Tüm alıştırma soruları

2195 soru

Soru 2081Soru

Consider the following argument: A municipal building authority plans to replace the conventional steam radiator heating systems in its historic administrative offices with low-temperature geothermal heat pumps. The authority claims that this modification will reduce total heating expenses for these buildings over the next decade because geothermal systems consume significantly less grid electricity per unit of thermal energy delivered than electric boiler steam systems.

True or False: The argument depends on the assumption that the total cost of installing and maintaining the geothermal heat pump system over the next decade will not exceed the monetary savings gained from reduced electricity consumption.

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Cevap: True

Cevap

True. The argument logically depends on the unstated assumption that installation and maintenance costs will not negate the energy cost savings over the ten-year period.
The author infers a reduction in overall ten-year heating expenses solely from a premise establishing that geothermal systems use less electricity per unit of heat. For operational energy efficiency to lead to lower total financial expenditure over time, non-operational costs—specifically initial system purchase, installation, and routine maintenance—must not exceed the monetary value of the energy saved.

Adım Adım Çözüm

1
Identify the argument's premise and conclusion.
Premise: Geothermal heat pumps consume less electricity per unit of heat than electric boilers. Conclusion: Replacing the system will decrease total heating expenses over the next decade.
Isolating the gap between lower energy consumption and lower overall financial expenditure reveals unstated assumptions.
2
Apply the Negation Test to the candidate assumption.
Negated claim: The total cost of installing and maintaining the geothermal system over the next decade WILL exceed the savings from reduced electricity consumption.
Negating a necessary assumption tests whether the author's conclusion can survive without it.
3
Assess the logical impact of the negated statement on the author's conclusion.
If initial installation and ongoing maintenance costs outweigh energy savings, total heating expenses over ten years will increase, falsifying the conclusion.
A statement is a required unstated assumption if its logical negation renders the conclusion untenable.

Anahtar Kavram

The Negation Test for Identifying Necessary Assumptions
Soru 2082Soru

A solar micro-grid facility utilizes two distinct types of energy storage battery modules: Type-X and Type-Y. On Monday, a configuration of 4 Type-X modules and 3 Type-Y modules stored a total of 180 kWh180\text{ kWh} of energy. On Tuesday, a configuration of 2 Type-X modules and 5 Type-Y modules stored a total of 160 kWh160\text{ kWh} of energy. Assuming each battery module of a given type stores a constant amount of energy, what is the individual storage capacity of one Type-X module and one Type-Y module, respectively?

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Cevap: Type-X = 30 kWh30\text{ kWh}, Type-Y = 20 kWh20\text{ kWh}

Cevap

Type-X = 30 kWh30\text{ kWh} and Type-Y = 20 kWh20\text{ kWh}
The correct option correctly states that Type-X has a capacity of 30 kWh30\text{ kWh} and Type-Y has a capacity of 20 kWh20\text{ kWh}. Substituting these values into both equations yields 4(30)+3(20)=1804(30) + 3(20) = 180 and 2(30)+5(20)=1602(30) + 5(20) = 160, confirming both daily constraints are satisfied.

Adım Adım Çözüm

1
Formulate a system of two linear equations in two variables.
Let xx represent the capacity of one Type-X module and yy represent the capacity of one Type-Y module. The given conditions translate to:
Equation (1): 4x+3y=1804x + 3y = 180
Equation (2): 2x+5y=1602x + 5y = 160
Simultaneous word problems require establishing algebraic equations representing total quantities for each scenario.
2
Eliminate variable xx by multiplying Equation (2) by 2.
Equation (2) multiplied by 2 becomes:
Equation (3): 4x+10y=3204x + 10y = 320
Aligning coefficients of xx enables linear elimination.
3
Subtract Equation (1) from Equation (3) to solve for yy.
(4x+10y)(4x+3y)=320180    7y=140    y=20(4x + 10y) - (4x + 3y) = 320 - 180 \implies 7y = 140 \implies y = 20
Subtracting the equations eliminates xx, producing a single variable equation in yy.
4
Substitute y=20y = 20 back into Equation (1) to find xx.
4x+3(20)=180    4x+60=180    4x=120    x=304x + 3(20) = 180 \implies 4x + 60 = 180 \implies 4x = 120 \implies x = 30
Determining the remaining unknown variable.

Anahtar Kavram

Solving Systems of Linear Equations in Two Variables
Soru 2083Soru

A municipal utility operates three water desalination plants—Plant Alpha, Plant Beta, and Plant Gamma—to process seawater into purified drinking water. Each plant operates at a constant total intake rate of seawater and yields a specific percentage of brine byproduct, with the remainder converted to purified drinking water:

- Plant Alpha: Total intake rate of 40,00040,000 gallons per hour; 15%15\% of intake becomes brine byproduct.
- Plant Beta: Total intake rate of 60,00060,000 gallons per hour; 10%10\% of intake becomes brine byproduct.
- Plant Gamma: Total intake rate of 50,00050,000 gallons per hour; 20%20\% of intake becomes brine byproduct.

Match each operational metric on the left with its corresponding calculated value on the right.

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Öğeler

The combined purified drinking water output rate of Plant Alpha and Plant Beta operating simultaneously (in thousands of gallons per hour).
The ratio of the total volume of brine byproduct produced by Plant Alpha in 55 hours to the total volume of brine byproduct produced by Plant Gamma in 44 hours.
The total operational time (in hours) required for Plant Beta to produce the exact volume of purified drinking water that Plant Gamma produces in 99 hours.

Eşleşmeler

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Cevap

The operational metrics match as follows: the combined output rate of Plant Alpha and Plant Beta is 8888 thousand gallons per hour; the ratio of brine byproduct volume produced by Plant Alpha (in 5 hours) to Plant Gamma (in 4 hours) is 3:43 : 4; and the time required for Plant Beta to equal Plant Gamma's 9-hour purified output is 203\frac{20}{3} hours.
Each calculation requires decomposing total plant intake into its constituent components (purified water and brine byproduct) using given percentages, followed by executing standard work-rate and ratio operations (R×T=WR \times T = W). The resulting values match 8888 thousand gallons per hour, 3:43 : 4, and 203\frac{20}{3} hours respectively.

