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Efficient quick tests to boost your GRE score
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Updated on: 05 Jun 2026, 12:38
Updated on: 05 Jun 2026, 12:38
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Efficient, quick tests to boost your GRE score
GRE Prep Club – Mini Test Series
Introduction:
Welcome to the GRE Prep Club Mini Test Series, an innovative and streamlined practice platform designed for busy students. This new project offers a series of condensed, high-impact practice sessions tailored to the specific demands of the GRE General Test.
Traditional practice tests are essential, but often require significant, uninterrupted blocks of time. This Mini Test Series addresses this challenge by providing a nimble, modular approach. It allows you to fit effective GRE prep into any window in your schedule—whether it’s twenty minutes on your commute, during a lunch break, or between lectures.
Efficiency and Balance
The Mini Test Series is built on the principle that consistent, focused effort leads to dramatic score improvements.
By distilling the full exam experience into shorter, adaptive segments, we help you avoid fatigue and maintain peak concentration. Each mini-test is carefully balanced, encompassing both core measures of the GRE General Test:
- Quantitative Reasoning: Practice essential problem-solving skills, interpretation of data, and the application of arithmetic, algebra, geometry, and data analysis. Our on-screen calculator interface and geometric visualization tools are designed to simulate the official testing environment.
- Verbal Reasoning: Sharpen your critical thinking, text completion, sentence equivalence, and reading comprehension abilities. Analyze complex discourse, evaluate arguments, and strengthen your vocabulary contextually.
Our Vision
The GRE Prep Club Mini Test Series is your flexible partner on the path to graduate school. Our mission is to provide you with a powerful tool that transforms fragmented moments into a comprehensive, balanced study regimen.
Don't wait for the 'perfect' study block. Use every moment. Start Your Mini Test Now!
Thanks to GeminiHeat for the precious collaboration.
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Efficient quick tests to boost your GRE score
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Updated on: 10 Jul 2026, 11:55
Updated on: 10 Jul 2026, 11:55
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Mini Test #2
Quantitative
Question #1
GRE In the figure, P R is.png [ 58.56 KiB | Viewed 2993 times ]
In the figure, PQ is the diameter of a semicircle with center O and radius 6. Point R lies on the semicircular arc such that the length of arc PR is twice the length of arc RQ. Point S lies on arc PR such that the measure of central angle ∠POS = 80°.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Question #2
The sum of the measures of the interior angles of a heptagon is \(p\) degrees. The sum of the measures of the interior angles of a nonagon is \(q\) degrees.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Question #3
Let \(n\) be a positive even integer.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Question #4
\(y^2-6 y+8<0 \)
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Question #5
A hospital records 120 patients, each tested for three conditions: hypertension, diabetes, and anemia. The total number of positive test results across all patients and conditions is 175. No patient tested positive for all three conditions.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
\(\begin{aligned}
&\text { Answer: Quantity A is greater. }\\
&n_1+n_2=120, n_1+2 n_2=175, n_3=0 \rightarrow n_2=55 \rightarrow \text { Quantity } \mathrm{A}=\mathbf{5 5}>50 .
\end{aligned}\)
Question #6
In a bakery, three ingredients - flour, sugar, and butter - are used in a recipe.
- The weight of flour is \(\frac{2}{3}\) kilogram.
- The weight of sugar is \(\frac{4}{5}\) kilogram.
- The ratio of flour to sugar is the same as the ratio of butter to a fourth ingredient, vanilla.
- The weight of butter is \(\frac{8}{15}\) kilogram.
What is the weight of vanilla, in kilograms?
Give your answer as a fraction.
Question #7
A quadratic function is defined by \(g(z)=z^2-4 z+3\) for all real numbers z.
What is the median of all possible values of g(z) where z is an integer and \(4 \leq z \leq 12\) ?
A. 15
B. 24
C. 35
D. 48
E. 63
Question #8
A sphere has a ratio of volume to surface area equal to \(\frac{5}{2}\).
(Note: Surface area \(=4 \pi r^2\), Volume \(=\frac{4}{3} \pi r^3\) )
What is the radius of the sphere?
A. \(\frac{5}{6}\)
B. \(\frac{3}{2}\)
C. \(\frac{5}{2}\)
D. \(\frac{15}{4}\)
E. \(\frac{15}{2}\)
Question #9
A researcher tracks the intensity of a radio signal over 8 time intervals.
At interval 0, the intensity is S watts.
- At the end of each odd-numbered interval (1st, 3rd, 5th, 7th), the intensity decreases by 20%.
- At the end of each even-numbered interval (2nd, 4th, 6th, 8th), the intensity increases by 20 %.
- Exception: At the end of interval 8 , the intensity increases by an additional \(\mathbf{1 0} \boldsymbol{\%}\) on top of the usual 20 % increase.
Which of the following represents the intensity, in watts, at the end of interval 8?
A. \(\left(0.96^3\right)(1.32) S\)
B. \(\left(0.96^4\right) S\)
C. \(\left(0.96^3\right)(1.056) S\)
D. \((0.8)(1.1)\left(0.96^3\right) S\)
E. \(\left(0.96^4\right)(1.1) S\)
Question #10
A patient has Q milligrams of a medication in the bloodstream. Beginning at 9:00 AM, the medication is administered at a constant rate of r milligrams per minute and eliminated at a constant rate of s milligrams per minute. If r<s, after how many minutes will the amount of medication in the bloodstream be \(\frac{5}{8} Q\) milligrams?
A. \(\frac{Q}{8(s-r)}\)
B. \(\frac{Q}{4(s-r)}\)
C. \(\frac{3 Q}{8(s-r)}\)
D. \(\frac{5 Q}{8(s-r)}\)
E. \(\frac{Q}{s-r}\)
Question #11
For all integers p and q, the operation \(\bigstar\) is defined as:
- \(p \bigstar q=p+q\) if \(p q\) is a multiple of 5 .
- \(p \bigstar q=p-q\) if \(p q\) is even and not a multiple of 5 .
- \(p \bigstar q=-(p+q)\) if \(p q\) is odd and not a multiple of 5 .
What is the value of \((6 \bigstar 4) \bigstar(3 \bigstar 5)\) ?
A. -18
B. -6
C. 6
D. 18
E. 22
Question #12
Let \(R=(7,234)^3 \times(1,987)^4+(5,619)^5\). What is the units digit of R ?
A. 1
B. 2
C. 3
D. 7
E. 9
Question #13
In the x y -plane, the points (1,3) and (5,-5) lie on line L . Which of the following points also lie on line L ?
Indicate all such points.
A. (-3,11)
B. (0,5)
C. (2,1)
D. (4,-3)
E. (6,-6)
Question #14
A landscape architect is designing a straight walkway divided into 4 sequential rectangular plots. Each plot will be planted with one of 6 available varieties of flowers. The architect may repeat flower varieties, but no two adjacent plots can contain the same variety. How many unique walkway designs are possible?
A. 150
B. 360
C. 480
D. 750
E. 1296
Question #15
GRE box plot.png [ 91.92 KiB | Viewed 2956 times ]
The box plots above summarize customer satisfaction ratings for two services. Each rating is an integer from 1 to 10.
Service A five-number summary: \(\operatorname{Min}=2, \mathrm{Q} 1=4\), \(\operatorname{Median}= 6, Q3 = 8\),\( \operatorname{Max}=10\)
Service B five-number summary: \(\operatorname{Min}=3, \mathrm{Q} 1=5, \operatorname{Median}=7, \mathrm{Q} 3=9, \operatorname{Max}=10\)
Which of the following statements must be true?
Indicate all such statements.
- A. The interquartile range for Service A is equal to the interquartile range for Service B.
- B. More than 50 % of the ratings for Service A are less than 6 .
- C. Service B received more ratings of 10 than Service A did.
- D. At least 25 % of the ratings for Service B are greater than or equal to 9 .
---------------------------------------------------------------------------------------------
Verbal
Question #1
To hear that the novelist’s latest work radiates such an unflaggingly __________ mood is a genuine surprise to readers accustomed to her barbed essays and relentless mockery of social pretension."
Question #2
The envoy's refusal to address the assembly in straightforward terms sorely taxed the delegates' forbearance, as his remarks grew ever more ________ with each passing hour.
Question #3
That the snow leopard has persistently eluded systematic field observation is hardly surprising, given that the near-inaccessibility of its high-altitude terrain and its notoriously elusive nature have together (i) ________ any rigorous attempt at study outside the (ii) ________ confines of zoological institutions.
Question #4
Why, ask a growing number of geophysicists, should the puzzling luminous displays occasionally reported above active fault lines be ascribed to esoteric tectonic mechanisms, when the far more (i) ________ account - one that the field's mainstream finds considerably more (ii) ________ — points to such (iii) ________ sources as pockets of escaping gas ignited by friction, or the piezoelectric discharge of stressed quartz?
Question #5/6
Question #7/8/9
Which of the following most accurately captures the overall concern of the passage?
A. Enumerating the obstacles that prevent scholars from locating evidentiary materials pertinent to women's historical lives
B. Tracing the genesis and proliferation of a specific historical mythology during the middle decades of the nineteenth century
C. Delineating a spectrum of scholarly postures toward the evidentiary value of a particular category of sources for investigating a given era
D. Chronicling the efforts undertaken by an individual researcher to recover the meaning embedded in a specific set of handcrafted artifacts
E. Recounting a dispute among academic practitioners regarding the lived experience of a particular demographic during a circumscribed historical interval
According to the passage, which of the following constitutes an impediment for scholars seeking to draw inferences from the ceremonial masks discussed in the passage?
A. The relative scarcity of such masks when set against the abundance of other surviving ritual artifacts from the same period
B. An insufficiently developed scholarly understanding of the mask-carving workshop system that produced these ritual objects
C. A lack of consensus among researchers concerning the reasons that such masks became objects of particular fascination during the nineteenth century
D. A framework of interpretation imposed upon these masks during the nineteenth century
E. A deficiency of written documentation that could contextualize and elucidate such masks
With respect to the "colonial antiquarianism" identified in the passage, it can be inferred that Kamara would most likely part company with the majority of scholars over
A. the degree to which this antiquarianism obstructs the effort to deploy certain artifacts as vehicles for historical understanding
B. the degree to which this antiquarianism developed as a reaction to conditions set in motion by European industrialization
C. whether this antiquarianism inadvertently preserves traces of the original significance of the ritual masks dating from the medieval period
D. whether this antiquarianism achieved particularly broad cultural currency during the nineteenth century
E. whether this antiquarianism served to adequately rationalize the political project of colonial administration
Question #10
Because direct observation of the Yellowstone magma chamber is impossible, scientists have __________ its presence from patterns of ground deformation and hydrothermal activity at the surface.
Question #11
Given how outlandish their plots and how remote their settings from present-day concerns, the remarkable ________ of the ancient Greek tragedies in the modern repertory strikes many observers as deeply perplexing.
Question #12
The director's public image as a vacillating and ineffectual leader is, by all accounts from those who have served under her, utterly ________: colleagues describe a decisive, analytically rigorous, and unyielding figure behind closed doors.
Question #13
The argument depends on which of the following being true?
A. Water lost to residential leakage represents a larger share of the municipal authority's total potable water deliveries now than it did four years ago.
B. The average volume of water lost per leaking household in Trevania has not risen markedly over the past four years.
C. Total potable water deliveries account for a larger proportion of the city's overall water output now than they did four years ago.
D. Trevania's total annual water output is not substantially smaller now than it was four years ago.
E. Plumbing deterioration severe enough to cause significant leakage typically progresses even after a household has taken advantage of the subsidy program.
Question #14/15
The passage indicates that the deployment of high-relief artificial reefs in areas where they never historically occurred requires ongoing institutional management. What is the reason offered for this necessity?
A. Such installations are prone to becoming economically unfeasible when evaluated over sufficiently long time spans.
B. Mariculture production entails a degree of technical intricacy that can only be sustained through vigilant supervision.
C. The pursuit of intensive mariculture is fundamentally at odds with the preservation of maximal benthic biodiversity.
D. The hydrodynamic changes induced by these structures can open pathways for organisms that disrupt benthic community stability.
E. Introducing artificial reefs into regions where they are no longer present constitutes an intrinsically undesirable ecological intervention.
In the passage, the word “intensive” as it appears in the phrase “intensive mariculture output” most nearly means
A. severe
B. rigorous
C. concentrated
D. scrupulous
E. resolute
Quantitative
Question #1
Attachment:
GRE In the figure, P R is.png [ 58.56 KiB | Viewed 2993 times ]
In the figure, PQ is the diameter of a semicircle with center O and radius 6. Point R lies on the semicircular arc such that the length of arc PR is twice the length of arc RQ. Point S lies on arc PR such that the measure of central angle ∠POS = 80°.
Quantity A |
Quantity B |
The length of arc RS |
The length of arc SQ minus \(2 \pi\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Show: ::
Step 1: Find the total arc length of the semicircle.
A full circle with radius 6 has circumference $2 \pi(6)=12 \pi$, so the semicircular $\operatorname{arc} \mathrm{PQ}$ has length $6 \pi$. In degrees, this entire arc spans $180^{\circ}$.
Step 2: Use the $\mathbf{P R} / \mathbf{R Q}$ relationship to split that arc.
Since $\operatorname{arc} \mathrm{PR}=2 \times \operatorname{arc} \mathrm{RQ}$, and $\operatorname{arc} \mathrm{PR}+\operatorname{arc} \mathrm{RQ}=6 \pi$, you get $\operatorname{arc} \mathrm{RQ}=2 \pi \operatorname{and} \operatorname{arc} \mathrm{PR}=4 \pi$. Converting to degrees (where $6 \pi$ corresponds to $180^{\circ}$ ), $\operatorname{arc} \mathrm{RQ}=60^{\circ}$ and $\operatorname{arc} \mathrm{PR}=120^{\circ}$. So going around the semicircle, the order is P , then $\mathrm{R}\left(120^{\circ}\right.$ later $)$, then Q (another $60^{\circ}$ later).
Step 3: Locate $S$ using the central angle.
