\frac{2}{1}\). - To compare, we can check if \(\frac{160}{84} \textless 2\). Multiplying by 84 gives \(160 \textless 2 \times 84\), which is \(160 \textless 168\). This is true. - Therefore, Statement III can be inferred.
Step 3: Final Answer:
Statements II and III can be inferred from the tables, but Statement I cannot. The correct option is (E).
How many students are either juniors or males or both?
Show Hint
- 678
- 766
- 948
- 1,130
- 1,312
The Correct Option is C
Solution and Explanation
This question asks for the total number of individuals in the union of two sets: the set of juniors and the set of males. We must be careful not to double-count the individuals who are in both sets (male juniors).
Step 2: Key Formula or Approach:
The principle of inclusion-exclusion for two sets states: \[ |A \cup B| = |A| + |B| - |A \cap B| \] Here, Set A = Juniors, and Set B = Males. Alternatively, we can add the total number of males to the number of juniors who are not male (i.e., female juniors).
Step 3: Detailed Explanation:
Method 1: Using Inclusion-Exclusion
1. Find the total number of juniors. - From the table: Male Juniors = 182, Female Juniors = 88. - Total Juniors = \(182 + 88 = 270\).
2. Find the total number of males. - From the table's total row: Total Males = 860.
3. Find the number of students who are both male and junior (the intersection). - From the table: Male Juniors = 182.
4. Apply the formula. - Number of (Juniors or Males) = (Total Juniors) + (Total Males) - (Male Juniors) - Number = \(270 + 860 - 182\) - Number = \(1130 - 182 = 948\)
Method 2: Direct Addition
The group "juniors or males" consists of two distinct groups: (1) all males, and (2) all juniors who are not male (i.e., female juniors).
Total number of males (this includes all male freshmen, sophomores, juniors, and seniors): 860
Number of female juniors: 88
Total = \(860 + 88 = 948\)
Step 4: Final Answer:
There are 948 students who are either juniors or males or both.
If the total enrollment is 12 percent greater than it was five years ago, what was the total enrollment five years ago?
Show Hint
- 1,180
- 1,192
- 1,220
- 1,232
- 1,250
The Correct Option is
Solution and Explanation
This is a reverse percentage problem. We are given the final value after a percentage increase (the current enrollment) and asked to find the original value (the enrollment five years ago).
Step 2: Key Formula or Approach:
Let \(E_0\) be the enrollment five years ago (the original value). The current enrollment, \(E_c\), is 12% greater. The relationship can be expressed with the formula: \[ E_c = E_0 + (0.12 \times E_0) = E_0 \times (1 + 0.12) = 1.12 \times E_0 \] To find the original enrollment, we rearrange the formula: \(E_0 = E_c / 1.12\).
Step 3: Detailed Explanation:
1. Identify the given values. - The current enrollment, \(E_c\), is 1,400 (from the information provided for the data interpretation questions). - The percentage increase is 12%, or 0.12.
2. Set up the equation. - Using the formula, we have: \(1400 = 1.12 \times E_0\).
3. Solve for the original enrollment, \(E_0\). - To isolate \(E_0\), we divide both sides by 1.12. \[ E_0 = \frac{1400}{1.12} \] - To make the division easier, remove the decimal by multiplying the numerator and denominator by 100: \[ E_0 = \frac{140000}{112} \] - Simplify the fraction. We can see both are divisible by 14: \(112 = 14 \times 8\) and \(140000 = 14 \times 10000\). \[ E_0 = \frac{10000}{8} \] - Perform the final division: \[ E_0 = 1250 \] Step 4: Final Answer:
The total enrollment five years ago was 1,250.
If the ratio of the number of English books to the number of all other books on a bookshelf is 4 to 1, what percent of the books on the bookshelf are English books?
Show Hint
- 20%
- 25%
- 50%
- 75%
- 80%
The Correct Option is
Solution and Explanation
This question requires converting a part-to-part ratio into a part-to-whole fraction, and then expressing that fraction as a percentage.
Step 2: Detailed Explanation:
1. Understand the ratio. - The ratio of (English books) to (all other books) is 4 to 1. - This is a part-to-part ratio. It means for every 4 English books, there is 1 non-English book.
2. Calculate the 'whole'. - To find the percentage of English books, we need to know what fraction they represent of the total. - We can think in terms of "ratio units". Total ratio units = (units for English books) + (units for other books) = \(4 + 1 = 5\).
3. Form the part-to-whole fraction. - Out of a total of 5 "ratio units", 4 belong to English books. - The fraction of books that are English is \(\frac{\text{Part}}{\text{Whole}} = \frac{4}{5}\).