Adım Adım Çözüm

1
Calculate individual rates for purified drinking water and brine byproduct for each plant.
Plant Alpha: Purified = 0.85×40=340.85 \times 40 = 34 k gal/hr, Brine = 0.15×40=60.15 \times 40 = 6 k gal/hr. Plant Beta: Purified = 0.90×60=540.90 \times 60 = 54 k gal/hr, Brine = 0.10×60=60.10 \times 60 = 6 k gal/hr. Plant Gamma: Purified = 0.80×50=400.80 \times 50 = 40 k gal/hr, Brine = 0.20×50=100.20 \times 50 = 10 k gal/hr.
Deconstructing the total intake rates into purified water rates and byproduct rates allows direct substitution into each multi-part question.
2
Sum the purified drinking water rates of Plant Alpha and Plant Beta.
Combined purified rate = 34+54=8834 + 54 = 88 thousand gallons per hour.
When two plants operate simultaneously, their effective production rates add together.
3
Compute total brine output for Plant Alpha in 5 hours and Plant Gamma in 4 hours, then simplify the resulting ratio.
Alpha brine volume = 6×5=306 \times 5 = 30 thousand gallons. Gamma brine volume = 10×4=4010 \times 4 = 40 thousand gallons. Ratio = 30:40=3:430 : 40 = 3 : 4.
Total volume equals hourly rate multiplied by operational duration.
4
Find total purified output of Plant Gamma in 9 hours, and divide by Plant Beta's hourly purified rate.
Gamma purified total = 40×9=36040 \times 9 = 360 thousand gallons. Required time for Beta = 36054=203\frac{360}{54} = \frac{20}{3} hours.
Time equals total required volume divided by the rate of production.

Anahtar Kavram

Work rates and percent composition decomposition in multi-unit processing systems.
Tahmini Süre:2m 30s
Soru 2084Soru

A freight logistics firm installed automated route-optimization software across its fleet in Region X while simultaneously introducing a new financial bonus for drivers who voluntarily reduce engine idling time. Over the following six months, fuel consumption per delivery dropped by 18%, and fleet idle time decreased significantly. Executive management concluded that the installation of the route-optimization software was the primary cause of the reduction in fuel consumption. Which of the following statements, if true, provides the strongest counterargument to management's conclusion by identifying an alternative causal explanation?

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Cevap: The financial bonus incentivized drivers to turn off engines during waiting periods, accounting for the reduced idle time and lower fuel consumption independently of the software.

Cevap

The statement that driver financial bonuses incentivized engine shutdown provides the strongest counterargument by introducing an alternative cause for the reduced fuel consumption.
The argument concludes that the software caused the drop in fuel consumption. However, the stem notes that financial bonuses for reducing idling time were introduced simultaneously. Pointing out that these bonuses directly incentivized lower idling and lower fuel use presents a compelling alternative explanation, showing that the outcome could have occurred regardless of the software.

Adım Adım Çözüm

1
Identify the causal claim in the argument stem.
Management claims that introducing route-optimization software (Cause) directly led to an 18% reduction in fuel consumption (Effect).
Understanding the precise cause-and-effect structure is essential before evaluating potential flaws or weak points in the reasoning.
2
Analyze concurrent events and potential confounding variables.
The company introduced two simultaneous changes: route-optimization software AND financial bonuses for reducing engine idling time.
When two potential causes are introduced at the same time, attributing the outcome solely to one cause without isolating variables commits a causal flaw.
3
Select the option that offers a valid alternative explanation for the observed outcome.
Attributing the reduced fuel consumption to the idling bonuses presents a direct, plausible alternative cause, neutralizing the conclusion that the software was the primary driver.
A causal argument is weakened when the observed outcome can be fully explained by an alternate independent factor.

Anahtar Kavram

Evaluating Alternative Causal Explanations and Confounding Variables
Soru 2085Soru

A semiconductor manufacturing facility operates two models of photolithography equipment: Model D and Model E. Over a 10-hour operational cycle, each Model D scanner consumes 400 kWh400\text{ kWh} of energy and processes 600600 silicon wafers, while each Model E scanner consumes 1,200 kWh1,200\text{ kWh} of energy and processes 1,0001,000 silicon wafers. If the combined fleet consumed a total of 9,600 kWh9,600\text{ kWh} of energy and processed 10,40010,400 wafers over the cycle, which of the following correctly identifies the number of Model D scanners and Model E scanners operated by the facility?

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Cevap: 9 Model D scanners and 5 Model E scanners

Cevap

9 Model D scanners and 5 Model E scanners
The correct answer states 9 Model D scanners and 5 Model E scanners. Setting up the system d+3e=24d + 3e = 24 (energy) and 3d+5e=523d + 5e = 52 (production) and solving by substitution gives e=5e = 5 and d=9d = 9, which uniquely satisfies both constraints.

Adım Adım Çözüm

1
Define variables and establish equations based on given rates and totals.
Let dd be the number of Model D scanners and ee be the number of Model E scanners.
Energy equation: 400d+1200e=9600400d + 1200e = 9600
Wafer equation: 600d+1000e=10400600d + 1000e = 10400
Translate the physical constraints into a system of two linear equations.
2
Simplify both linear equations by dividing by their greatest common divisors.
Dividing the energy equation by 400400 gives:
d+3e=24— (Equation 1)d + 3e = 24 \quad \text{--- (Equation 1)}
Dividing the wafer equation by 200200 gives:
3d+5e=52— (Equation 2)3d + 5e = 52 \quad \text{--- (Equation 2)}
Simplifying constants reduces calculation complexity and prevents arithmetic errors.
3
Solve the system using substitution or elimination.
From Equation 1, express dd in terms of ee:
d=243ed = 24 - 3e
Substitute this expression into Equation 2:
3(243e)+5e=523(24 - 3e) + 5e = 52
729e+5e=5272 - 9e + 5e = 52
724e=5272 - 4e = 52
4e=20    e=54e = 20 \implies e = 5
Now calculate dd:
d=243(5)=2415=9d = 24 - 3(5) = 24 - 15 = 9
Isolating one variable yields exact values for both equipment models.
4
Verify values against both constraints.
Energy: 400(9)+1200(5)=3600+6000=9600 kWh400(9) + 1200(5) = 3600 + 6000 = 9600\text{ kWh}
Wafers: 600(9)+1000(5)=5400+5000=10400 wafers600(9) + 1000(5) = 5400 + 5000 = 10400\text{ wafers}
Ensures the solution satisfies both independent constraints simultaneously.

Anahtar Kavram

Simultaneous Linear Equations in Two Variables
Soru 2086Soru

In response to high-profile accounting scandals, regulatory bodies increasingly mandate clawback provisions that require publicly traded firms to recoup executive bonuses if financial results are subsequently restated due to material noncompliance. Proponents argue that such provisions align managerial incentives with reporting accuracy by penalizing opportunistic accounting. However, empirical studies examining corporate financial reporting following the adoption of mandatory clawbacks reveal an unexpected shift in executive behavior. While formal financial restatements—specifically those resulting from deliberate accounting irregularities—decreased significantly, firms subject to clawback mandates exhibited a marked increase in the use of aggressive non-GAAP (Generally Accepted Accounting Principles) earnings adjustments.