$\angle \mathrm{POS}=80^{\circ}$ is a central angle (vertex at the actual center O ), so it directly tells you the arc measure: $\operatorname{arc} P S=80^{\circ}$. Since $S$ is specified to lie on arc $P R$, and arc $P R$ is $120^{\circ}$ total, $S$ sits $80^{\circ}$ of the way from $P$ toward $R$, leaving $120^{\circ}-80^{\circ}=40^{\circ}$ remaining between $S$ and $R$.
Step 4: Compute arc RS (Quantity A).
$\operatorname{ArcRS}=40^{\circ}$. Converting to length using the formula $($ degrees $/ 180) \times 6 \pi$ : $\operatorname{arc} \operatorname{RS}=(40 / 180) \times 6 \pi=4 \pi / 3$.
Step 5: Compute arc SQ, then Quantity B.
Arc SQ is everything left over from S to Q: $180^{\circ}$ (total) $-80^{\circ}(\operatorname{arc} P S)=100^{\circ}$. $\operatorname{arcSQ}=(100 / 180) \times 6 \pi=10 \pi / 3$.
Quantity $\mathrm{B}=\operatorname{arc} \mathrm{SQ}-2 \pi=10 \pi / 3-6 \pi / 3=4 \pi / 3$.
Step 6: Compare.
Quantity $\mathrm{A}=4 \pi / 3$ and Quantity $\mathrm{B}=4 \pi / 3$ - they're identical.
Answer: (C) The two quantities are equal.
GRE In the figure, PQ.png [ 35.19 KiB | Viewed 2067 times ]
The teal arc is the semicircle (diameter PQ, center O), the dashed lines mark the radii OR and OS, and the small amber arc near O highlights the 80° central angle ∠POS. From this you can read off the same structure used in the solution: R sits 60° from Q, S sits 80° from P along arc PR, leaving exactly 40° between R and S.
A full circle with radius 6 has circumference $2 \pi(6)=12 \pi$, so the semicircular $\operatorname{arc} \mathrm{PQ}$ has length $6 \pi$. In degrees, this entire arc spans $180^{\circ}$.
Step 2: Use the $\mathbf{P R} / \mathbf{R Q}$ relationship to split that arc.
Since $\operatorname{arc} \mathrm{PR}=2 \times \operatorname{arc} \mathrm{RQ}$, and $\operatorname{arc} \mathrm{PR}+\operatorname{arc} \mathrm{RQ}=6 \pi$, you get $\operatorname{arc} \mathrm{RQ}=2 \pi \operatorname{and} \operatorname{arc} \mathrm{PR}=4 \pi$. Converting to degrees (where $6 \pi$ corresponds to $180^{\circ}$ ), $\operatorname{arc} \mathrm{RQ}=60^{\circ}$ and $\operatorname{arc} \mathrm{PR}=120^{\circ}$. So going around the semicircle, the order is P , then $\mathrm{R}\left(120^{\circ}\right.$ later $)$, then Q (another $60^{\circ}$ later).
Step 3: Locate $S$ using the central angle.
$\angle \mathrm{POS}=80^{\circ}$ is a central angle (vertex at the actual center O ), so it directly tells you the arc measure: $\operatorname{arc} P S=80^{\circ}$. Since $S$ is specified to lie on arc $P R$, and arc $P R$ is $120^{\circ}$ total, $S$ sits $80^{\circ}$ of the way from $P$ toward $R$, leaving $120^{\circ}-80^{\circ}=40^{\circ}$ remaining between $S$ and $R$.
Step 4: Compute arc RS (Quantity A).
$\operatorname{ArcRS}=40^{\circ}$. Converting to length using the formula $($ degrees $/ 180) \times 6 \pi$ : $\operatorname{arc} \operatorname{RS}=(40 / 180) \times 6 \pi=4 \pi / 3$.
Step 5: Compute arc SQ, then Quantity B.
Arc SQ is everything left over from S to Q: $180^{\circ}$ (total) $-80^{\circ}(\operatorname{arc} P S)=100^{\circ}$. $\operatorname{arcSQ}=(100 / 180) \times 6 \pi=10 \pi / 3$.
Quantity $\mathrm{B}=\operatorname{arc} \mathrm{SQ}-2 \pi=10 \pi / 3-6 \pi / 3=4 \pi / 3$.
Step 6: Compare.
Quantity $\mathrm{A}=4 \pi / 3$ and Quantity $\mathrm{B}=4 \pi / 3$ - they're identical.
Answer: (C) The two quantities are equal.
Attachment:
GRE In the figure, PQ.png [ 35.19 KiB | Viewed 2067 times ]
The teal arc is the semicircle (diameter PQ, center O), the dashed lines mark the radii OR and OS, and the small amber arc near O highlights the 80° central angle ∠POS. From this you can read off the same structure used in the solution: R sits 60° from Q, S sits 80° from P along arc PR, leaving exactly 40° between R and S.
Question #2
The sum of the measures of the interior angles of a heptagon is \(p\) degrees. The sum of the measures of the interior angles of a nonagon is \(q\) degrees.
Quantity A |
Quantity B |
\(p+180\) |
\(q-180\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Show: ::
Solution
Step 1 - Interior angle sum formula
For an \(n\)-sided polygon:
\(\text { Sum }=(n-2) \times 180\)
Step 2 - Calculate \(p\) (heptagon, \(n=7\) )
\(p=(7-2) \times 180=5 \times 180=900\)
Step 3 - Calculate \(q\) (nonagon, \(n=9\) )
\(q=(9-2) \times 180=7 \times 180=1260\)
Step 4 - Quantity A
\(p+180=900+180=1080\)
Step 5 - Quantity B
\(q-180=1260-180=1080\)
Step 6 - Compare
\(1080=1080\)
C - The two quantities are equal
Step 1 - Interior angle sum formula
For an \(n\)-sided polygon:
\(\text { Sum }=(n-2) \times 180\)
Step 2 - Calculate \(p\) (heptagon, \(n=7\) )
\(p=(7-2) \times 180=5 \times 180=900\)
Step 3 - Calculate \(q\) (nonagon, \(n=9\) )
\(q=(9-2) \times 180=7 \times 180=1260\)
Step 4 - Quantity A
\(p+180=900+180=1080\)
Step 5 - Quantity B
\(q-180=1260-180=1080\)
Step 6 - Compare
\(1080=1080\)
C - The two quantities are equal
Question #3
Let \(n\) be a positive even integer.
Quantity A |
Quantity B |
The units digit of \(n^2+2 n+1\) |
5 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Show: ::
Solution
Step 1 - Simplify the expression
\(n^2+2 n+1=(n+1)^2\)
Step 2 - Use the fact that n is even
If n is even, then n+1 is odd.
An odd number squared is odd.
So \((n+1)^2\) is odd.
Step 3 - Units digit possibilities for an odd number
Odd numbers have units digits: 1,3,5,7, or 9 .
Step 4 - Compare to Quantity B = 5
- If units digit \(=5 \rightarrow \mathrm{~A}=\mathrm{B}\)
- If units digit =1,3,7$, or 9 \(\rightarrow \mathrm{~A}<\mathrm{B}\)
Check:
\(\begin{tabular}{|l|l|}
\hline Units digit & Comparison to 5 \\
\hline 1 & \mathrm{A}<\mathrm{B} \\
\hline 3 & \mathrm{A}<\mathrm{B} \\
\hline 5 & \mathrm{A}=\mathrm{B} \\
\hline 7 & \mathrm{A}>\mathrm{B} \\
\hline 9 & A>B \\
\hline
\end{tabular}
\)
Since the units digit can be 1,3,5,7, or 9 depending on n :
- \(n=2 \rightarrow(3)^2=9 \rightarrow\) units digit 9 \(\rightarrow \mathrm{~A}>\mathrm{B}\)
- \(n=4 \rightarrow(5)^2=25 \rightarrow\) units digit 5 \(\rightarrow \mathrm{~A}=\mathrm{B}\)
- \(n=6 \rightarrow(7)^2=49 \rightarrow\) units digit 9 \(\rightarrow \mathrm{~A}>\mathrm{B}\)
- \(n=8 \rightarrow(9)^2=81 \rightarrow\) units digit 1 \(\rightarrow \mathrm{~A}<\mathrm{B}\)
Different n give different relationships.
Step 5 - Conclusion
The relationship cannot be determined from the information given.
Step 1 - Simplify the expression
\(n^2+2 n+1=(n+1)^2\)
Step 2 - Use the fact that n is even
If n is even, then n+1 is odd.
An odd number squared is odd.
So \((n+1)^2\) is odd.
Step 3 - Units digit possibilities for an odd number
Odd numbers have units digits: 1,3,5,7, or 9 .
Step 4 - Compare to Quantity B = 5
- If units digit \(=5 \rightarrow \mathrm{~A}=\mathrm{B}\)
- If units digit =1,3,7$, or 9 \(\rightarrow \mathrm{~A}<\mathrm{B}\)
Check:
\(\begin{tabular}{|l|l|}
\hline Units digit & Comparison to 5 \\
\hline 1 & \mathrm{A}<\mathrm{B} \\
\hline 3 & \mathrm{A}<\mathrm{B} \\
\hline 5 & \mathrm{A}=\mathrm{B} \\
\hline 7 & \mathrm{A}>\mathrm{B} \\
\hline 9 & A>B \\
\hline
\end{tabular}
\)
Since the units digit can be 1,3,5,7, or 9 depending on n :
- \(n=2 \rightarrow(3)^2=9 \rightarrow\) units digit 9 \(\rightarrow \mathrm{~A}>\mathrm{B}\)
- \(n=4 \rightarrow(5)^2=25 \rightarrow\) units digit 5 \(\rightarrow \mathrm{~A}=\mathrm{B}\)
- \(n=6 \rightarrow(7)^2=49 \rightarrow\) units digit 9 \(\rightarrow \mathrm{~A}>\mathrm{B}\)
- \(n=8 \rightarrow(9)^2=81 \rightarrow\) units digit 1 \(\rightarrow \mathrm{~A}<\mathrm{B}\)
Different n give different relationships.
Step 5 - Conclusion
The relationship cannot be determined from the information given.
Question #4
\(y^2-6 y+8<0 \)
Quantity A |
Quantity B |
\(y-2\) |
\(2\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Show: ::
Step 1 - Solve the inequality
\(y^2-6 y+8<0\)
Factor:
\((y-2)(y-4)<0\)
Step 2 - Determine the interval
A quadratic opening upward is negative between the roots:
\(2<y<4\)
Step 3 - Analyze Quantity A = $y-2$ within the interval
- At \(y=2.1: y-2=0.1 \rightarrow \mathrm{~A}<\mathrm{B}(2)\)
- At \(y=3: y-2=1 \rightarrow \mathrm{~A}<\mathrm{B}(2)\)
- At \(y=3.9: y-2=1.9 \rightarrow \mathrm{~A}<\mathrm{B}(2)\)
All values in \(2<y<4\) give \(0<y-2<2\), so A is always less than 2 .
That means Quantity B is always greater.
Step 4 - Test boundary values
- y approaches 2 from above: y-2 approaches \(0 \rightarrow \mathrm{~A}<\mathrm{B}\)
- y=3: \(y-2=1 \rightarrow \mathrm{~A}<\mathrm{B}\)
- y approaches 4 from below: y-2 approaches \(2 \rightarrow \mathrm{~A}<\mathrm{B}\) (since strictly less than 2 )
So indeed, for all y satisfying 2<y<4 :
\(0<y-2<2\)
Thus A is always less than 2 .
Step 5 - Conclusion
Quantity B is greater
\(y^2-6 y+8<0\)
Factor:
\((y-2)(y-4)<0\)
Step 2 - Determine the interval
A quadratic opening upward is negative between the roots:
\(2<y<4\)
Step 3 - Analyze Quantity A = $y-2$ within the interval
- At \(y=2.1: y-2=0.1 \rightarrow \mathrm{~A}<\mathrm{B}(2)\)
- At \(y=3: y-2=1 \rightarrow \mathrm{~A}<\mathrm{B}(2)\)
- At \(y=3.9: y-2=1.9 \rightarrow \mathrm{~A}<\mathrm{B}(2)\)
All values in \(2<y<4\) give \(0<y-2<2\), so A is always less than 2 .
That means Quantity B is always greater.
Step 4 - Test boundary values
- y approaches 2 from above: y-2 approaches \(0 \rightarrow \mathrm{~A}<\mathrm{B}\)
- y=3: \(y-2=1 \rightarrow \mathrm{~A}<\mathrm{B}\)
- y approaches 4 from below: y-2 approaches \(2 \rightarrow \mathrm{~A}<\mathrm{B}\) (since strictly less than 2 )
So indeed, for all y satisfying 2<y<4 :
\(0<y-2<2\)
Thus A is always less than 2 .
Step 5 - Conclusion
Quantity B is greater
Question #5
A hospital records 120 patients, each tested for three conditions: hypertension, diabetes, and anemia. The total number of positive test results across all patients and conditions is 175. No patient tested positive for all three conditions.
Quantity A |
Quantity B |
Patients with at least two positive results |
50 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Show: ::
\(\begin{aligned}
&\text { Answer: Quantity A is greater. }\\
&n_1+n_2=120, n_1+2 n_2=175, n_3=0 \rightarrow n_2=55 \rightarrow \text { Quantity } \mathrm{A}=\mathbf{5 5}>50 .
\end{aligned}\)
Question #6
In a bakery, three ingredients - flour, sugar, and butter - are used in a recipe.
- The weight of flour is \(\frac{2}{3}\) kilogram.
- The weight of sugar is \(\frac{4}{5}\) kilogram.
- The ratio of flour to sugar is the same as the ratio of butter to a fourth ingredient, vanilla.
- The weight of butter is \(\frac{8}{15}\) kilogram.
What is the weight of vanilla, in kilograms?
Give your answer as a fraction.
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We have:
\(\frac{\text { flour }}{\text { sugar }}=\frac{\text { butter }}{\text { vanilla }}\)
Let \(F=\frac{2}{3}, S=\frac{4}{5}, B=\frac{8}{15}, V=\) ?