4. Convert the fraction to a percentage. - To convert a fraction to a percentage, we multiply by 100%. \[ \text{Percentage} = \frac{4}{5} \times 100% = 0.8 \times 100% = 80% \] Step 3: Final Answer:
80 percent of the books on the bookshelf are English books.
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Questions Asked in GRE exam
In early-twentieth-century England, it was fashionable to claim that only a completely new style of writing could address a world undergoing unprecedented transformation — just as one literary critic recently claimed that only the new ”aesthetic of exploratory excess” can address a world undergoing . . . well, you know. Yet in early-twentieth-century England, T. S. Eliot, a man fascinated by the ”presence” of the past, wrote the most innovative poetry of his time. The lesson for today’s literary community seems obvious: a reorientation toward tradition would benefit writers no less than readers. But if our writers and critics indeed respect the novel’s rich tradition (as they claim to), then why do they disdain the urge to tell an exciting story?
- GRE - 2024
- Reading Comprehension
In the 1970’s, two debates engaged many scholars of early United States history. One focused on the status of women, primarily White women. Turning on the so-called golden age the ory, which posited that during the eighteenth-century colonial era, American women enjoyed a brief period of high status relative to their English contemporaries and to nineteenth-century American women, this debate pitted scholars who believed women’s lives deteriorated after 1800 against those who thought women’s lives had been no better before 1800. At issue were the causes of women’s subordination: were these causes already in place when the English first settled North America or did they emerge with the rise of nineteenth-century industrial capital ism? The second debate, the so-called origins debate, concerned the emergence of racial slavery in the southern colonies: was slavery the inevitable result of the deep-rooted racial prejudice of early British colonists or did racial prejudice arise only after these planters instituted slave labor?
Although these debates are parallel in some respects, key differences distinguished them. Whereas the debate over women’s status revolved around implicit comparisons of colonial women to their counterparts in the antebellum period (1800-1860), thus inviting comment from scholars of both historical periods, the origins debate was primarily confined to a discussion about slavery in colonial America. Second, in contrast to the newness of the debate over women’s status and its continued currency throughout the early 1980’s, the debate over race and slavery, begun in the 1950’s, had lost some of its urgency with the publication of Morgan’s American Slavery, American Freedom (1975), widely regarded as the last word on the subject. Each debate also assumed a different relationship to the groups whose histories it concerned. In its heyday, the origins debate focused mainly on White attitudes toward Africans rather than on Africans themselves. With few exceptions, such as Wood’s Black Majority (1974) and Mullin’s Flight and Rebellion (1972), which were centrally concerned with enslaved African men, most works pertaining to the origins debate focused on the White architects, mostly male, of racial slavery. In contrast, although women’s historians were interested in the institutions and ide ologies contributing to women’s subordination, they were equally concerned with documenting women’s experiences. As in the origins debate, however, early scholarship on colonial women defined its historical constituency narrowly, women’s historians focusing mainly on affluent White women.
Over time, however, some initial differences between the approaches taken by scholars in the two fields faded. In the 1980’s, historians of race and slavery in colonial America shifted their attention to enslaved people; interest in African American culture grew, thereby bringing en slaved women more prominently into view. Historians of early American women moved in similar directions during the decade and began to consider the effect of racial difference on women’s experience.- GRE - 2024
- Reading Comprehension
The most plausible justification for higher taxes on automobile fuel is that fuel consumption harms the environment and thus adds to the costs of traffic congestion. But the fact that burning fuel creates these ”negative externalities” does not imply that no tax on fuel could ever be too high. Economics is precise about the tax that should, in principle, be levied to deal with negative externalities: the tax on a liter of fuel should be equal to the harm caused by using a liter of fuel. If the tax is more than that, its costs (including the inconvenience to those who would rather have used their cars) will exceed its benefits (including any reduction in congestion and pollution).
- GRE - 2024
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- GRE - 2024
- Reading Comprehension
Music critics have consistently defined James P. Johnson as a great early jazz pianist, originator of the 1920’s Harlem ”stride” style, and an important blues and jazz composer. In addition, however, Johnson was an innovator in classical music, composing symphonic music that incor porated American, and especially African American, traditions.
Such a blend of musical elements was not entirely new: by 1924 both Milhaud and Gershwin had composed classical works that incorporated elements of jazz. Johnson, a serious musician more experienced than most classical composers with jazz, blues, spirituals, and popular music, was particularly suited to expand Milhaud’s and Gershwin’s experiments. In 1927 he completed his first large-scale work, the blues- and jazz-inspired Yamekraw, which included borrowings from spirituals and Johnson’s own popular songs. Yamekraw, premiered successfully in Carnegie Hall, was a major achievement for Johnson, becoming his most frequently performed extended work. It demonstrated vividly the possibility of assimilating contemporary popular music into the symphonic tradition.- GRE - 2024
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