Corporate governance analysts attribute this divergence to the precise legal trigger of clawback enforcement. Because clawback mechanisms are typically activated only by explicit restatements of audited GAAP financial statements, executives seeking to inflate perceived performance divert their reporting discretion toward non-GAAP metrics, which fall outside the scope of traditional clawback triggers. Furthermore, auditor scrutiny remains primarily concentrated on GAAP compliance, leaving non-GAAP reconciliations subject to less rigorous oversight. Consequently, while mandatory clawbacks successfully deter explicit GAAP violations, they inadvertently incentivize executives to channel reporting bias into less regulated reporting avenues, thereby altering the form rather than the substance of aggressive financial reporting.

Which of the following inferences regarding corporate executive compensation and financial reporting is most strongly supported by the passage?

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Cevap: An executive who inflates perceived corporate earnings exclusively through aggressive non-GAAP adjustments would generally avoid triggering mandatory bonus recoupment under traditional clawback provisions.

Cevap

An executive who inflates perceived corporate earnings exclusively through aggressive non-GAAP adjustments would generally avoid triggering mandatory bonus recoupment under traditional clawback provisions.
The passage states that traditional clawback mechanisms are activated exclusively by explicit restatements of audited GAAP statements, and that non-GAAP metrics fall outside the scope of these triggers. Therefore, if an executive inflates earnings using only non-GAAP adjustments without restating GAAP statements, the explicit condition required to trigger bonus recoupment is not met.

Adım Adım Çözüm

1
Identify the explicit premises in the passage regarding clawback triggers.
The text states that clawback mechanisms are activated only by explicit restatements of audited GAAP statements and that non-GAAP metrics fall outside the scope of traditional clawback triggers.
Establishing the precise boundary of clawback activation is necessary to derive a valid logical inference.
2
Evaluate the logical consequence of using non-GAAP adjustments exclusively.
Because non-GAAP adjustments do not constitute explicit GAAP restatements, engaging solely in non-GAAP manipulation does not activate the legal trigger required to recoup executive bonuses.
Connecting the legal trigger condition to executive behavior yields a provable claim without requiring external assumptions.

Anahtar Kavram

Drawing Logical Inferences from Passage Premises
Tahmini Süre:2m 0s
Soru 2087Soru

To reduce water waste, a major agricultural cooperative plans to equip all member farms with automated soil-moisture sensors that trigger irrigation only when soil moisture falls below a critical threshold. The cooperative claims that implementing this system across all member farms will significantly decrease total regional water consumption for agricultural irrigation over the next five years.

Which of the following is an assumption on which the agricultural cooperative's claim depends?

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Cevap: Farmers participating in the cooperative will not substantially expand their irrigated crop acreage in response to the water savings provided by the sensors.

Cevap

The argument depends on assuming that farmers participating in the cooperative will not substantially expand their irrigated crop acreage in response to the water savings provided by the sensors.
The argument relies on a leap from per-farm technological efficiency to a net decrease in total regional water volume. The correct answer identifies a necessary assumption regarding farm behavior: if farmers respond to per-acre water savings by expanding their total irrigated crop acreage, the volume of water consumed across the expanded cropland could offset any efficiency gains. Negating this choice shatters the author's conclusion, proving it is a required unstated assumption.

Adım Adım Çözüm

1
Identify the argument structure (premises and conclusion)
Premise: Automated soil-moisture sensors irrigate only when soil moisture drops below a threshold. Conclusion: Implementing this system across all member farms will decrease total regional water consumption for agricultural irrigation.
Understanding the logic gap between sensor-level efficiency and total regional water volume is required to locate the unstated assumption.
2
Identify potential logical gaps or rebound effects
Per-acre efficiency gains might be cancelled out if total cultivated area increases (a classic rebound effect).
Total volume consumed depends on both per-acre usage rate and total acres irrigated.
3
Apply the Negation Test to the correct option
Negated statement: 'Farmers WILL substantially expand their irrigated crop acreage in response to water savings.' If acreage expands, total water used across the larger area could equal or exceed original levels, causing the conclusion to collapse.
A statement is a necessary assumption if its logical negation invalidates the argument's conclusion.

Anahtar Kavram

Negation Test for Unstated Assumptions
Soru 2088Soru

Consider the following argument:

A regional port authority plans to replace all diesel-powered cargo cranes with hydrogen fuel-cell cranes to achieve a net reduction in total carbon emissions within its maritime operating region. Critics point out that producing hydrogen fuel requires substantial electrical energy, which can generate significant carbon emissions depending on the source.

Statement to evaluate: The port authority's argument relies on the unstated assumption that the electricity used to produce the hydrogen fuel will not generate carbon emissions equal to or greater than the emissions saved by eliminating the diesel cranes.

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Cevap: True

Cevap

True. The statement represents a necessary unstated assumption required for the port authority's conclusion to hold logically.
The statement accurately identifies a necessary unstated assumption. For the port authority to conclude that switching fuel types yields a net overall reduction in atmospheric carbon emissions, the upstream emissions created during hydrogen fuel generation must not offset or surpass the downstream emissions saved at the dock. Negating this statement directly invalidates the claim of a net reduction.

Adım Adım Çözüm

1
Deconstruct the argument structure
Premise: Diesel cranes are being replaced with hydrogen fuel-cell cranes. Premise: Hydrogen production requires electricity that may emit carbon. Conclusion: The transition will achieve a net reduction in carbon emissions.
Identifying the explicit premises and conclusion isolates the gap between the action taken and the intended outcome.
2
Apply the Negation Test to the evaluated statement
Negated claim: Electricity generation for hydrogen fuel production will produce carbon emissions equal to or greater than the emissions eliminated from diesel cranes.
Logical negation of a valid underlying assumption must invalidate the argument's conclusion.
3
Evaluate the impact of the negated statement on the conclusion
If off-site hydrogen production emissions match or exceed on-site diesel savings, the overall regional carbon footprint does not decrease.
The conclusion of a net reduction becomes logically impossible, proving the original statement is a necessary assumption.

Anahtar Kavram

Negation Test for Unstated Assumptions
Soru 2089Soru

Passage:
In abyssal benthic ecosystems, hydrothermal vent archaea rely on chemolithoautotrophy, oxidizing reduced sulfur compounds to fix inorganic carbon in total darkness. Recent biochemical studies of Pyrococcus isolates from the Mid-Atlantic Ridge demonstrate that these microorganisms express modified hydrogenase enzymes whose catalytic efficiency peaks only at hydrostatic pressures exceeding 30 megapascals (MPa). When cultured at atmospheric pressure (0.1 MPa) while maintaining identical temperature and nutrient concentrations, the enzymatic turnover rate drops by over 90 percent due to structural destabilization of the enzyme's active site. Furthermore, while surface-dwelling sulfur-oxidizing bacteria utilize heat-shock proteins to maintain enzyme integrity during thermal spikes, Pyrococcus isolates lack the genes encoding these specific heat-shock chaperones, relying instead on pressure-induced conformational rigidity to prevent thermal denaturation.