\(\frac{F}{S}=\frac{2 / 3}{4 / 5}=\frac{2}{3} \times \frac{5}{4}=\frac{10}{12}=\frac{5}{6}\)
Set equal to \(\frac{B}{V}\) :
\(\begin{aligned}
\frac{5}{6} & =\frac{8 / 15}{V} \\
\frac{5}{6} & =\frac{8}{15} \times \frac{1}{V} \\
\frac{5}{6} & =\frac{8}{15 V}
\end{aligned}\)
Cross-multiply:
\(\begin{gathered}
5 \times 15 V=8 \times 6 \\
75 V=48 \\
V=\frac{48}{75}=\frac{16}{25} \\
\end{gathered}\)
\(\frac{\text { flour }}{\text { sugar }}=\frac{\text { butter }}{\text { vanilla }}\)
Let \(F=\frac{2}{3}, S=\frac{4}{5}, B=\frac{8}{15}, V=\) ?
\(\frac{F}{S}=\frac{2 / 3}{4 / 5}=\frac{2}{3} \times \frac{5}{4}=\frac{10}{12}=\frac{5}{6}\)
Set equal to \(\frac{B}{V}\) :
\(\begin{aligned}
\frac{5}{6} & =\frac{8 / 15}{V} \\
\frac{5}{6} & =\frac{8}{15} \times \frac{1}{V} \\
\frac{5}{6} & =\frac{8}{15 V}
\end{aligned}\)
Cross-multiply:
\(\begin{gathered}
5 \times 15 V=8 \times 6 \\
75 V=48 \\
V=\frac{48}{75}=\frac{16}{25} \\
\end{gathered}\)
Question #7
A quadratic function is defined by \(g(z)=z^2-4 z+3\) for all real numbers z.
What is the median of all possible values of g(z) where z is an integer and \(4 \leq z \leq 12\) ?
A. 15
B. 24
C. 35
D. 48
E. 63
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Step 1 - List integer values of z from 4 to 12 inclusive
\(z=4,5,6,7,8,9,10,11,12\)
Step 2 - Compute \(g(z)=z^2-4 z+3\) for each
\(\begin{aligned}
z=4: & 16-16+3=3 \\
z=5: & 25-20+3=8 \\
z=6: & 36-24+3=15 \\
z=7: & 49-28+3=24 \\
z=8: & 64-32+3=35 \\
z=9: & 81-36+3=48 \\
z=10: & 100-40+3=63 \\
z=11: & 121-44+3=80 \\
z=12: & 144-48+3=99
\end{aligned}\)
Step 3 - Ordered values
\(3,8,15,24,35,48,63,80,99\)
Step 4 - Find the median
There are 9 values (odd count). The median is the 5th value in the ordered list.
\(\text { Median }=35\)
Step 5 - Match to answer choices
35
\(z=4,5,6,7,8,9,10,11,12\)
Step 2 - Compute \(g(z)=z^2-4 z+3\) for each
\(\begin{aligned}
z=4: & 16-16+3=3 \\
z=5: & 25-20+3=8 \\
z=6: & 36-24+3=15 \\
z=7: & 49-28+3=24 \\
z=8: & 64-32+3=35 \\
z=9: & 81-36+3=48 \\
z=10: & 100-40+3=63 \\
z=11: & 121-44+3=80 \\
z=12: & 144-48+3=99
\end{aligned}\)
Step 3 - Ordered values
\(3,8,15,24,35,48,63,80,99\)
Step 4 - Find the median
There are 9 values (odd count). The median is the 5th value in the ordered list.
\(\text { Median }=35\)
Step 5 - Match to answer choices
35
Question #8
A sphere has a ratio of volume to surface area equal to \(\frac{5}{2}\).
(Note: Surface area \(=4 \pi r^2\), Volume \(=\frac{4}{3} \pi r^3\) )
What is the radius of the sphere?
A. \(\frac{5}{6}\)
B. \(\frac{3}{2}\)
C. \(\frac{5}{2}\)
D. \(\frac{15}{4}\)
E. \(\frac{15}{2}\)
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Step 1-Set up the equation.
You're given that \(\frac{\text { Volume }}{\text { Surface Area }}=\frac{5}{2}\). Substitute the formulas:
\(\frac{\frac{4}{3} \pi r^3}{4 \pi r^2}=\frac{5}{2}\)
Step 2 - Simplify the left side.
The \(4 \pi r^2\) cancels:
\(\frac{\frac{4}{3} \pi r^3}{4 \pi r^2}=\frac{4 \pi r^3}{3} \times \frac{1}{4 \pi r^2}=\frac{r}{3}\)
So the equation becomes:
\(\frac{r}{3}=\frac{5}{2}\)
Step 3 - Solve for r.
\(r=3 \times \frac{5}{2}=\frac{15}{2}\)
Answer: \(\frac{15}{2} \)
You're given that \(\frac{\text { Volume }}{\text { Surface Area }}=\frac{5}{2}\). Substitute the formulas:
\(\frac{\frac{4}{3} \pi r^3}{4 \pi r^2}=\frac{5}{2}\)
Step 2 - Simplify the left side.
The \(4 \pi r^2\) cancels:
\(\frac{\frac{4}{3} \pi r^3}{4 \pi r^2}=\frac{4 \pi r^3}{3} \times \frac{1}{4 \pi r^2}=\frac{r}{3}\)
So the equation becomes:
\(\frac{r}{3}=\frac{5}{2}\)
Step 3 - Solve for r.
\(r=3 \times \frac{5}{2}=\frac{15}{2}\)
Answer: \(\frac{15}{2} \)
Question #9
A researcher tracks the intensity of a radio signal over 8 time intervals.
At interval 0, the intensity is S watts.
- At the end of each odd-numbered interval (1st, 3rd, 5th, 7th), the intensity decreases by 20%.
- At the end of each even-numbered interval (2nd, 4th, 6th, 8th), the intensity increases by 20 %.
- Exception: At the end of interval 8 , the intensity increases by an additional \(\mathbf{1 0} \boldsymbol{\%}\) on top of the usual 20 % increase.
Which of the following represents the intensity, in watts, at the end of interval 8?
A. \(\left(0.96^3\right)(1.32) S\)
B. \(\left(0.96^4\right) S\)
C. \(\left(0.96^3\right)(1.056) S\)
D. \((0.8)(1.1)\left(0.96^3\right) S\)
E. \(\left(0.96^4\right)(1.1) S\)
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1. Set up the multipliers:
- Decrease by 20 % : Multiply by 0.8
- Increase by 20 % : Multiply by 1.2
- The "pair" (one odd interval followed by one even interval) results in a multiplier of (0.8)(1.2)=0.96 .
2. Track the intervals:
- There are 4 full pairs (1 & 2,3 & 4,5 & 6,7 & 8) .
- Normally, the intensity after 8 intervals would be \(S \times(0.96)^4\) .
3. Apply the exception:
- The exception states that at the end of interval 8, there is an additional 10 % increase on top of the usual 20 % increase.
- The "usual" increase at interval 8 (an even interval) is already included in the \(0.96^4\) term (which uses 1.2).
- An additional 10 % increase means we must multiply the result by 1.1.
4. Formulate the final expression:
- \(\quad\) Starting intensity =S
- \(\quad\) Result \(=S \times(0.96)^3 \times(0.8 \times 1.2 \times 1.1)\)
- Wait, let's look at the final step specifically:
- Intervals \(1-6=S(0.96)^3 \)
- Interval 7 (decrease 20 % ) \(=\times 0.8\)
- Interval 8 (increase 20 %+ extra 10 %)\(=\times(1.2 \times 1.1)=\times 1.32\)
- Combined for last pair: \(0.8 \times 1.32=1.056\)
- Therefore, the intensity is \(S(0.96)^3(1.056)\) .
Correct Answer: C
- Decrease by 20 % : Multiply by 0.8
- Increase by 20 % : Multiply by 1.2
- The "pair" (one odd interval followed by one even interval) results in a multiplier of (0.8)(1.2)=0.96 .
2. Track the intervals:
- There are 4 full pairs (1 & 2,3 & 4,5 & 6,7 & 8) .
- Normally, the intensity after 8 intervals would be \(S \times(0.96)^4\) .
3. Apply the exception:
- The exception states that at the end of interval 8, there is an additional 10 % increase on top of the usual 20 % increase.
- The "usual" increase at interval 8 (an even interval) is already included in the \(0.96^4\) term (which uses 1.2).
- An additional 10 % increase means we must multiply the result by 1.1.
4. Formulate the final expression:
- \(\quad\) Starting intensity =S
- \(\quad\) Result \(=S \times(0.96)^3 \times(0.8 \times 1.2 \times 1.1)\)
- Wait, let's look at the final step specifically:
- Intervals \(1-6=S(0.96)^3 \)
- Interval 7 (decrease 20 % ) \(=\times 0.8\)
- Interval 8 (increase 20 %+ extra 10 %)\(=\times(1.2 \times 1.1)=\times 1.32\)
- Combined for last pair: \(0.8 \times 1.32=1.056\)
- Therefore, the intensity is \(S(0.96)^3(1.056)\) .
Correct Answer: C
Question #10
A patient has Q milligrams of a medication in the bloodstream. Beginning at 9:00 AM, the medication is administered at a constant rate of r milligrams per minute and eliminated at a constant rate of s milligrams per minute. If r<s, after how many minutes will the amount of medication in the bloodstream be \(\frac{5}{8} Q\) milligrams?
A. \(\frac{Q}{8(s-r)}\)
B. \(\frac{Q}{4(s-r)}\)
C. \(\frac{3 Q}{8(s-r)}\)
D. \(\frac{5 Q}{8(s-r)}\)
E. \(\frac{Q}{s-r}\)
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Let $t$ be the number of minutes after 9:00 AM.
The account starts with Q milligrams. Each minute, $r$ milligrams are added and s milligrams are removed, so the net change per minute is r-s. Since r<s, the amount is decreasing.
So after t minutes, the amount is
\(Q+r t-s t=Q-(s-r) t\)
We want this to equal \(\frac{5}{8} Q\), so set up:
\(Q-(s-r) t=\frac{5}{8} Q\)
Subtract \(\frac{5}{8} Q\) from both sides:
\(\frac{3}{8} Q=(s-r) t\)
Now solve for t :
\(
t=\frac{3 Q}{8(s-r)}\)
So the correct answer is:
\(\frac{3 Q}{8(s-r)}\)
A quick way to see it: the amount has to drop by \(\frac{3}{8} Q\), and it drops at a rate of s-r per minute, so time \(= change \div rate\).
The account starts with Q milligrams. Each minute, $r$ milligrams are added and s milligrams are removed, so the net change per minute is r-s. Since r<s, the amount is decreasing.
So after t minutes, the amount is
\(Q+r t-s t=Q-(s-r) t\)
We want this to equal \(\frac{5}{8} Q\), so set up:
\(Q-(s-r) t=\frac{5}{8} Q\)
Subtract \(\frac{5}{8} Q\) from both sides:
\(\frac{3}{8} Q=(s-r) t\)
Now solve for t :
\(
t=\frac{3 Q}{8(s-r)}\)
So the correct answer is:
\(\frac{3 Q}{8(s-r)}\)
A quick way to see it: the amount has to drop by \(\frac{3}{8} Q\), and it drops at a rate of s-r per minute, so time \(= change \div rate\).
Question #11
For all integers p and q, the operation \(\bigstar\) is defined as:
- \(p \bigstar q=p+q\) if \(p q\) is a multiple of 5 .
- \(p \bigstar q=p-q\) if \(p q\) is even and not a multiple of 5 .
- \(p \bigstar q=-(p+q)\) if \(p q\) is odd and not a multiple of 5 .
What is the value of \((6 \bigstar 4) \bigstar(3 \bigstar 5)\) ?
A. -18
B. -6
C. 6
D. 18
E. 22
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Explanation
To find the value of \((6 \bigstar 4) \bigstar(3 \bigstar 5)\), the expression must be evaluated sequentially following the order of operations, starting with the inner parentheses.
Step 1: Evaluate \((6 \bigstar 4)\)
- Identify the values: p=6 and q=4.
- Calculate the product: \(p q=6 \times 4=24\).
- Determine the applicable condition: The product 24 is even and is not a multiple of 5 .
Therefore, the second rule applies: \(p \bigstar q=p-q\).
- Calculate the result: 6-4=2.
- Substitute this back into the original expression: \(2 \bigstar(3 \bigstar 5)\).
Step 2: Evaluate \((3 \bigstar 5)\)
- Identify the values: p=3 and q=5.
- Calculate the product: \(p q=3 \times 5=15\).
- Determine the applicable condition: The product 15 is a multiple of 5 . Therefore, the first rule applies: \(p \bigstar q=p+q\).
- Calculate the result: 3+5=8.
- Substitute this back into the expression: \(2 \bigstar 8\).
Step 3: Evaluate the final operation \((2 \bigstar 8)\)
- Identify the values: p=2 and q=8.
- Calculate the product: \(p q=2 \times 8=16\).
- Determine the applicable condition: The product 16 is even and is not a multiple of 5 . Therefore, the second rule applies: \(p \bigstar q=p-q\).
- Calculate the final result: 2-8=-6.
The correct answer is B.
To find the value of \((6 \bigstar 4) \bigstar(3 \bigstar 5)\), the expression must be evaluated sequentially following the order of operations, starting with the inner parentheses.
Step 1: Evaluate \((6 \bigstar 4)\)
- Identify the values: p=6 and q=4.
- Calculate the product: \(p q=6 \times 4=24\).
- Determine the applicable condition: The product 24 is even and is not a multiple of 5 .
Therefore, the second rule applies: \(p \bigstar q=p-q\).
- Calculate the result: 6-4=2.
- Substitute this back into the original expression: \(2 \bigstar(3 \bigstar 5)\).
Step 2: Evaluate \((3 \bigstar 5)\)
- Identify the values: p=3 and q=5.
- Calculate the product: \(p q=3 \times 5=15\).
- Determine the applicable condition: The product 15 is a multiple of 5 . Therefore, the first rule applies: \(p \bigstar q=p+q\).
- Calculate the result: 3+5=8.
- Substitute this back into the expression: \(2 \bigstar 8\).
Step 3: Evaluate the final operation \((2 \bigstar 8)\)
- Identify the values: p=2 and q=8.
- Calculate the product: \(p q=2 \times 8=16\).
- Determine the applicable condition: The product 16 is even and is not a multiple of 5 . Therefore, the second rule applies: \(p \bigstar q=p-q\).