Statement: Based on the passage, Pyrococcus enzymes are more vulnerable to thermal denaturation when exposed to thermal spikes at atmospheric pressure than when exposed to the same thermal spikes under high hydrostatic pressure.

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Cevap: True

Cevap

True
The statement logically follows from the premises in the text. The passage establishes that Pyrococcus isolates do not possess heat-shock chaperone genes and instead rely entirely on pressure-induced conformational rigidity to guard against thermal denaturation. At atmospheric pressure, hydrostatic pressure is insufficient to induce this rigidity, resulting in structural destabilization. Consequently, during a thermal spike at atmospheric pressure, the enzymes lack both chaperones and pressure-induced rigidity, rendering them more vulnerable to thermal denaturation than they would be under high hydrostatic pressure.

Adım Adım Çözüm

1
Identify the mechanism that protects Pyrococcus enzymes from thermal denaturation.
The passage specifies that Pyrococcus isolates lack heat-shock chaperones and depend on pressure-induced conformational rigidity to prevent thermal denaturation.
Understanding the protective mechanism is necessary to evaluate enzyme stability under different physical conditions.
2
Analyze the structural state of the enzymes at atmospheric pressure.
At atmospheric pressure (0.1 MPa), pressure-induced conformational rigidity is lost, causing structural destabilization.
Determining whether protective rigidity exists at low pressure establishes the enzyme's baseline vulnerability.
3
Deduce relative vulnerability to thermal denaturation under atmospheric versus high hydrostatic pressure.
Because Pyrococcus lacks heat-shock chaperones and loses pressure-induced conformational rigidity at atmospheric pressure, its enzymes are more susceptible to thermal denaturation at atmospheric pressure than under high hydrostatic pressure.
Linking the absence of pressure-induced rigidity to increased vulnerability during thermal spikes validates the statement as a necessary logical inference.

Anahtar Kavram

Drawing necessary logical inferences from explicit passage premises.
Soru 2090Soru

To meet new regional environmental targets, Apex Airways plans to replace conventional jet fuel across its entire short-haul fleet with synthetic fuel manufactured from captured atmospheric carbon dioxide. The airline's executives claim that implementing this plan will reduce Apex Airways' overall annual net carbon emissions by at least 30 percent over the next two years. They point out that burning synthetic fuel releases only the carbon dioxide previously extracted from the atmosphere during its production. Which of the following is an assumption on which the executives' claim depends?

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Cevap: The electricity used in the synthesis of the new fuel does not generate carbon emissions that offset a substantial portion of the net emissions reduction achieved during flights.

Cevap

The argument depends on assuming that the electricity used to synthesize the fuel does not generate emissions that negate the expected carbon reduction.
The argument concludes that Apex Airways will achieve a 30 percent net reduction in carbon emissions by switching to synthetic fuel. The premise notes that burning synthetic fuel adds no net carbon because it releases only captured atmospheric carbon. However, if the manufacturing process itself relies on electricity generated from high-emissions sources (such as coal or natural gas), the overall carbon footprint across the lifecycle of the fuel could offset the flight-stage savings. Therefore, the executives must assume that energy used in production does not negate these savings.

Adım Adım Çözüm

1
Identify the argument's premises and conclusion.
Premise: Synthetic fuel releases only previously captured CO2 when burned. Conclusion: Overall annual net carbon emissions of the airline will drop by at least 30%.
Understanding the precise leap from premise to conclusion highlights logical gaps.
2
Locate the logical gap in the lifecycle of the synthetic fuel.
The argument focuses strictly on the flight phase (combustion) and atmospheric extraction, but overlooks the energy inputs required during the fuel synthesis process.
If producing the fuel requires high-carbon energy, total net emissions could remain unchanged or increase.
3
Apply the Negation Test to the correct option.
Negating the statement yields: 'The electricity used in manufacturing DOES generate emissions that offset a substantial portion of the net emissions reduction.' This completely shatters the conclusion.
A required assumption must cause the conclusion to collapse when logically negated.

Anahtar Kavram

Identifying Unstated Assumptions using the Negation Test
Soru 2091Soru

A regional logistics node routes cargo containers through a three-stage automated sorting process (k=1,2,3k = 1, 2, 3). At the start of Stage 1 (state k=0k = 0), the node holds V0=120V_0 = 120 heavy units and W0=80W_0 = 80 light units. For each stage k{1,2,3}k \in \{1, 2, 3\}, the counts of heavy units (VkV_k) and light units (WkW_k) transition according to the following rules:

- Vk=12Vk1+20V_k = \frac{1}{2} V_{k-1} + 20
- Wk=Wk1+14Vk110W_k = W_{k-1} + \frac{1}{4} V_{k-1} - 10

Which of the following statements regarding the state of the cargo units across these three stages are correct?

Geçerli olan tümünü seçin

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Cevap: At the end of Stage 2 (k=2k = 2), the number of light units is 110110.; The total number of units (heavy plus light) at the end of Stage 3 (k=3k = 3) is 165165.

Cevap

The correct statements are that at the end of Stage 2 (k=2k = 2), the number of light units is 110110, and the total number of units (heavy plus light) at the end of Stage 3 (k=3k = 3) is 165165.
Evaluating the multi-stage updates step by step shows that at Stage 2 (k=2k=2), W2=110W_2 = 110, making the statement about 110 light units at Stage 2 correct. At Stage 3 (k=3k=3), V3=50V_3 = 50 and W3=115W_3 = 115, giving a total of 50+115=16550 + 115 = 165 units, making the total unit statement at Stage 3 correct.

Adım Adım Çözüm

1
Calculate state values at the end of Stage 1 (k=1k = 1)
V1=12(120)+20=80V_1 = \frac{1}{2}(120) + 20 = 80; W1=80+14(120)10=100W_1 = 80 + \frac{1}{4}(120) - 10 = 100. Total units T1=80+100=180T_1 = 80 + 100 = 180.
Apply the given transition rules to initial values V0=120V_0 = 120 and W0=80W_0 = 80.
2
Calculate state values at the end of Stage 2 (k=2k = 2)
V2=12(80)+20=60V_2 = \frac{1}{2}(80) + 20 = 60; W2=100+14(80)10=110W_2 = 100 + \frac{1}{4}(80) - 10 = 110. Total units T2=60+110=170T_2 = 60 + 110 = 170.
Apply transition rules to V1=80V_1 = 80 and W1=100W_1 = 100.
3
Calculate state values at the end of Stage 3 (k=3k = 3)
V3=12(60)+20=50V_3 = \frac{1}{2}(60) + 20 = 50; W3=110+14(60)10=115W_3 = 110 + \frac{1}{4}(60) - 10 = 115. Total units T3=50+115=165T_3 = 50 + 115 = 165.
Apply transition rules to V2=60V_2 = 60 and W2=110W_2 = 110.
4
Evaluate each candidate statement against the computed values
Statement regarding light units being 110 at Stage 2 is TRUE (W2=110W_2 = 110). Statement regarding total units being 165 at Stage 3 is TRUE (T3=165T_3 = 165). All other statements are false.
Compare calculated stage states directly with the statement claims.