- Calculate the final result: 2-8=-6.
The correct answer is B.
Question #12
Let \(R=(7,234)^3 \times(1,987)^4+(5,619)^5\). What is the units digit of R ?
A. 1
B. 2
C. 3
D. 7
E. 9
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Explanation
To find the units digit of the expression \(R=(7,234)^3 \times(1,987)^4+(5,619)^5\), we do not need to calculate the full values. The units digit of any large number raised to a power is determined entirely by the units digit of its base. We can evaluate each term by finding the repeating pattern (cyclicity) of its units digit.
Step 1: Find the units digit of \((7,234)^3\)
- The base ends in 4. The units digits of the powers of 4 repeat in a cycle of two:
- 4\(^1=4\)
- \(4^2=16\) (ends in 6)
- \(4^3=64\) (ends in 4 )
- The pattern is \(\mathbf{4 , 6 , 4 , 6 \ldots}\) * Because the exponent (3) is an odd number, the units digit for this term is 4.
Step 2: Find the units digit of \((1,987)^4\)
- The base ends in 7. The units digits of the powers of 7 repeat in a cycle of four:
- \(\quad 7^1=7\)
- \(7^2=49\) (ends in 9)
- \(7^3=343\) (ends in 3)
- \(7^4=2,401\) (ends in 1)
- The pattern is \(\mathbf{7 , 9 , 3 , 1 . . .}\) * Because the exponent (4) is a multiple of the 4 -step cycle, it lands perfectly on the end of the pattern. The units digit for this term is 1.
Step 3: Find the units digit of \((5,619)^5\)
- The base ends in 9 . The units digits of the powers of 9 repeat in a cycle of two:
- \(9^1=9\)
- \(9^2=81\) (ends in 1)
- \(9^3=729\) (ends in 9)
- The pattern is 9, 1, 9, 1...
- Because the exponent ( 5 ) is an odd number, the units digit for this term is 9 .
Step 4: Combine the units digits
Substitute the derived units digits back into the original algebraic structure of the problem:
(Units digit of 1st term) × (Units digit of 2nd term) + (Units digit of 3rd term)
\(4 \times 1+9\)
Following the order of operations (PEMDAS), multiplication must be performed before addition:
\(4+9=13\)
The units digit of 13 is 3 .
The correct answer is 3 .
To find the units digit of the expression \(R=(7,234)^3 \times(1,987)^4+(5,619)^5\), we do not need to calculate the full values. The units digit of any large number raised to a power is determined entirely by the units digit of its base. We can evaluate each term by finding the repeating pattern (cyclicity) of its units digit.
Step 1: Find the units digit of \((7,234)^3\)
- The base ends in 4. The units digits of the powers of 4 repeat in a cycle of two:
- 4\(^1=4\)
- \(4^2=16\) (ends in 6)
- \(4^3=64\) (ends in 4 )
- The pattern is \(\mathbf{4 , 6 , 4 , 6 \ldots}\) * Because the exponent (3) is an odd number, the units digit for this term is 4.
Step 2: Find the units digit of \((1,987)^4\)
- The base ends in 7. The units digits of the powers of 7 repeat in a cycle of four:
- \(\quad 7^1=7\)
- \(7^2=49\) (ends in 9)
- \(7^3=343\) (ends in 3)
- \(7^4=2,401\) (ends in 1)
- The pattern is \(\mathbf{7 , 9 , 3 , 1 . . .}\) * Because the exponent (4) is a multiple of the 4 -step cycle, it lands perfectly on the end of the pattern. The units digit for this term is 1.
Step 3: Find the units digit of \((5,619)^5\)
- The base ends in 9 . The units digits of the powers of 9 repeat in a cycle of two:
- \(9^1=9\)
- \(9^2=81\) (ends in 1)
- \(9^3=729\) (ends in 9)
- The pattern is 9, 1, 9, 1...
- Because the exponent ( 5 ) is an odd number, the units digit for this term is 9 .
Step 4: Combine the units digits
Substitute the derived units digits back into the original algebraic structure of the problem:
(Units digit of 1st term) × (Units digit of 2nd term) + (Units digit of 3rd term)
\(4 \times 1+9\)
Following the order of operations (PEMDAS), multiplication must be performed before addition:
\(4+9=13\)
The units digit of 13 is 3 .
The correct answer is 3 .
Question #13
In the x y -plane, the points (1,3) and (5,-5) lie on line L . Which of the following points also lie on line L ?
Indicate all such points.
A. (-3,11)
B. (0,5)
C. (2,1)
D. (4,-3)
E. (6,-6)
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Solution
Step 1 - Find the slope
\(m=\frac{-5-3}{5-1}=\frac{-8}{4}=-2\)
Step 2 - Find line equation
Using (1,3) :
\(\begin{gathered}
y-3=-2(x-1) \\
y-3=-2 x+2 \\
y=-2 x+5
\end{gathered}\)
Step 3 - Check each point
- \((-3,11):-2(-3)+5=6+5=11\)
- \((0,5):-2(0)+5=5\)
- \((2,1):-2(2)+5=-4+5=1\)
- \((4,-3):-2(4)+5=-8+5=-3\)
- \((6,-6):-2(6)+5=-12+5=-7 \neq-6\)
Step 4 - Conclusion
\((-3,11),(0,5),(2,1),(4,-3)\)
Step 1 - Find the slope
\(m=\frac{-5-3}{5-1}=\frac{-8}{4}=-2\)
Step 2 - Find line equation
Using (1,3) :
\(\begin{gathered}
y-3=-2(x-1) \\
y-3=-2 x+2 \\
y=-2 x+5
\end{gathered}\)
Step 3 - Check each point
- \((-3,11):-2(-3)+5=6+5=11\)
- \((0,5):-2(0)+5=5\)
- \((2,1):-2(2)+5=-4+5=1\)
- \((4,-3):-2(4)+5=-8+5=-3\)
- \((6,-6):-2(6)+5=-12+5=-7 \neq-6\)
Step 4 - Conclusion
\((-3,11),(0,5),(2,1),(4,-3)\)
Question #14
A landscape architect is designing a straight walkway divided into 4 sequential rectangular plots. Each plot will be planted with one of 6 available varieties of flowers. The architect may repeat flower varieties, but no two adjacent plots can contain the same variety. How many unique walkway designs are possible?
A. 150
B. 360
C. 480
D. 750
E. 1296
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Explanation
To find the total number of unique walkway designs, evaluate the number of choices available for each of the 4 plots sequentially.
Step 1: The First Plot
The architect can choose any of the available flower varieties.
- Choices for Plot 1=6
Step 2: The Second Plot
This plot is adjacent to the first, so it cannot use the variety just planted in Plot 1. However, all other varieties are available.
- Choices for Plot 2=5
Step 3: The Third Plot
This plot is adjacent to the second plot, so it cannot use the variety planted in Plot 2. It can, however, use the variety planted in Plot 1. Therefore, the pool of choices resets.
- Choices for Plot 3=5
Step 4: The Fourth Plot
Following the same logic as the third plot, this plot cannot match Plot 3, but can be anything else.
- Choices for Plot 4=5
Step 5: Calculate the Total
Multiply the independent choices together to find the total number of combinations:
\(\text { Total }=6 \times 5 \times 5 \times 5=750\)
The correct answer is D.
To find the total number of unique walkway designs, evaluate the number of choices available for each of the 4 plots sequentially.
Step 1: The First Plot
The architect can choose any of the available flower varieties.
- Choices for Plot 1=6
Step 2: The Second Plot
This plot is adjacent to the first, so it cannot use the variety just planted in Plot 1. However, all other varieties are available.
- Choices for Plot 2=5
Step 3: The Third Plot
This plot is adjacent to the second plot, so it cannot use the variety planted in Plot 2. It can, however, use the variety planted in Plot 1. Therefore, the pool of choices resets.
- Choices for Plot 3=5
Step 4: The Fourth Plot
Following the same logic as the third plot, this plot cannot match Plot 3, but can be anything else.
- Choices for Plot 4=5
Step 5: Calculate the Total
Multiply the independent choices together to find the total number of combinations:
\(\text { Total }=6 \times 5 \times 5 \times 5=750\)
The correct answer is D.
Question #15
Attachment:
GRE box plot.png [ 91.92 KiB | Viewed 2956 times ]
The box plots above summarize customer satisfaction ratings for two services. Each rating is an integer from 1 to 10.
Service A five-number summary: \(\operatorname{Min}=2, \mathrm{Q} 1=4\), \(\operatorname{Median}= 6, Q3 = 8\),\( \operatorname{Max}=10\)
Service B five-number summary: \(\operatorname{Min}=3, \mathrm{Q} 1=5, \operatorname{Median}=7, \mathrm{Q} 3=9, \operatorname{Max}=10\)
Which of the following statements must be true?
Indicate all such statements.
- A. The interquartile range for Service A is equal to the interquartile range for Service B.
- B. More than 50 % of the ratings for Service A are less than 6 .
- C. Service B received more ratings of 10 than Service A did.
- D. At least 25 % of the ratings for Service B are greater than or equal to 9 .
Show: ::
A box plot shows the minimum, Q1, median, Q3, and maximum, so it tells you about spread and center, but not exact counts of each score.
- A is true because both IQRs are Q 3-Q 1=4 .
- D is true because if Q 3=9 , then at least 25 % of ratings are 9 or higher.
- B is not guaranteed because a median of 6 does not mean more than half the ratings are below 6 .
- C is not guaranteed because the plot does not show how many 10 s there are.
So the correct choices are \(\mathbf{A}$ and $\mathbf{D} \).
------------------------------------------
- A. The interquartile range (IQR) for Service A is equal to the interquartile range for Service B.
- Logic: The IQR is the range of the middle 50 % of the data, calculated as Q 3-Q 1 .
- Service A: 8-4=4.
- Service B: 9-5=4 .
- Conclusion: This statement is True because 4=4 . It is a sound, verifiable mathematical fact based on the provided five-number summary.
- B. More than 50 % of the ratings for Service A are less than 6.
- Logic: The median is defined as the 50 th percentile. By definition, 50 % of the data points are less than or equal to the median.
- Conclusion: This statement is False. Because the median is 6 , we know 50 % are \(\leq 6\) , but we cannot guarantee that strictly more than 50 % are less than 6 , as we do not know the frequency of the value "6." This is a sound, logical "trap" common in high-level testing.
- C. Service B received more ratings of 10 than Service A did.
- Logic: A box plot summarizes the distribution and spread of data, not the absolute number (frequency) of specific data points.
- Conclusion: This statement is False. This is soundly excluded because the data does not provide the total number of survey respondents.
- D. At least 25 % of the ratings for Service B are greater than or equal to 9 .
- Logic: The third quartile ( Q 3 ) is the 75th percentile, meaning 25 % of the data lies above it.
- Service B: Since Q 3=9 and the Maximum =10 , the top 25 % of all ratings must fall within the range of 9 to 10.
- Conclusion: This statement is True. This is a sound inference based on the definition of quartiles.
- A is true because both IQRs are Q 3-Q 1=4 .
- D is true because if Q 3=9 , then at least 25 % of ratings are 9 or higher.
- B is not guaranteed because a median of 6 does not mean more than half the ratings are below 6 .
- C is not guaranteed because the plot does not show how many 10 s there are.
So the correct choices are \(\mathbf{A}$ and $\mathbf{D} \).
------------------------------------------
- A. The interquartile range (IQR) for Service A is equal to the interquartile range for Service B.
- Logic: The IQR is the range of the middle 50 % of the data, calculated as Q 3-Q 1 .
- Service A: 8-4=4.
- Service B: 9-5=4 .
- Conclusion: This statement is True because 4=4 . It is a sound, verifiable mathematical fact based on the provided five-number summary.
- B. More than 50 % of the ratings for Service A are less than 6.
- Logic: The median is defined as the 50 th percentile. By definition, 50 % of the data points are less than or equal to the median.
- Conclusion: This statement is False. Because the median is 6 , we know 50 % are \(\leq 6\) , but we cannot guarantee that strictly more than 50 % are less than 6 , as we do not know the frequency of the value "6." This is a sound, logical "trap" common in high-level testing.
- C. Service B received more ratings of 10 than Service A did.
- Logic: A box plot summarizes the distribution and spread of data, not the absolute number (frequency) of specific data points.
- Conclusion: This statement is False. This is soundly excluded because the data does not provide the total number of survey respondents.
- D. At least 25 % of the ratings for Service B are greater than or equal to 9 .
- Logic: The third quartile ( Q 3 ) is the 75th percentile, meaning 25 % of the data lies above it.
- Service B: Since Q 3=9 and the Maximum =10 , the top 25 % of all ratings must fall within the range of 9 to 10.
- Conclusion: This statement is True. This is a sound inference based on the definition of quartiles.
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Verbal
Question #1
To hear that the novelist’s latest work radiates such an unflaggingly __________ mood is a genuine surprise to readers accustomed to her barbed essays and relentless mockery of social pretension."
| Blank (i) |
|---|
| A. genial |
| B. caustic |
| C. waggish | D. impious | E. punctilious |
Show: ::
Why A is the correct choice:
- Genial means friendly, affable, and cheerful. This creates the necessary contrast with the "barbed" and "mocking" tone mentioned in the sentence.
Why the other choices are incorrect:
- B. Caustic: This means biting or sarcastic. This is a "thematic trap" because it describes the author's usual style rather than the surprising new one.
- C. Waggish: This means humorous in a playful or mischievous way. While it isn't "barbed," it is too specific and does not offer the same broad, warm contrast that "genial" provides to "mockery".
- D. Impious: This means lacking respect. This is too close to "mockery" and does not create the surprise contrast required.
- E. Punctilious: This means showing great attention to detail or correct behavior. This is irrelevant to the tone of her writing and does not contrast with her previous "barbed" style.
- Genial means friendly, affable, and cheerful. This creates the necessary contrast with the "barbed" and "mocking" tone mentioned in the sentence.
Why the other choices are incorrect:
- B. Caustic: This means biting or sarcastic. This is a "thematic trap" because it describes the author's usual style rather than the surprising new one.
- C. Waggish: This means humorous in a playful or mischievous way. While it isn't "barbed," it is too specific and does not offer the same broad, warm contrast that "genial" provides to "mockery".
- D. Impious: This means lacking respect. This is too close to "mockery" and does not create the surprise contrast required.
- E. Punctilious: This means showing great attention to detail or correct behavior. This is irrelevant to the tone of her writing and does not contrast with her previous "barbed" style.
Question #2
The envoy's refusal to address the assembly in straightforward terms sorely taxed the delegates' forbearance, as his remarks grew ever more ________ with each passing hour.
| Blank (i) |
|---|
| A. unequivocal |
| B. bombastic |
| C. limpid | D. glib | E. pellucid |
Show: ::
Explanation
The sentence states that the envoy refused to address the assembly "in straightforward terms," and this "sorely taxed the delegates' forbearance." The subordinate clause explains the consequence: "his remarks grew ever more _______ with each passing hour." Since the envoy deliberately avoided plain speech, his remarks must have become increasingly pompous, inflated, or grandiloquent - the opposite of straightforward. The blank must mean pretentiously verbose, high-flown, or bombastic.
- A. unequivocal - Leaving no doubt; unambiguous; perfectly clear. This is the opposite of what the sentence requires. If the remarks were unequivocal, they would be straightforward - and the delegates would not be taxed. Incorrect.
- B. bombastic - High-sounding but with little meaning; inflated, pompous, pretentious. "His remarks grew ever more bombastic" perfectly captures the consequence of refusing to speak plainly: the language becomes increasingly puffed up and irritating. Correct.
- C. limpid - Clear, transparent, easily understood. Like "unequivocal," this means the opposite of what is required. Limpid remarks would be a relief, not a tax on forbearance. Incorrect.
- D. glib - Fluent but insincere and shallow; superficially smooth. While "glib" describes speech that lacks substance, it emphasizes superficial ease rather than pompous inflation. A glib speaker is slick and effortless; the envoy's speech is described as increasingly irritating and overblown. Incorrect.
- E. pellucid - Translucently clear; easily understood. Like "limpid" and "unequivocal," this means the opposite of the required meaning. Incorrect.
The sentence states that the envoy refused to address the assembly "in straightforward terms," and this "sorely taxed the delegates' forbearance." The subordinate clause explains the consequence: "his remarks grew ever more _______ with each passing hour." Since the envoy deliberately avoided plain speech, his remarks must have become increasingly pompous, inflated, or grandiloquent - the opposite of straightforward. The blank must mean pretentiously verbose, high-flown, or bombastic.
- A. unequivocal - Leaving no doubt; unambiguous; perfectly clear. This is the opposite of what the sentence requires. If the remarks were unequivocal, they would be straightforward - and the delegates would not be taxed. Incorrect.
- B. bombastic - High-sounding but with little meaning; inflated, pompous, pretentious. "His remarks grew ever more bombastic" perfectly captures the consequence of refusing to speak plainly: the language becomes increasingly puffed up and irritating. Correct.
- C. limpid - Clear, transparent, easily understood. Like "unequivocal," this means the opposite of what is required. Limpid remarks would be a relief, not a tax on forbearance. Incorrect.
- D. glib - Fluent but insincere and shallow; superficially smooth. While "glib" describes speech that lacks substance, it emphasizes superficial ease rather than pompous inflation. A glib speaker is slick and effortless; the envoy's speech is described as increasingly irritating and overblown. Incorrect.
- E. pellucid - Translucently clear; easily understood. Like "limpid" and "unequivocal," this means the opposite of the required meaning. Incorrect.
Question #3
That the snow leopard has persistently eluded systematic field observation is hardly surprising, given that the near-inaccessibility of its high-altitude terrain and its notoriously elusive nature have together (i) ________ any rigorous attempt at study outside the (ii) ________ confines of zoological institutions.
| Blank (i) | Blank (ii) |
|---|---|
| A. encompassed | D. simulated |
| B. facilitated | E. pristine |
| C. foreclosed | F. contrived |
Show: ::
Blank (i)
The sentence first establishes a fact: the snow leopard has "persistently eluded systematic field observation." This is "hardly surprising," given two factors: "the near-inaccessibility of its highaltitude terrain" and "its notoriously elusive nature." Together, these factors have done something to "any rigorous attempt at study outside the ______ confines of zoological institutions." The "outside" phrase implies that study within zoological institutions is possible, but study outside them is not. The blank must therefore mean prevented, ruled out, or made impossible.
- A. encompassed - Included, contained, embraced. If the factors encompassed rigorous study, they would include or enable it - the opposite of what the sentence describes. Incorrect.
- B. facilitated - Made easier, assisted, promoted. If the factors facilitated study, field observation would be easier, not elusive. Incorrect.
- C. foreclosed - Prevented, precluded, ruled out in advance. "Have together foreclosed any rigorous attempt at study outside the contrived confines" perfectly captures the idea that natural conditions make field research impossible. Correct.
Blank (ii)
The sentence contrasts study "outside" zoological institutions (in the wild, where it is foreclosed) with study within them. The word "confines" suggests limitation and enclosure. The blank must describe the artificial, human-constructed, or unnatural character of zoo environments, especially in contrast to the natural high-altitude terrain.
- D. simulated - Imitated, reproduced artificially. While zoo environments may simulate natural habitats, "simulated" does not carry the slightly pejorative connotation of "unnatural" that "confines" suggests. Incorrect.
- E. pristine - Original, unspoiled, in its natural state. This is the opposite of what the blank requires. Zoological institutions are not pristine; they are artificial. Incorrect.
- F. contrived - Artificially created; deliberately arranged rather than natural; forced. "The contrived confines of zoological institutions" perfectly captures the artificial, human-constructed nature of captivity, directly contrasting with the natural high-altitude terrain. Correct.
The sentence first establishes a fact: the snow leopard has "persistently eluded systematic field observation." This is "hardly surprising," given two factors: "the near-inaccessibility of its highaltitude terrain" and "its notoriously elusive nature." Together, these factors have done something to "any rigorous attempt at study outside the ______ confines of zoological institutions." The "outside" phrase implies that study within zoological institutions is possible, but study outside them is not. The blank must therefore mean prevented, ruled out, or made impossible.
- A. encompassed - Included, contained, embraced. If the factors encompassed rigorous study, they would include or enable it - the opposite of what the sentence describes. Incorrect.
- B. facilitated - Made easier, assisted, promoted. If the factors facilitated study, field observation would be easier, not elusive. Incorrect.
- C. foreclosed - Prevented, precluded, ruled out in advance. "Have together foreclosed any rigorous attempt at study outside the contrived confines" perfectly captures the idea that natural conditions make field research impossible. Correct.
Blank (ii)
The sentence contrasts study "outside" zoological institutions (in the wild, where it is foreclosed) with study within them. The word "confines" suggests limitation and enclosure. The blank must describe the artificial, human-constructed, or unnatural character of zoo environments, especially in contrast to the natural high-altitude terrain.
- D. simulated - Imitated, reproduced artificially. While zoo environments may simulate natural habitats, "simulated" does not carry the slightly pejorative connotation of "unnatural" that "confines" suggests. Incorrect.
- E. pristine - Original, unspoiled, in its natural state. This is the opposite of what the blank requires. Zoological institutions are not pristine; they are artificial. Incorrect.
- F. contrived - Artificially created; deliberately arranged rather than natural; forced. "The contrived confines of zoological institutions" perfectly captures the artificial, human-constructed nature of captivity, directly contrasting with the natural high-altitude terrain. Correct.
Question #4
Why, ask a growing number of geophysicists, should the puzzling luminous displays occasionally reported above active fault lines be ascribed to esoteric tectonic mechanisms, when the far more (i) ________ account - one that the field's mainstream finds considerably more (ii) ________ — points to such (iii) ________ sources as pockets of escaping gas ignited by friction, or the piezoelectric discharge of stressed quartz?
| Blank (i) | Blank (ii) | Blank (iii) |
|---|---|---|
| A. overwrought | D. seductive | G. recherche |
| B. prosaic | E. compelling | H. commonplace |
| C. intricate | F. divisive | I. imperceptible |
Show: ::
Step-by-Step Breakdown
- Blank (i): The sentence asks why we should use "esoteric" explanations when a "far more ________ account" exists. Since the alternative is based on common, tangible phenomena (gas/friction/quartz), the word must be the antonym of "esoteric."
- Selection: (B) Prosaic. "Prosaic" means commonplace, unromantic, or matter-of-factthe perfect contrast to "esoteric."
- Why not (A) or (C)? "Overwrought" (too complex) and "intricate" (complex) would be synonyms for "esoteric," which fails the contrast logic.
- Blank (ii): This blank describes how the "field's mainstream" views this "prosaic" account. In scientific arguments, if the mainstream accepts an explanation over an esoteric one, they find it more convincing.
- Selection: (E) Compelling. "Compelling" implies a strong, believable, and persuasive argument.
- Why not (D) or (F)? "Seductive" is often used for arguments that are appealing but potentially misleading. "Divisive" would imply that the mainstream disagrees, but the context of the sentence suggests they do agree with the simpler explanation.
- Blank (iii): This blank describes the nature of the sources: "pockets of escaping gas ignited by friction, or the piezoelectric discharge of stressed quartz." These are well-known physical phenomena.
- Selection: (H) Commonplace. This ties back to "prosaic" in Blank (i); it confirms that these are ordinary, well-understood occurrences.
- Why not (G) or (I)? "Recherché" (esoteric/rare) is a synonym for the "esoteric" side of the argument, not the "mainstream" side. "Imperceptible" makes no sense in this context, as these phenomena must be perceptible enough for scientists to study them.
- Blank (i): The sentence asks why we should use "esoteric" explanations when a "far more ________ account" exists. Since the alternative is based on common, tangible phenomena (gas/friction/quartz), the word must be the antonym of "esoteric."
- Selection: (B) Prosaic. "Prosaic" means commonplace, unromantic, or matter-of-factthe perfect contrast to "esoteric."
- Why not (A) or (C)? "Overwrought" (too complex) and "intricate" (complex) would be synonyms for "esoteric," which fails the contrast logic.
- Blank (ii): This blank describes how the "field's mainstream" views this "prosaic" account. In scientific arguments, if the mainstream accepts an explanation over an esoteric one, they find it more convincing.
- Selection: (E) Compelling. "Compelling" implies a strong, believable, and persuasive argument.
- Why not (D) or (F)? "Seductive" is often used for arguments that are appealing but potentially misleading. "Divisive" would imply that the mainstream disagrees, but the context of the sentence suggests they do agree with the simpler explanation.
- Blank (iii): This blank describes the nature of the sources: "pockets of escaping gas ignited by friction, or the piezoelectric discharge of stressed quartz." These are well-known physical phenomena.
- Selection: (H) Commonplace. This ties back to "prosaic" in Blank (i); it confirms that these are ordinary, well-understood occurrences.
- Why not (G) or (I)? "Recherché" (esoteric/rare) is a synonym for the "esoteric" side of the argument, not the "mainstream" side. "Imperceptible" makes no sense in this context, as these phenomena must be perceptible enough for scientists to study them.
Question #5/6
In his popular treatise on linguistic etymology, Marcus Ridley contends that when Roman sculptors adopted the term sincerus to describe unblemished marble, they drew upon a workshop convention: supposedly, unscrupulous artisans would conceal flaws in low-grade stone with beeswax, and the phrase sine cera (“without wax”) came to guarantee authenticity. In fact, Romance-language philology reveals that sincerus predates any attested wax-related workshop terminology in Latin epigraphy by at least three centuries. Ridley’s sole cited authority for this anecdote is Etymological Curiosities, whose compiler, Helena Vance, provides no primary-source documentation but who likely garbled a speculative aside offered in 1927—nearly two millennia after the Roman era—by the classicist Alistair Fowles and mentioned in a monograph Vance lists among her references. Fowles had mused that sincerus might derive from an unattested Etruscan commercial term relating to unadulterated goods, not from any Latin workshop jargon; Vance appears to have conflated this with the unrelated wax-filling practice, which is documented only in medieval guild records.
The author of the passage would be most likely to concur with which of the following claims regarding the relationship between Fowles’s conjecture and Ridley’s account?
Consider each of the choices separately and select all that apply.
A. Ridley’s claim can be traced, through a chain of intermediary distortions, to an ultimately garbled interpretation of Fowles’s conjecture.
B. The monograph that Ridley includes in his bibliography indicates that he had direct acquaintance with Fowles’s original speculation.
C. Ridley composed his treatise almost two millennia after the period during which Fowles situated his conjecture.
The author draws attention to the chronological span separating Fowles’s conjecture from the Roman era primarily in order to
A. establish that Fowles published his conjecture well before Ridley produced his etymological treatise.
B. underscore the intrinsically conjectural character of Fowles’s proposed derivation.
C. account for the dearth of any credible explanation for the origin of sincerus in the centuries immediately following the Roman period.
D. illustrate the remarkable durability of certain commercial terminology across vast stretches of time.
E. intimate that the lexical frequency patterns Fowles relied upon may have shifted in the intervening centuries.
Consider each of the choices separately and select all that apply.
A. Ridley’s claim can be traced, through a chain of intermediary distortions, to an ultimately garbled interpretation of Fowles’s conjecture.
B. The monograph that Ridley includes in his bibliography indicates that he had direct acquaintance with Fowles’s original speculation.
C. Ridley composed his treatise almost two millennia after the period during which Fowles situated his conjecture.
The author draws attention to the chronological span separating Fowles’s conjecture from the Roman era primarily in order to
A. establish that Fowles published his conjecture well before Ridley produced his etymological treatise.
B. underscore the intrinsically conjectural character of Fowles’s proposed derivation.
C. account for the dearth of any credible explanation for the origin of sincerus in the centuries immediately following the Roman period.
D. illustrate the remarkable durability of certain commercial terminology across vast stretches of time.
E. intimate that the lexical frequency patterns Fowles relied upon may have shifted in the intervening centuries.
Show: ::
Question 1
The passage says Ridley’s claim about sincerus comes from a chain of indirect sources, and that chain likely distorted an earlier guess by Fowles. That makes A correct, because Ridley’s account can indeed be traced back through intermediary distortion to Fowles’s conjecture. B is wrong because merely listing a monograph in the bibliography does not prove Ridley personally knew Fowles’s original idea. C is correct in substance because the passage emphasizes that Fowles’s conjecture was made nearly two millennia after the Roman era, which is the same kind of “much later” timing contrast shown in the original screen question.