Anahtar Kavram

Sequential state transitions involve iteratively updating state variables through defined algebraic relationships across multiple stages.
Soru 2092Soru

A large public university introduced interactive virtual laboratory simulations across its online introductory physics courses to address high course drop rates. In the semester following the introduction of these simulations, overall course completion rates increased by 22%22\%, and average student ratings for course engagement doubled. The university administration concluded that the interactive virtual laboratory simulations directly caused the increase in student retention by helping students visualize complex physical concepts.

Select the statement that most strongly supports the university administration's causal conclusion, and select the statement that most strongly undermines it. Make exactly one selection in each column.

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Öğeler

Statement that most strongly SUPPORTS the causal conclusion
Statement that most strongly UNDERMINES the causal conclusion

Eşleşmeler

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Cevap

The statement that most strongly supports the conclusion is the concurrent trial showing higher retention in sections with virtual simulations compared to identical sections without them taught by the same instructors. The statement that most strongly undermines the conclusion is that the university lowered the minimum passing score from 70%70\% to 55%55\% at the start of the semester.
To support the causal claim, we need evidence isolating the virtual labs as the factor driving retention. The controlled comparison between sections with and without simulations taught by the same instructors directly reinforces the causal connection. To undermine the causal claim, we need an alternative factor that explains the higher completion rates; lowering the passing grade threshold from 70%70\% to 55%55\% provides a direct alternative explanation for why more students completed the course.

Adım Adım Çözüm

1
Identify the author's core causal claim
Claim: Interactive virtual laboratory simulations directly caused the 22%22\% increase in student course completion rates.
Evaluating support or weakness requires isolating the explicit cause (virtual labs) and effect (completion rate increase).
2
Evaluate candidate statements to find the strong supporter
The statement comparing identical sections with and without simulations taught by the same instructors isolates the virtual lab variable, eliminating instructor bias and external temporal factors.
Controlled comparison directly strengthens a causal link by demonstrating that the effect occurs when the cause is present and does not occur to the same degree when the cause is absent.
3
Evaluate candidate statements to find the strong underminer
The statement regarding lowering the passing grade from 70%70\% to 55%55\% introduces an obvious alternative explanation for why completion rates rose.
Introducing a viable alternative cause for the observed outcome weakens the argument that the virtual labs were responsible for the increase.

Anahtar Kavram

Causal Arguments and Alternative Explanations in Two-Part Analysis
Soru 2093Soru

A institutional review board classifies biomedical research protocols into three oversight streams based on two parameters: Participant Risk Level (High, Medium, or Low) and Data Integrity Score (SS, where 0S1000 \le S \le 100). The classification is governed by the following strict hierarchy of rules:

1. Full Board Audit: Assigned if the protocol has a High Participant Risk Level OR a Data Integrity Score of S<60S < 60.
2. Expedited Committee Review: Assigned if the protocol does not require a Full Board Audit AND meets at least one of the following conditions: Medium Participant Risk Level OR a Data Integrity Score in the range 60S8060 \le S \le 80.
3. Administrative Exemption: Assigned to any protocol that does not meet the criteria for either Full Board Audit or Expedited Committee Review (i.e., Low Participant Risk Level AND S>80S > 80).

Four trial protocols are currently under review:
- Protocol 101: Medium Participant Risk; S=55S = 55
- Protocol 102: High Participant Risk; S=85S = 85
- Protocol 103: Low Participant Risk; S=75S = 75
- Protocol 104: Low Participant Risk; S=90S = 90

Match each research protocol to its specific oversight stream classification.

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Öğeler

Protocol 101 (Medium Risk; S=55S = 55)
Protocol 102 (High Risk; S=85S = 85)
Protocol 103 (Low Risk; S=75S = 75)
Protocol 104 (Low Risk; S=90S = 90)

Eşleşmeler

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Cevap

Protocol 101 matches Full Board Audit triggered by S<60S < 60; Protocol 102 matches Full Board Audit triggered by High Risk; Protocol 103 matches Expedited Committee Review; Protocol 104 matches Administrative Exemption.
Each protocol must be evaluated strictly sequentially according to the rule hierarchy: Full Board Audit criteria first, then Expedited Committee Review criteria, and finally Administrative Exemption criteria.

Adım Adım Çözüm

1
Evaluate Rule 1 (Full Board Audit criteria) for all protocols
Protocol 101 meets S<60S < 60 (S=55S = 55). Protocol 102 meets High Participant Risk. Both are assigned to Full Board Audit.
Rule 1 is evaluated first in the hierarchy. Any protocol meeting either High Risk or S<60S < 60 is classified under Full Board Audit.
2
Evaluate Rule 2 (Expedited Committee Review criteria) for remaining protocols
Protocol 103 has Low Risk and S=75S = 75, which satisfies 60S8060 \le S \le 80. It is assigned to Expedited Committee Review.
Protocol 103 did not meet Rule 1 criteria, so Rule 2 is evaluated next.
3
Evaluate Rule 3 (Administrative Exemption criteria) for remaining protocols
Protocol 104 has Low Risk and S=90>80S = 90 > 80, satisfying Administrative Exemption.
Protocol 104 does not meet Rule 1 or Rule 2 criteria, defaulting to Rule 3.

Anahtar Kavram

Multi-attribute categorical classification governed by strict hierarchical decision rules.
Soru 2094Soru

A hybrid microgrid power station generates electricity using Solar Array S and Wind Turbine W. In Month 1, the ratio of the energy output produced by Solar Array S to that produced by Wind Turbine W was 4:34 : 3.

In Month 2, the energy output of Solar Array S increased by 30%30\% relative to Month 1, while the energy output of Wind Turbine W increased by 10%10\% relative to Month 1. The total energy output produced by both sources combined in Month 2 was 1,700 MWh1,700\text{ MWh}.

Based on the information provided, which of the following options correctly pairs the energy output of Solar Array S in Month 1 (Column 1) with the energy output of Wind Turbine W in Month 2 (Column 2)?