Question 2
The highlighted phrase “nearly two millennia after the Roman era” is there to emphasize a huge time gap between the ancient Roman period and Fowles’s later speculation. Its main purpose is not to prove that Fowles published before Ridley, nor to comment on word-frequency patterns, nor to celebrate the survival of terminology. The best answer is C, because the date gap helps explain why Fowles’s conjecture is not a credible direct source for the ancient origin of sincerus.
The passage says Ridley’s claim about sincerus comes from a chain of indirect sources, and that chain likely distorted an earlier guess by Fowles. That makes A correct, because Ridley’s account can indeed be traced back through intermediary distortion to Fowles’s conjecture. B is wrong because merely listing a monograph in the bibliography does not prove Ridley personally knew Fowles’s original idea. C is correct in substance because the passage emphasizes that Fowles’s conjecture was made nearly two millennia after the Roman era, which is the same kind of “much later” timing contrast shown in the original screen question.
Question 2
The highlighted phrase “nearly two millennia after the Roman era” is there to emphasize a huge time gap between the ancient Roman period and Fowles’s later speculation. Its main purpose is not to prove that Fowles published before Ridley, nor to comment on word-frequency patterns, nor to celebrate the survival of terminology. The best answer is C, because the date gap helps explain why Fowles’s conjecture is not a credible direct source for the ancient origin of sincerus.
Question #7/8/9
Confronted with the near-total absence of written records produced by inhabitants of the medieval Mali Empire, scholars of pre-colonial West African social organization have demonstrated considerable ingenuity in exploiting non-documentary evidence. In recent years, Mariam Kamara has directed her attention to the ceremonial masks preserved by Mande descendant communities, arguing that artifacts such as the ntomo face mask and the ci-wara antelope headdress encode the "rhythm of communal obligation" even as they furnish an implicit framework for understanding dynastic transitions. Extracting dependable historical insight from these ritual objects is fraught with difficulty, however. Between contemporary researchers and fourteenth-century Mali there intervenes a potent nineteenth-century colonial antiquarianism that sentimentalized the pre-colonial Sahel as a realm of static, hierarchical harmony governed by immutable custom. This idealized construct arose in part to justify the colonial civilizing mission by presenting indigenous societies as simultaneously noble and irredeemably frozen in time. As traditional mask-carving workshops dwindled under the pressure of imported European manufactures, colonial administrators and ethnographers assiduously collected, catalogued, and displayed these ritual objects as emblems of a supposedly vanishing authenticity. Acutely sensitive to the ideological contaminations introduced by colonial-era curation, most scholars remain deeply skeptical that the original social significance of Malian masks can ever be recovered, maintaining that such artifacts now testify more faithfully to the preoccupations of nineteenth-century European collectors than to the lived realities of fourteenth-century Mande society. Kamara, in a striking departure from this consensus, declines to dismiss the colonial collectors, crediting them instead with preserving objects that would otherwise have been lost to the communities whose history she seeks to reconstruct.
Which of the following most accurately captures the overall concern of the passage?
A. Enumerating the obstacles that prevent scholars from locating evidentiary materials pertinent to women's historical lives
B. Tracing the genesis and proliferation of a specific historical mythology during the middle decades of the nineteenth century
C. Delineating a spectrum of scholarly postures toward the evidentiary value of a particular category of sources for investigating a given era
D. Chronicling the efforts undertaken by an individual researcher to recover the meaning embedded in a specific set of handcrafted artifacts
E. Recounting a dispute among academic practitioners regarding the lived experience of a particular demographic during a circumscribed historical interval
According to the passage, which of the following constitutes an impediment for scholars seeking to draw inferences from the ceremonial masks discussed in the passage?
A. The relative scarcity of such masks when set against the abundance of other surviving ritual artifacts from the same period
B. An insufficiently developed scholarly understanding of the mask-carving workshop system that produced these ritual objects
C. A lack of consensus among researchers concerning the reasons that such masks became objects of particular fascination during the nineteenth century
D. A framework of interpretation imposed upon these masks during the nineteenth century
E. A deficiency of written documentation that could contextualize and elucidate such masks
With respect to the "colonial antiquarianism" identified in the passage, it can be inferred that Kamara would most likely part company with the majority of scholars over
A. the degree to which this antiquarianism obstructs the effort to deploy certain artifacts as vehicles for historical understanding
B. the degree to which this antiquarianism developed as a reaction to conditions set in motion by European industrialization
C. whether this antiquarianism inadvertently preserves traces of the original significance of the ritual masks dating from the medieval period
D. whether this antiquarianism achieved particularly broad cultural currency during the nineteenth century
E. whether this antiquarianism served to adequately rationalize the political project of colonial administration
Show: ::
Explanation:
Step 1 - Map the passage structure.
- Paragraph 1: Problem (no texts) → solution (Kamara turns to masks) → complication (colonial antiquarianism intervenes)
- Paragraph 2: Colonial myth described → masks collected → scholarly consensus (masks reveal more about collectors than about Mali) → Kamara's dissent (credits collectors)
Step 2 - Identify the central thread.
The passage is not only about Kamara, nor only about the colonial myth, nor only about the difficulty. It is fundamentally about how scholars relate to these objects as historical sources - the range of attitudes from the skeptical majority to Kamara's appreciative counter-stance. This is a spectrum of scholarly postures toward the evidentiary value of a category of sources (ceremonial masks) for a particular period (medieval Mali).
Step 3 - Eliminate wrong answers.
- A: The passage concerns the interpretive difficulty of existing sources, not the scarcity of sources. The problem is the intervening myth, not a shortage of material. Also, the passage is not about "women's historical lives" - that belongs to the original.
- B: The colonial myth is a complicating factor in the discussion, not the primary subject. The passage's focus is on how historians respond to the myth's effect on source interpretation.
- C (Correct): "A spectrum of scholarly postures" captures the range from the skeptical majority ("most scholars remain deeply skeptical") to Kamara's dissent ("striking departure from this consensus"). The "particular category of sources" is ceremonial masks; the "given era" is medieval Mali.
- D: Kamara's work is a central example, but the passage is not a chronicle of her efforts. It embeds her approach within a broader methodological debate. The primary concern is that debate, not the individual researcher.
- E: The passage does not recount a debate about "the lived experience of a particular demographic." The disagreement is methodological - about how to interpret sources - not about the nature of women's (or Mande) experience itself.
Explanation:
Step 1 - Locate the difficulty in the passage.
The passage states: "Between contemporary researchers and fourteenth-century Mali there intervenes a potent nineteenth-century colonial antiquarianism that sentimentalized the precolonial Sahel..." It later elaborates: "most scholars remain deeply skeptical that the original social significance of Malian masks can ever be recovered, maintaining that such artifacts now testify more faithfully to the preoccupations of nineteenth-century European collectors than to the lived realities of fourteenth-century Mande society."
Step 2 - Identify the nature of the impediment.
The difficulty is not the absence of material but the distorting lens applied by nineteenth-century collectors and ethnographers. Their "sentimentalized" and "idealized" framework of interpretation has contaminated the objects, making it difficult to see past the colonial-era overlay to the original Mande meanings. This is an interpretive context imposed during the nineteenth century.
Step 3 - Eliminate wrong answers.
- A: No relative shortage is discussed. The passage concerns the masks that were collected and preserved, not a scarcity compared to other artifacts.
- B: The passage does not suggest that scholars don't understand the production system. The problem is the colonial interpretive overlay, not ignorance of craft techniques.
- C: The passage does not present a "lack of consensus" about why the masks became prized. The colonial motivations are described with authorial confidence ("arose in part to justify..."), not as a matter of scholarly dispute. The consensus that is discussed concerns whether the masks can be interpreted, not why they were collected.
- D (Correct): The "potent nineteenth-century colonial antiquarianism" and its sentimentalizing, idealizing framework constitute precisely an "interpretive context applied during the nineteenth century" that now obstructs scholars.
- E: While the passage opens by noting an "absence of written records," this is the background condition that motivates turning to masks in the first place - not the impediment to interpretir the masks. The impediment is the colonial myth, not the pre-existing lack of texts.
Explanation:
Step 1 - Identify the consensus view.
Most scholars "remain deeply skeptical that the original social significance of Malian masks can ever be recovered" and believe the masks "now testify more faithfully to the preoccupations of nineteenth-century European collectors than to the lived realities of fourteenth-century Mande society." For the majority, the colonial myth is a near-fatal obstruction to historical interpretation.
Step 2 -Identify Kamara's dissent.
"Kamara, in a striking departure from this consensus, declines to dismiss the colonial collectors, crediting them instead with preserving objects that would otherwise have been lost to the communities whose history she seeks to reconstruct." Kamara views the collectors positively they saved the objects, enabling her historical project. This implies she believes the myth does not fatally obstruct interpretation; the objects can still yield historical insight despite their colonial provenance.
Step 3 - Pinpoint the locus of disagreement.
The disagreement is fundamentally about how much the colonial antiquarianism interferes with historical use of the masks. Most say: too much - original meaning is irrecoverable. Kamara says: not so much - the objects were preserved, and I can work with them.
Step 4 - Eliminate wrong answers.
- A (Correct): Kamara disagrees with most historians over "the degree to which this antiquarianism obstructs" the use of masks as historical sources. The majority sees severe obstruction; Kamara sees the preservation as enabling.
- B: The passage attributes the myth's emergence to justifying colonialism, not to industrialization. But even if industrialization were mentioned, there is no evidence Kamara disagrees about the cause of the myth - only about its effect on source usability.
- C: The passage does not suggest Kamara believes the myth "contains clues to the original meaning." She values the mythmakers for preserving the objects, not for providing interpretive clues embedded in the myth itself.
- D: The passage provides no basis to infer a disagreement about how "widespread" the myth was. Both Kamara and the majority would likely agree it was pervasive.
- E: Whether the myth "adequately rationalized" colonial administration is a political judgment not addressed in the passage. The disagreement is methodological, not political.
Step 1 - Map the passage structure.
- Paragraph 1: Problem (no texts) → solution (Kamara turns to masks) → complication (colonial antiquarianism intervenes)
- Paragraph 2: Colonial myth described → masks collected → scholarly consensus (masks reveal more about collectors than about Mali) → Kamara's dissent (credits collectors)
Step 2 - Identify the central thread.
The passage is not only about Kamara, nor only about the colonial myth, nor only about the difficulty. It is fundamentally about how scholars relate to these objects as historical sources - the range of attitudes from the skeptical majority to Kamara's appreciative counter-stance. This is a spectrum of scholarly postures toward the evidentiary value of a category of sources (ceremonial masks) for a particular period (medieval Mali).
Step 3 - Eliminate wrong answers.
- A: The passage concerns the interpretive difficulty of existing sources, not the scarcity of sources. The problem is the intervening myth, not a shortage of material. Also, the passage is not about "women's historical lives" - that belongs to the original.
- B: The colonial myth is a complicating factor in the discussion, not the primary subject. The passage's focus is on how historians respond to the myth's effect on source interpretation.
- C (Correct): "A spectrum of scholarly postures" captures the range from the skeptical majority ("most scholars remain deeply skeptical") to Kamara's dissent ("striking departure from this consensus"). The "particular category of sources" is ceremonial masks; the "given era" is medieval Mali.
- D: Kamara's work is a central example, but the passage is not a chronicle of her efforts. It embeds her approach within a broader methodological debate. The primary concern is that debate, not the individual researcher.
- E: The passage does not recount a debate about "the lived experience of a particular demographic." The disagreement is methodological - about how to interpret sources - not about the nature of women's (or Mande) experience itself.
Explanation:
Step 1 - Locate the difficulty in the passage.
The passage states: "Between contemporary researchers and fourteenth-century Mali there intervenes a potent nineteenth-century colonial antiquarianism that sentimentalized the precolonial Sahel..." It later elaborates: "most scholars remain deeply skeptical that the original social significance of Malian masks can ever be recovered, maintaining that such artifacts now testify more faithfully to the preoccupations of nineteenth-century European collectors than to the lived realities of fourteenth-century Mande society."
Step 2 - Identify the nature of the impediment.
The difficulty is not the absence of material but the distorting lens applied by nineteenth-century collectors and ethnographers. Their "sentimentalized" and "idealized" framework of interpretation has contaminated the objects, making it difficult to see past the colonial-era overlay to the original Mande meanings. This is an interpretive context imposed during the nineteenth century.
Step 3 - Eliminate wrong answers.
- A: No relative shortage is discussed. The passage concerns the masks that were collected and preserved, not a scarcity compared to other artifacts.
- B: The passage does not suggest that scholars don't understand the production system. The problem is the colonial interpretive overlay, not ignorance of craft techniques.
- C: The passage does not present a "lack of consensus" about why the masks became prized. The colonial motivations are described with authorial confidence ("arose in part to justify..."), not as a matter of scholarly dispute. The consensus that is discussed concerns whether the masks can be interpreted, not why they were collected.
- D (Correct): The "potent nineteenth-century colonial antiquarianism" and its sentimentalizing, idealizing framework constitute precisely an "interpretive context applied during the nineteenth century" that now obstructs scholars.
- E: While the passage opens by noting an "absence of written records," this is the background condition that motivates turning to masks in the first place - not the impediment to interpretir the masks. The impediment is the colonial myth, not the pre-existing lack of texts.
Explanation:
Step 1 - Identify the consensus view.
Most scholars "remain deeply skeptical that the original social significance of Malian masks can ever be recovered" and believe the masks "now testify more faithfully to the preoccupations of nineteenth-century European collectors than to the lived realities of fourteenth-century Mande society." For the majority, the colonial myth is a near-fatal obstruction to historical interpretation.
Step 2 -Identify Kamara's dissent.
"Kamara, in a striking departure from this consensus, declines to dismiss the colonial collectors, crediting them instead with preserving objects that would otherwise have been lost to the communities whose history she seeks to reconstruct." Kamara views the collectors positively they saved the objects, enabling her historical project. This implies she believes the myth does not fatally obstruct interpretation; the objects can still yield historical insight despite their colonial provenance.
Step 3 - Pinpoint the locus of disagreement.
The disagreement is fundamentally about how much the colonial antiquarianism interferes with historical use of the masks. Most say: too much - original meaning is irrecoverable. Kamara says: not so much - the objects were preserved, and I can work with them.
Step 4 - Eliminate wrong answers.
- A (Correct): Kamara disagrees with most historians over "the degree to which this antiquarianism obstructs" the use of masks as historical sources. The majority sees severe obstruction; Kamara sees the preservation as enabling.
- B: The passage attributes the myth's emergence to justifying colonialism, not to industrialization. But even if industrialization were mentioned, there is no evidence Kamara disagrees about the cause of the myth - only about its effect on source usability.
- C: The passage does not suggest Kamara believes the myth "contains clues to the original meaning." She values the mythmakers for preserving the objects, not for providing interpretive clues embedded in the myth itself.
- D: The passage provides no basis to infer a disagreement about how "widespread" the myth was. Both Kamara and the majority would likely agree it was pervasive.
- E: Whether the myth "adequately rationalized" colonial administration is a political judgment not addressed in the passage. The disagreement is methodological, not political.
Question #10
Because direct observation of the Yellowstone magma chamber is impossible, scientists have __________ its presence from patterns of ground deformation and hydrothermal activity at the surface.
| Two Answers |
|---|
| A. corroborated |
| B. conjectured |
| C. inferred | D. documented | E. predicted |
| F. extrapolated |
Show: ::
In Sentence Equivalence, the two correct choices must result in sentences that have the same meaning.
- Inferred: This means to reach a conclusion based on evidence and reasoning rather than explicit statement. It fits perfectly: we are "inferring" the existence of the magma chamber from the ground deformation.
- Extrapolated: This means to extend the application of (a method or conclusion) to an unknown situation by assuming that existing trends will continue. In this scientific context, it implies "extending" our knowledge from surface observations to the hidden interior.
Why the Other Choices Fail
- Corroborated (A) \& Documented (D): These are "Evidence Traps." They imply that scientists have found hard, physical proof or direct records. The sentence explicitly tells us direct observation is "impossible," so these are logical contradictions.
- Conjectured (B): While scientists are "guessing" (conjecturing), this word implies a lack of evidence or a mere hunch. In a scientific context, "inferring" or "extrapolating" sounds more professional and methodological, which is what the GRE favors.
- Predicted (E): This refers to the future. The scientists are not predicting that a magma chamber will exist; they are concluding that it currently exists.
- Inferred: This means to reach a conclusion based on evidence and reasoning rather than explicit statement. It fits perfectly: we are "inferring" the existence of the magma chamber from the ground deformation.
- Extrapolated: This means to extend the application of (a method or conclusion) to an unknown situation by assuming that existing trends will continue. In this scientific context, it implies "extending" our knowledge from surface observations to the hidden interior.
Why the Other Choices Fail
- Corroborated (A) \& Documented (D): These are "Evidence Traps." They imply that scientists have found hard, physical proof or direct records. The sentence explicitly tells us direct observation is "impossible," so these are logical contradictions.
- Conjectured (B): While scientists are "guessing" (conjecturing), this word implies a lack of evidence or a mere hunch. In a scientific context, "inferring" or "extrapolating" sounds more professional and methodological, which is what the GRE favors.
- Predicted (E): This refers to the future. The scientists are not predicting that a magma chamber will exist; they are concluding that it currently exists.
Question #11
Given how outlandish their plots and how remote their settings from present-day concerns, the remarkable ________ of the ancient Greek tragedies in the modern repertory strikes many observers as deeply perplexing.
| Two Answers |
|---|
| A. ubiquity |
| B. endurance |
| C. allure | D. transience | E. durability |
| F. evanescence |
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Explanation
The sentence opens with a "Given how..." phrase that establishes two negative qualities: the plays have "outlandish" plots and "remote" settings from present-day concerns. The main clause then states that "the remarkable ______ of the ancient Greek tragedies in the modern repertory strikes many observers as deeply perplexing." The word "remarkable" signals that the blank must be a positive, surprising quality given the negative framing. Despite being outlandish and remote, the tragedies are still performed. The puzzle is their continued existence, lasting power, or sustained presence. The blank must mean lasting quality, ability to endure, or sustained survival.
The correct pair must be tight synonyms that both describe the capacity to continue existing over a long period despite adverse conditions.
- A. ubiquity - The state of being everywhere; widespread presence. While Greek tragedies might be widely performed, the sentence emphasizes their survival over time ("in the modern repertory," despite being "remote"), not their geographical spread. Incorrect.
- B. endurance - The capacity to last or withstand hardship; lasting quality; persistence. "The remarkable endurance of the ancient Greek tragedies" perfectly captures their puzzling ability to survive into the modern age despite outlandishness and remoteness. Correct.
- C. allure - Appeal, attraction, charm. While the tragedies certainly have allure, the puzzle is not their attractiveness but their survival despite being implausible and remote. Something can have allure yet not endure; something can endure without allure. Incorrect.
- D. transience - Short-livedness, fleetingness, ephemerality. This is the opposite of what the sentence requires. If the tragedies were transient, their presence in the modern repertory would not be remarkable - it would be non-existent. Incorrect.
- E. durability - The ability to withstand wear or damage; lasting quality; resilience. "The remarkable durability of the ancient Greek tragedies" produces a sentence virtually identical in meaning to the one with "endurance." Both describe their puzzling capacity to survive. Correct.
- F. evanescence - The quality of vanishing quickly; fleetingness. Like "transience," this is the opposite of the required meaning. Incorrect.
The sentence opens with a "Given how..." phrase that establishes two negative qualities: the plays have "outlandish" plots and "remote" settings from present-day concerns. The main clause then states that "the remarkable ______ of the ancient Greek tragedies in the modern repertory strikes many observers as deeply perplexing." The word "remarkable" signals that the blank must be a positive, surprising quality given the negative framing. Despite being outlandish and remote, the tragedies are still performed. The puzzle is their continued existence, lasting power, or sustained presence. The blank must mean lasting quality, ability to endure, or sustained survival.
The correct pair must be tight synonyms that both describe the capacity to continue existing over a long period despite adverse conditions.
- A. ubiquity - The state of being everywhere; widespread presence. While Greek tragedies might be widely performed, the sentence emphasizes their survival over time ("in the modern repertory," despite being "remote"), not their geographical spread. Incorrect.
- B. endurance - The capacity to last or withstand hardship; lasting quality; persistence. "The remarkable endurance of the ancient Greek tragedies" perfectly captures their puzzling ability to survive into the modern age despite outlandishness and remoteness. Correct.
- C. allure - Appeal, attraction, charm. While the tragedies certainly have allure, the puzzle is not their attractiveness but their survival despite being implausible and remote. Something can have allure yet not endure; something can endure without allure. Incorrect.
- D. transience - Short-livedness, fleetingness, ephemerality. This is the opposite of what the sentence requires. If the tragedies were transient, their presence in the modern repertory would not be remarkable - it would be non-existent. Incorrect.
- E. durability - The ability to withstand wear or damage; lasting quality; resilience. "The remarkable durability of the ancient Greek tragedies" produces a sentence virtually identical in meaning to the one with "endurance." Both describe their puzzling capacity to survive. Correct.
- F. evanescence - The quality of vanishing quickly; fleetingness. Like "transience," this is the opposite of the required meaning. Incorrect.
Question #12
The director's public image as a vacillating and ineffectual leader is, by all accounts from those who have served under her, utterly ________: colleagues describe a decisive, analytically rigorous, and unyielding figure behind closed doors.
| Two Answers |
|---|
| A. irrevocable |
| B. ubiquitous |
| C. spurious | D. rampant | E. unfounded |
| F. overblown |
Show: ::
Explanation
The sentence presents a contrast between public image and private reality. The director's "public image" is that of a "vacillating and ineffectual leader." The colon introduces the reality: colleagues describe her as "decisive, analytically rigorous, and unyielding." The phrase "by all accounts from those who have served under her" signals that firsthand testimony contradicts the public perception. The blank, modified by "utterly," must therefore mean false, baseless, or without foundation.
The correct pair must be tight synonyms that both describe something that is not true, lacks evidence, or is deceptive.
- A. irrevocable - Impossible to retract or undo; irreversible. This describes something that cannot be changed, not something that is false. A reputation can be irrevocable (fixed) yet accurate. Incorrect.
- B. ubiquitous - Present everywhere; pervasive. The sentence is about the truth-value of the reputation, not its prevalence. A reputation can be ubiquitous yet well-founded. Incorrect.
- C. spurious - Not genuine, authentic, or true; false; based on erroneous reasoning. "Utterly spurious" perfectly captures the idea that the public image is a complete falsehood, contradicted by firsthand evidence. Correct.
- D. rampant - Spreading unchecked; rife. Like "ubiquitous," this describes prevalence, not truthvalue. A reputation can be rampant yet deserved. Incorrect.
- E. unfounded - Having no foundation in fact; baseless. "Utterly unfounded" produces a sentence virtually identical in meaning to the one with "spurious." Both convey that the reputation is entirely without evidence or truth. Correct.
- F. overblown - Exaggerated; overstated. This is a strong distractor. "Overblown" means there is some truth that has been exaggerated. But the colon reveals a complete contradiction: the director is not somewhat stronger than her reputation suggests; she is its opposite - decisive where she is thought vacillating, unyielding where she is thought ineffectual. The contrast is absolute, not a matter of degree. "Spurious" and "unfounded" capture this totality; "overblown" implies partial truth. Incorrect.
The sentence presents a contrast between public image and private reality. The director's "public image" is that of a "vacillating and ineffectual leader." The colon introduces the reality: colleagues describe her as "decisive, analytically rigorous, and unyielding." The phrase "by all accounts from those who have served under her" signals that firsthand testimony contradicts the public perception. The blank, modified by "utterly," must therefore mean false, baseless, or without foundation.
The correct pair must be tight synonyms that both describe something that is not true, lacks evidence, or is deceptive.
- A. irrevocable - Impossible to retract or undo; irreversible. This describes something that cannot be changed, not something that is false. A reputation can be irrevocable (fixed) yet accurate. Incorrect.
- B. ubiquitous - Present everywhere; pervasive. The sentence is about the truth-value of the reputation, not its prevalence. A reputation can be ubiquitous yet well-founded. Incorrect.
- C. spurious - Not genuine, authentic, or true; false; based on erroneous reasoning. "Utterly spurious" perfectly captures the idea that the public image is a complete falsehood, contradicted by firsthand evidence. Correct.
- D. rampant - Spreading unchecked; rife. Like "ubiquitous," this describes prevalence, not truthvalue. A reputation can be rampant yet deserved. Incorrect.
- E. unfounded - Having no foundation in fact; baseless. "Utterly unfounded" produces a sentence virtually identical in meaning to the one with "spurious." Both convey that the reputation is entirely without evidence or truth. Correct.
- F. overblown - Exaggerated; overstated. This is a strong distractor. "Overblown" means there is some truth that has been exaggerated. But the colon reveals a complete contradiction: the director is not somewhat stronger than her reputation suggests; she is its opposite - decisive where she is thought vacillating, unyielding where she is thought ineffectual. The contrast is absolute, not a matter of degree. "Spurious" and "unfounded" capture this totality; "overblown" implies partial truth. Incorrect.
Question #13
The municipal authority of Trevania supplies potable water to all registered households within the city limits. Four years ago, with leakage from aging residential plumbing accounting for 8 percent of the city's total annual water output, the authority launched a comprehensive pipe-replacement subsidy program. Although the program demonstrably succeeded in reducing the number of households with substandard plumbing by a wide margin, it manifestly failed to curtail the annual volume of water lost to residential leakage, given that such leakage now constitutes 10 percent of the city's total annual water output.
The argument depends on which of the following being true?
A. Water lost to residential leakage represents a larger share of the municipal authority's total potable water deliveries now than it did four years ago.
B. The average volume of water lost per leaking household in Trevania has not risen markedly over the past four years.
C. Total potable water deliveries account for a larger proportion of the city's overall water output now than they did four years ago.
D. Trevania's total annual water output is not substantially smaller now than it was four years ago.
E. Plumbing deterioration severe enough to cause significant leakage typically progresses even after a household has taken advantage of the subsidy program.
Show: ::
Explanation
Step 1 - Identify the argument's logical structure.
- Goal: Reduce water lost to residential leakage ( $8 \%$ of total output).
- Action: Pipe-replacement subsidy program.
- Result: Number of households with bad plumbing dropped substantially.
- Conclusion: Program failed to reduce leakage volume.
- Evidence for conclusion: Leakage now $=10 \%$ of total water output.
Step 2 - Locate the logical gap.
The evidence is a percentage of total output. The conclusion is about absolute volume lost. A percentage can increase even while the absolute quantity decreases - if the denominator (total water output) shrinks enough. For example:
- Four years ago: Total output =1,000 million liters; Leakage =8 %=80 million liters.
- Now: Total output = 600 million liters; Leakage = 10 % = 60 million liters.
In this scenario, leakage dropped from 80 to 60 million liters (a real reduction), yet the percentage rose from 8 % to 10 % . The argument's inference - that the campaign "manifestly failed" - is invalid if total output declined.
Step 3 - Identify the necessary assumption.
For the percentage increase to validly signal a failure to reduce absolute leakage, we must assume the denominator (total annual water output) has not decreased significantly. This is choice D.
Step 4 - Eliminate wrong answers.
- A: This compares leakage as a share of potable water deliveries, not total water output. The argument's percentages are about total water output. This introduces a new category not mentioned in the argument. Even if true, it doesn't address the percentage-vs-absolute gap.
- B: The argument concerns total leakage volume, not leakage per household. Even if perhousehold leakage remained constant, total leakage could still drop if the number of leaking households dropped (which the program achieved). This is not a necessary assumption; in fact, the argument could work without it.
- C: This shifts the denominator to total water deliveries as a share of overall water output. The argument's percentages are about leakage as a share of total output, not deliveries as a share of output. Irrelevant shift of categories.
- D (Correct): If total water output shrank substantially, 10 % of a smaller total could represent less absolute leakage than 8 % of a larger total. The argument must assume this didn't happen.