Cevabı ve açıklamayı göster

Cevap: Column 1: 800 MWh; Column 2: 660 MWh

Cevap

Column 1: 800 MWh; Column 2: 660 MWh
The option specifying Column 1 as 800 MWh and Column 2 as 660 MWh correctly identifies the Month 1 Solar Array S output (4×200=800 MWh4 \times 200 = 800\text{ MWh}) and the Month 2 Wind Turbine W output (3.3×200=660 MWh3.3 \times 200 = 660\text{ MWh}).

Adım Adım Çözüm

1
Define variables based on Month 1 ratio
Let Month 1 output for Solar Array S be S1=4xS_1 = 4x and for Wind Turbine W be W1=3xW_1 = 3x.
The given ratio of Solar output to Wind output in Month 1 is 4:34 : 3.
2
Express Month 2 outputs in terms of xx
S2=4x×(1+0.30)=5.2xS_2 = 4x \times (1 + 0.30) = 5.2x and W2=3x×(1+0.10)=3.3xW_2 = 3x \times (1 + 0.10) = 3.3x.
Solar output increased by 30%30\% and Wind output increased by 10%10\% in Month 2.
3
Set up and solve the total output equation for Month 2
5.2x+3.3x=8.5x=1,700    x=200 MWh5.2x + 3.3x = 8.5x = 1,700 \implies x = 200\text{ MWh}.
The combined Month 2 output is given as 1,700 MWh1,700\text{ MWh}.
4
Calculate the target quantities for Column 1 and Column 2
Column 1 (S1S_1) = 4×200=800 MWh4 \times 200 = 800\text{ MWh}; Column 2 (W2W_2) = 3.3×200=660 MWh3.3 \times 200 = 660\text{ MWh}.
Column 1 asks for Solar output in Month 1, and Column 2 asks for Wind output in Month 2.

Anahtar Kavram

Two-Part Rate and Ratio Analysis with Multi-Stage Percentage Changes
Tahmini Süre:2m 30s
Soru 2095Soru

A subscription service evaluates customer activity over a three-month period (k=1,2,3k = 1, 2, 3). At the end of each month kk, a customer's total loyalty points PkP_k update based on their points from the previous month Pk1P_{k-1} and the net points earned during month kk (Δk\Delta_k), according to the state transition rule:

Pk=0.8×Pk1+ΔkP_k = \lfloor 0.8 \times P_{k-1} \rfloor + \Delta_k

where x\lfloor x \rfloor represents the greatest integer less than or equal to xx.

At the end of Month 3 (k=3k = 3), membership tiers are assigned based on final points P3P_3:
- VIP Tier: P3150P_3 \ge 150
- Premium Tier: 80P3<15080 \le P_3 < 150
- Standard Tier: P3<80P_3 < 80

Match each initial customer profile (defined by initial points P0P_0 and monthly additions Δ1,Δ2,Δ3\Delta_1, \Delta_2, \Delta_3) to its corresponding final state at the end of Month 3.

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Öğeler

Profile 1: P0=100P_0 = 100; additions Δ1=50,Δ2=10,Δ3=40\Delta_1 = 50, \Delta_2 = 10, \Delta_3 = 40
Profile 2: P0=150P_0 = 150; additions Δ1=30,Δ2=40,Δ3=50\Delta_1 = 30, \Delta_2 = 40, \Delta_3 = 50
Profile 3: P0=90P_0 = 90; additions Δ1=0,Δ2=10,Δ3=20\Delta_1 = 0, \Delta_2 = 10, \Delta_3 = 20
Profile 4: P0=200P_0 = 200; additions Δ1=0,Δ2=10,Δ3=30\Delta_1 = 0, \Delta_2 = 10, \Delta_3 = 30

Eşleşmeler

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Cevap

Profile 1 matches Final Points: 131 (Premium Tier); Profile 2 matches Final Points: 178 (VIP Tier); Profile 3 matches Final Points: 73 (Standard Tier); Profile 4 matches Final Points: 140 (Premium Tier).
Each profile is evaluated by computing the exact state update Pk=0.8Pk1+ΔkP_k = \lfloor 0.8 \cdot P_{k-1} \rfloor + \Delta_k sequentially over three transitions. Profile 1 yields 131 points (Premium Tier), Profile 2 yields 178 points (VIP Tier), Profile 3 yields 73 points (Standard Tier), and Profile 4 yields 140 points (Premium Tier).

Adım Adım Çözüm

1
Apply the state transition formula Pk=0.8×Pk1+ΔkP_k = \lfloor 0.8 \times P_{k-1} \rfloor + \Delta_k iteratively across months k=1,2,3k = 1, 2, 3 for Profile 1.
P1=80+50=130P_1 = 80 + 50 = 130; P2=104+10=114P_2 = 104 + 10 = 114; P3=91+40=131P_3 = 91 + 40 = 131. Tier: Premium.
Tracking sequential updates ensures each intermediate decay and point addition step is accounted for accurately.
2
Apply the state transition formula iteratively across months k=1,2,3k = 1, 2, 3 for Profile 2.
P1=120+30=150P_1 = 120 + 30 = 150; P2=120+40=160P_2 = 120 + 40 = 160; P3=128+50=178P_3 = 128 + 50 = 178. Tier: VIP.
Continuous accumulation and decay calculation determines the final state threshold reached.
3
Apply the state transition formula iteratively across months k=1,2,3k = 1, 2, 3 for Profile 3.
P1=72+0=72P_1 = 72 + 0 = 72; P2=57+10=67P_2 = 57 + 10 = 67; P3=53+20=73P_3 = 53 + 20 = 73. Tier: Standard.
Floor function truncation must be evaluated at each step prior to adding monthly points.
4
Apply the state transition formula iteratively across months k=1,2,3k = 1, 2, 3 for Profile 4.
P1=160+0=160P_1 = 160 + 0 = 160; P2=128+10=138P_2 = 128 + 10 = 138; P3=110+30=140P_3 = 110 + 30 = 140. Tier: Premium.
Evaluating high starting values shows how retention decay influences final tier classification.

Anahtar Kavram

Sequential state transitions with floor function decay and additive step updates
Soru 2096Soru

The table below presents operational data for seven regional flight routes operated by an airline during Q1 2026:

Route CodeDistance (miles)Flights ScheduledOn-Time Arrival RateAverage Passenger Load FactorFuel Consumption (gallons/flight)
R-10145012088%82%1,400
R-1028209075%86%2,300
R-1031,2506092%78%3,600
R-10431015084%74%1,100
R-1059608080%90%2,850
R-1061,5004594%85%4,200
R-10768011085%88%1,950

Match each of the following statements to its corresponding truth value and evaluation justification based on the table.