- E: This suggests the program might be counteracted by ongoing deterioration. But the argument's logic is: percentage increased, therefore volume didn't decrease. This assumption about ongoing deterioration is not required for that logical move. The argument depends on the percentage meaning what the author thinks it means, not on why leakage might persist.
Step 1 - Identify the argument's logical structure.
- Goal: Reduce water lost to residential leakage ( $8 \%$ of total output).
- Action: Pipe-replacement subsidy program.
- Result: Number of households with bad plumbing dropped substantially.
- Conclusion: Program failed to reduce leakage volume.
- Evidence for conclusion: Leakage now $=10 \%$ of total water output.
Step 2 - Locate the logical gap.
The evidence is a percentage of total output. The conclusion is about absolute volume lost. A percentage can increase even while the absolute quantity decreases - if the denominator (total water output) shrinks enough. For example:
- Four years ago: Total output =1,000 million liters; Leakage =8 %=80 million liters.
- Now: Total output = 600 million liters; Leakage = 10 % = 60 million liters.
In this scenario, leakage dropped from 80 to 60 million liters (a real reduction), yet the percentage rose from 8 % to 10 % . The argument's inference - that the campaign "manifestly failed" - is invalid if total output declined.
Step 3 - Identify the necessary assumption.
For the percentage increase to validly signal a failure to reduce absolute leakage, we must assume the denominator (total annual water output) has not decreased significantly. This is choice D.
Step 4 - Eliminate wrong answers.
- A: This compares leakage as a share of potable water deliveries, not total water output. The argument's percentages are about total water output. This introduces a new category not mentioned in the argument. Even if true, it doesn't address the percentage-vs-absolute gap.
- B: The argument concerns total leakage volume, not leakage per household. Even if perhousehold leakage remained constant, total leakage could still drop if the number of leaking households dropped (which the program achieved). This is not a necessary assumption; in fact, the argument could work without it.
- C: This shifts the denominator to total water deliveries as a share of overall water output. The argument's percentages are about leakage as a share of total output, not deliveries as a share of output. Irrelevant shift of categories.
- D (Correct): If total water output shrank substantially, 10 % of a smaller total could represent less absolute leakage than 8 % of a larger total. The argument must assume this didn't happen.
- E: This suggests the program might be counteracted by ongoing deterioration. But the argument's logic is: percentage increased, therefore volume didn't decrease. This assumption about ongoing deterioration is not required for that logical move. The argument depends on the percentage meaning what the author thinks it means, not on why leakage might persist.
Question #14/15
Deploying artificial reef structures to replace lost marine habitat after seabed destruction by trawling is frequently justifiable in settings where commercial aquaculture is the overriding objective and where structurally complex benthic assemblages are historically prevalent. Yet the case for installing high-relief artificial formations in locations that never naturally supported them rests on far shakier ground. The difficulty is that such interventions reconfigure local current dynamics, and this hydrodynamic alteration in turn creates entry points for invasive sessile organisms that can destabilize the entire benthic community. These intrinsically unstable ecological configurations are defensible solely where there exist perpetual institutional commitments to actively curating the sites for intensive mariculture output. Where such commitments are absent — and they are unwarranted in any context where intensive mariculture neither aligns with conservation mandates nor proves economically viable over multi-decadal time horizons — the deployment of artificial reefs becomes ecologically reckless.
The introduction of artificial structures to establish complex habitat on trawl-damaged substrates may also prove counterproductive in light of alternative conservation priorities. Expansive, slowly recuperating, undisturbed tracts of seafloor frequently harbor considerable cryptic biodiversity. In the aftermath of submarine lava flows, for instance, certain unsalvaged and unreconstructed benthic zones have been documented to support remarkably diverse assemblages of endemic macroinvertebrates — a finding that underscores the wisdom of restraint.
The introduction of artificial structures to establish complex habitat on trawl-damaged substrates may also prove counterproductive in light of alternative conservation priorities. Expansive, slowly recuperating, undisturbed tracts of seafloor frequently harbor considerable cryptic biodiversity. In the aftermath of submarine lava flows, for instance, certain unsalvaged and unreconstructed benthic zones have been documented to support remarkably diverse assemblages of endemic macroinvertebrates — a finding that underscores the wisdom of restraint.
The passage indicates that the deployment of high-relief artificial reefs in areas where they never historically occurred requires ongoing institutional management. What is the reason offered for this necessity?
A. Such installations are prone to becoming economically unfeasible when evaluated over sufficiently long time spans.
B. Mariculture production entails a degree of technical intricacy that can only be sustained through vigilant supervision.
C. The pursuit of intensive mariculture is fundamentally at odds with the preservation of maximal benthic biodiversity.
D. The hydrodynamic changes induced by these structures can open pathways for organisms that disrupt benthic community stability.
E. Introducing artificial reefs into regions where they are no longer present constitutes an intrinsically undesirable ecological intervention.
In the passage, the word “intensive” as it appears in the phrase “intensive mariculture output” most nearly means
A. severe
B. rigorous
C. concentrated
D. scrupulous
E. resolute
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Explanation
Step 1 — Understand what the question is asking.
The question asks for the reason that ongoing institutional management is required for artificial reefs placed where they never naturally occurred. This is a causal question: what is it about these structures that necessitates perpetual management?
Step 2 — Locate the relevant causal chain in the passage.
The passage establishes this sequence:
Action: Installing high-relief artificial formations in locations that never naturally supported them.
Consequence: "such interventions reconfigure local current dynamics, and this hydrodynamic alteration in turn creates entry points for invasive sessile organisms that can destabilize the entire benthic community."
Conclusion: "These intrinsically unstable ecological configurations are defensible solely where there exist perpetual institutional commitments to actively curating the sites..."
The logic is: artificial reefs in unnatural locations cause hydrodynamic changes → those changes allow invasive species to enter → the ecosystem becomes unstable (intrinsically unstable) → therefore, constant management is required to keep the instability in check. The reason management is necessary is the invasive species risk created by the hydrodynamic alteration.
Step 3 — Match this reason to the correct answer.
Choice D states: "The hydrodynamic changes induced by these structures can open pathways for organisms that disrupt benthic community stability." This directly paraphrases the causal mechanism: hydrodynamic alteration → entry points for invasive sessile organisms → destabilization. "Open pathways" corresponds to "creates entry points"; "organisms that disrupt benthic community stability" corresponds to "invasive sessile organisms that can destabilize the entire benthic community."
Step 4 — Eliminate the wrong answers.
A (Incorrect): Economic unfeasibility is discussed in the passage, but it plays a different logical role. The passage states that a commitment to management is "unwarranted in any context where intensive mariculture neither aligns with conservation mandates nor proves economically viable." Economic unviability is a reason the management commitment may be unjustified (i.e., a reason not to deploy the reefs at all). It is not the reason the management is required once reefs are deployed. The question asks for the latter.
B (Incorrect): The passage never claims that mariculture production is technically intricate or that it demands vigilant supervision. The need for management arises from the ecological instability of the artificial reefs, not from any inherent complexity of mariculture as a practice. This is an out-of-scope distractor.
C (Incorrect): The passage notes in its second paragraph that undisturbed seafloor tracts "harbor considerable cryptic biodiversity," implying that intensive mariculture may reduce biodiversity in those areas. However, the passage does not frame this as the reason management is needed for artificial reefs. The biodiversity concern is a separate argument against deploying reefs in certain contexts (alternative conservation priorities), not the causal mechanism requiring perpetual curation.
D (Correct): As explained in Step 3.
E (Incorrect): This choice essentially restates the conclusion in different words — it is undesirable to introduce reefs where they don't belong. But the question asks for the reason management is required, not a restatement that management is required. The passage gives a specific causal mechanism (invasive species via hydrodynamic change); this answer offers only a circular judgment. It's the difference between saying "this is bad" and explaining why it's bad in a way that demands management.
Explanation
Step 1 — Identify how the word is used in context.
The phrase appears in this sentence: "These intrinsically unstable ecological configurations are defensible solely where there exist perpetual institutional commitments to actively curating the sites for intensive mariculture output."
"Intensive" here modifies "mariculture output" — it describes a mode of production. In agricultural and aquacultural terminology, "intensive" farming or mariculture refers to systems that aim for high productivity per unit area, typically through high stocking densities, substantial inputs (feed, energy, infrastructure), and active management. It contrasts with "extensive" aquaculture, which involves lower densities and relies more on natural productivity.
Step 2 — Test each answer choice in the phrase.
A — severe: "Severe mariculture output" is not idiomatic. Severe means harsh, strict, or extremely serious in a punitive or austere sense. One might speak of "severe consequences" or "severe weather," but not "severe output." The word does not fit the technical register of the passage.
B — rigorous: Rigorous means extremely thorough, meticulous, or demanding strict precision. One can have "rigorous standards" or "rigorous management," but "rigorous output" is an awkward collocation. The word describes how something is done (the process), not the density or concentration of production (the output). It misses the technical meaning.
C — concentrated: Concentrated means gathered closely together, dense, intense in a confined area. "Concentrated mariculture output" accurately captures the meaning of intensive aquaculture — high-density, high-yield production within a limited spatial footprint. This is the standard technical sense of "intensive" in agriculture and aquaculture. It fits the context precisely.
D — scrupulous: Scrupulous means having moral integrity, being extremely attentive to ethical standards, or being meticulously careful about avoiding wrongdoing. "Scrupulous mariculture output" would describe the ethical character of the production, not its productive density. This meaning is wholly absent from the passage.
E — resolute: Resolute means admirably purposeful, determined, and unwavering. "Resolute mariculture output" is nonsensical — output cannot be determined or purposeful. The word describes a human character trait, not a mode of production.
Step 1 — Understand what the question is asking.
The question asks for the reason that ongoing institutional management is required for artificial reefs placed where they never naturally occurred. This is a causal question: what is it about these structures that necessitates perpetual management?
Step 2 — Locate the relevant causal chain in the passage.
The passage establishes this sequence:
Action: Installing high-relief artificial formations in locations that never naturally supported them.
Consequence: "such interventions reconfigure local current dynamics, and this hydrodynamic alteration in turn creates entry points for invasive sessile organisms that can destabilize the entire benthic community."
Conclusion: "These intrinsically unstable ecological configurations are defensible solely where there exist perpetual institutional commitments to actively curating the sites..."
The logic is: artificial reefs in unnatural locations cause hydrodynamic changes → those changes allow invasive species to enter → the ecosystem becomes unstable (intrinsically unstable) → therefore, constant management is required to keep the instability in check. The reason management is necessary is the invasive species risk created by the hydrodynamic alteration.
Step 3 — Match this reason to the correct answer.
Choice D states: "The hydrodynamic changes induced by these structures can open pathways for organisms that disrupt benthic community stability." This directly paraphrases the causal mechanism: hydrodynamic alteration → entry points for invasive sessile organisms → destabilization. "Open pathways" corresponds to "creates entry points"; "organisms that disrupt benthic community stability" corresponds to "invasive sessile organisms that can destabilize the entire benthic community."
Step 4 — Eliminate the wrong answers.
A (Incorrect): Economic unfeasibility is discussed in the passage, but it plays a different logical role. The passage states that a commitment to management is "unwarranted in any context where intensive mariculture neither aligns with conservation mandates nor proves economically viable." Economic unviability is a reason the management commitment may be unjustified (i.e., a reason not to deploy the reefs at all). It is not the reason the management is required once reefs are deployed. The question asks for the latter.
B (Incorrect): The passage never claims that mariculture production is technically intricate or that it demands vigilant supervision. The need for management arises from the ecological instability of the artificial reefs, not from any inherent complexity of mariculture as a practice. This is an out-of-scope distractor.
C (Incorrect): The passage notes in its second paragraph that undisturbed seafloor tracts "harbor considerable cryptic biodiversity," implying that intensive mariculture may reduce biodiversity in those areas. However, the passage does not frame this as the reason management is needed for artificial reefs. The biodiversity concern is a separate argument against deploying reefs in certain contexts (alternative conservation priorities), not the causal mechanism requiring perpetual curation.
D (Correct): As explained in Step 3.
E (Incorrect): This choice essentially restates the conclusion in different words — it is undesirable to introduce reefs where they don't belong. But the question asks for the reason management is required, not a restatement that management is required. The passage gives a specific causal mechanism (invasive species via hydrodynamic change); this answer offers only a circular judgment. It's the difference between saying "this is bad" and explaining why it's bad in a way that demands management.
Explanation
Step 1 — Identify how the word is used in context.
The phrase appears in this sentence: "These intrinsically unstable ecological configurations are defensible solely where there exist perpetual institutional commitments to actively curating the sites for intensive mariculture output."
"Intensive" here modifies "mariculture output" — it describes a mode of production. In agricultural and aquacultural terminology, "intensive" farming or mariculture refers to systems that aim for high productivity per unit area, typically through high stocking densities, substantial inputs (feed, energy, infrastructure), and active management. It contrasts with "extensive" aquaculture, which involves lower densities and relies more on natural productivity.
Step 2 — Test each answer choice in the phrase.
A — severe: "Severe mariculture output" is not idiomatic. Severe means harsh, strict, or extremely serious in a punitive or austere sense. One might speak of "severe consequences" or "severe weather," but not "severe output." The word does not fit the technical register of the passage.
B — rigorous: Rigorous means extremely thorough, meticulous, or demanding strict precision. One can have "rigorous standards" or "rigorous management," but "rigorous output" is an awkward collocation. The word describes how something is done (the process), not the density or concentration of production (the output). It misses the technical meaning.
C — concentrated: Concentrated means gathered closely together, dense, intense in a confined area. "Concentrated mariculture output" accurately captures the meaning of intensive aquaculture — high-density, high-yield production within a limited spatial footprint. This is the standard technical sense of "intensive" in agriculture and aquaculture. It fits the context precisely.
D — scrupulous: Scrupulous means having moral integrity, being extremely attentive to ethical standards, or being meticulously careful about avoiding wrongdoing. "Scrupulous mariculture output" would describe the ethical character of the production, not its productive density. This meaning is wholly absent from the passage.
E — resolute: Resolute means admirably purposeful, determined, and unwavering. "Resolute mariculture output" is nonsensical — output cannot be determined or purposeful. The word describes a human character trait, not a mode of production.