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Öğeler

Statement I: For all routes with a distance greater than 800 miles, the median On-Time Arrival Rate is greater than 85%.
Statement II: The route with the highest Average Passenger Load Factor also has the fewest total number of scheduled flights.
Statement III: The ratio of Fuel Consumption per flight to Distance is strictly decreasing as Route Distance increases across all seven routes.

Eşleşmeler

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Cevap

Statement I matches with the evaluation of True (median rate is 86%). Statement II matches with the evaluation of False (R-105 has 80 flights while minimum is 45). Statement III matches with the evaluation of False (the ratio increases from R-102 to R-105).
Each statement is evaluated against the quantitative data provided in the table. Statement I correctly identifies the four routes exceeding 800 miles and calculates their median as 86%. Statement II correctly identifies that R-105 has the highest load factor (90%) but 80 flights, whereas R-106 has the minimum flights (45). Statement III correctly identifies a counterexample where the fuel-to-distance ratio increases from R-102 to R-105.

Adım Adım Çözüm

1
Filter and compute the median for Statement I.
Qualifying routes (>800 miles): R-102 (75%), R-105 (80%), R-103 (92%), R-106 (94%). Sorted rates: [75%, 80%, 92%, 94%]. Median = \(\frac{80\% + 92\%}{2} = 86\%\) > 85%.
Identify sub-population based on distance criterion and determine the median of an even-sized dataset.
2
Locate maximum load factor and compare scheduled flights for Statement II.
Max load factor = 90% (R-105, 80 flights). Fewest flights overall = 45 flights (R-106). Since 80 != 45, statement is False.
Identify row-level extrema across two independent columns (Load Factor and Flights Scheduled).
3
Calculate rates/ratios for Statement III across increasing distances.
R-102 (820 miles): \(\frac{2300}{820} \approx 2.805\) gal/mi. R-105 (960 miles): \(\frac{2850}{960} = 2.96875\) gal/mi. Ratio increases, so trend is not strictly decreasing.
Test monotonic trend hypothesis by evaluating specific calculated ratios across sorted distances.

Anahtar Kavram

Multi-statement boolean verification requiring subset filtering, descriptive statistics (median of even-sized set), cross-column extrema matching, and rate trend testing.
Soru 2097Soru

The table below presents response metrics for eight municipal fire stations.

Station IDDistrictAverage Response Time (min)On-Time Response Rate (%)Annual Emergency Calls
Station 101North4.893.0%1,420
Station 102North5.291.0%1,850
Station 103East4.296.0%1,100
Station 104South5.888.5%2,100
Station 105West4.895.0%1,600
Station 106East5.589.0%1,350
Station 107West4.595.5%1,750
Station 108South5.092.5%1,900

True or False: If the table is sorted in ascending order by Average Response Time (min), with any ties broken by sorting in descending order by On-Time Response Rate (%), Station 101 is ranked 4th from the top.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True
Sorting primarily by Average Response Time (ascending) places Station 103 (4.2) first, Station 107 (4.5) second, and creates a tie between Station 101 and Station 105 at 4.8 minutes. Applying the secondary sort by On-Time Response Rate (descending) puts Station 105 (95.0%) in 3rd place and Station 101 (93.0%) in 4th place, confirming the statement.

Adım Adım Çözüm

1
Sort the dataset by the primary criterion: Average Response Time (min) in ascending order.
Station 103 (4.2 min) is 1st, Station 107 (4.5 min) is 2nd. Station 101 and Station 105 tie for the next positions with 4.8 min.
Ascending order places smaller response times first.
2
Apply the secondary tie-breaker criterion to the tied stations (Station 101 and Station 105): On-Time Response Rate (%) in descending order.
Station 105 (95.0%) is ranked 3rd, and Station 101 (93.0%) is ranked 4th.
Descending order places higher percentages above lower percentages.
3
Verify the rank of Station 101 against the statement in the prompt.
Station 101 is indeed ranked 4th overall.
The evaluation confirms the statement is true.

Anahtar Kavram

Multi-Column Table Sorting and Tie-Breaking
Tahmini Süre:1m 30s
Soru 2098Soru

A commercial roastery blends two batches of coffee beans, Batch A and Batch R. Batch A contains whole beans and cracked beans in a mass ratio of 7:37:3. Batch R contains whole beans and cracked beans in a mass ratio of 3:23:2. A roaster combines xx kilograms of Batch A with yy kilograms of Batch R to create an unroasted blend in which the overall mass ratio of whole beans to cracked beans is 13:713:7.

During the roasting process, moisture evaporation causes whole beans to lose 10%10\% of their mass and cracked beans to lose 20%20\% of their mass. If the total mass of the roasted blend is 346346 kilograms, what was the initial mass xx of Batch A, in kilograms?

Cevabı ve açıklamayı göster

Cevap: 200

Cevap

The initial mass of Batch A (xx) is 200 kg.
The correct calculation shows that equal masses of Batch A and Batch R (x=yx = y) satisfy the combined unroasted ratio of 13:713:7. Applying the respective 10%10\% and 20%20\% mass losses for whole and cracked beans results in a total roasted mass factor of 1.73x1.73x. Equating 1.73x=3461.73x = 346 gives x=200x = 200 kg.

Adım Adım Çözüm

1
Set up expressions for initial whole and cracked bean masses
Batch A has 0.7x0.7x kg whole and 0.3x0.3x kg cracked beans; Batch R has 0.6y0.6y kg whole and 0.4y0.4y kg cracked beans.
Ratios 7:37:3 and 3:23:2 convert directly to component fractions 7/10=0.77/10 = 0.7, 3/10=0.33/10 = 0.3 for A, and 3/5=0.63/5 = 0.6, 2/5=0.42/5 = 0.4 for R.
2
Equate the total component ratio to 13:713:7 to find the relationship between xx and yy
x=yx = y
Setting 0.7x+0.6y0.3x+0.4y=137\frac{0.7x + 0.6y}{0.3x + 0.4y} = \frac{13}{7} and cross-multiplying yields 4.9x+4.2y=3.9x+5.2y4.9x + 4.2y = 3.9x + 5.2y, simplifying to x=yx = y.
3
Apply roasting mass loss percentages to compute total roasted mass in terms of xx
Total roasted mass = 1.73x1.73x
Whole beans retain 90%90\% mass (0.90×1.3x=1.17x0.90 \times 1.3x = 1.17x) and cracked beans retain 80%80\% mass (0.80×0.7x=0.56x0.80 \times 0.7x = 0.56x). Summing yields 1.17x+0.56x=1.73x1.17x + 0.56x = 1.73x.
4
Solve for xx given total roasted mass of 346346 kg
x=200x = 200
Dividing 346346 by 1.731.73 yields 200200 kg.

Anahtar Kavram

Weighted average ratios combined with proportional percentage change
Soru 2099Soru

Historically, economic historians accounted for the rapid technological diffusion in early modern European metallurgy by emphasizing the role of formal patent privileges granted by territorial sovereigns. According to this traditional framework, patents offered inventors temporary monopoly protection, thereby incentivizing the public disclosure of technical specifications that would otherwise have remained guarded secrets. Consequently, public patent registries were posited as the primary engine driving cross-regional knowledge transfers and subsequent industrial innovation.

However, recent quantitative analyses of archival probate records and workshop apprenticeships challenge this state-centric narrative. Economic historian Elena Rostova demonstrates that formal patents in seventeenth-century metallurgical centers were exceedingly rare and frequently ignored by practicing artisans. Instead, technological knowledge circulated primarily through informal, highly organized artisan fraternities and regional guild networks. These networks relied not on state-sanctioned legal monopolies, but on reciprocal transparency: master metalworkers freely shared incremental innovations in smelting techniques with network members while collectively excluding non-affiliated competitors.

Furthermore, Rostova argues that where patents were actively enforced, they often impeded rather than accelerated technical progress. By granting exclusive rights to broad metallurgical processes, early patents frequently led to prolonged litigation that suppressed complementary innovations by rival workshops. Thus, rather than serving as the foundational stimulus for technological progress, formal patent systems were frequently peripheral—and occasionally detrimental—to the organic, network-driven mechanisms of early industrial knowledge sharing.

Which of the following best describes the logical structure of the passage as a whole?

Cevabı ve açıklamayı göster

Cevap: It presents a long-standing explanation for a historical phenomenon, introduces empirical evidence that undermines that explanation, and concludes by asserting that the factor previously credited with driving progress may have actually hindered it.

Cevap

The passage presents a long-standing explanation for a historical phenomenon, introduces empirical evidence that undermines that explanation, and concludes by asserting that the factor previously credited with driving progress may have actually hindered it.
The correct answer accurately maps the passage's three-part logical development: first introducing the traditional thesis (patents drove diffusion), then presenting Rostova's empirical evidence refuting that thesis in favor of guild networks, and finally concluding that patents were often detrimental rather than beneficial.

Adım Adım Çözüm

1
Analyze the structural role of Paragraph 1
Paragraph 1 establishes the traditional view: patents drove technological diffusion in early modern European metallurgy.
Understanding the baseline thesis is necessary to track how the author shifts the argument.
2
Identify the structural pivot and analyze Paragraph 2
The pivot word 'However' introduces Rostova's opposing evidence showing patents were rare and guild networks actually facilitated knowledge sharing.
Recognizing the pivot reveals that the passage is structured as a challenge to an established paradigm.
3
Analyze Paragraph 3 and synthesize the overall rhetorical plan
Paragraph 3 takes the critique a step further, arguing patents were often detrimental due to litigation. The full arc moves from traditional paradigm -> empirical counter-evidence -> assertion of negative impact.
Synthesizing the progression across all three paragraphs yields the complete logical structure.

Anahtar Kavram

Analyzing Logical Structure and Rhetorical Plan
Soru 2100Soru

An automated pharmaceutical freeze-drying facility uses two types of sublimation condensers, Unit Type A and Unit Type B, to process frozen liquid formulations into powder.

- Under standard mode, 4 units of Type A and 5 units of Type B operating simultaneously for 8 hours process a combined total of 5,120 kg5,120\text{ kg} of formulation.
- Under high-efficiency mode, the hourly processing rate of each Type A unit increases by 20%20\%, while the hourly processing rate of each Type B unit decreases by 15%15\%. When operating in high-efficiency mode, 3 units of Type A and 8 units of Type B running simultaneously for 5 hours process a combined total of 3,570 kg3,570\text{ kg} of formulation.

Select the hourly processing rate (in kg/hr) for a single Type A unit operating under high-efficiency mode, and the hourly processing rate (in kg/hr) for a single Type B unit operating under standard mode.

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Öğeler

Hourly processing rate of 1 Type A unit under high-efficiency mode (kg/hr)
Hourly processing rate of 1 Type B unit under standard mode (kg/hr)

Eşleşmeler

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Cevap

High-efficiency rate of Type A = 102 kg/hr; Standard rate of Type B = 60 kg/hr.
Solving the system of linear equations yields standard rates of 85 kg/hr85\text{ kg/hr} for Type A and 60 kg/hr60\text{ kg/hr} for Type B. Applying the 20%20\% increase to Type A gives 1.20×85=102 kg/hr1.20 \times 85 = 102\text{ kg/hr} for the high-efficiency Type A column, while the standard Type B column requires 60 kg/hr60\text{ kg/hr}.

Adım Adım Çözüm

1
Define variables for the standard hourly rates of Type A and Type B units.
Let xx be the standard hourly processing rate of 1 Type A unit (in kg/hr), and let yy be the standard hourly processing rate of 1 Type B unit (in kg/hr).
Establishing individual unit rates allows setting up linear equations based on total mass processed.
2
Formulate the first linear equation using standard mode data.
Total hourly rate for 4 Type A and 5 Type B units is 4x+5y4x + 5y. Operating for 8 hours gives 8(4x+5y)=5,120    4x+5y=6408(4x + 5y) = 5,120 \implies 4x + 5y = 640.
Dividing total mass by hours yields the combined hourly processing capacity of the configuration.
3
Formulate the second linear equation using high-efficiency mode data.
High-efficiency Type A rate =1.20x= 1.20x, and high-efficiency Type B rate =0.85y= 0.85y.
For 3 Type A and 8 Type B units running 5 hours: 5(3(1.20x)+8(0.85y))=3,570    5(3.6x+6.8y)=3,570    3.6x+6.8y=7145(3(1.20x) + 8(0.85y)) = 3,570 \implies 5(3.6x + 6.8y) = 3,570 \implies 3.6x + 6.8y = 714.
Multiply by 10 to clear decimals: 36x+68y=7,140    9x+17y=1,78536x + 68y = 7,140 \implies 9x + 17y = 1,785.
Applying percentage rate modifications gives the adjusted unit rates for high-efficiency mode.
4
Solve the system of simultaneous linear equations for xx and yy.
From Equation 1 (4x+5y=6404x + 5y = 640), express x=6405y4x = \frac{640 - 5y}{4}.
Substitute into Equation 2 (9x+17y=1,7859x + 17y = 1,785):
9(6405y4)+17y=1,7859\left(\frac{640 - 5y}{4}\right) + 17y = 1,785
5,76045y+68y=7,1405,760 - 45y + 68y = 7,140
23y=1,380    y=6023y = 1,380 \implies y = 60.
Substituting y=60y = 60 back into 4x+5(60)=640    4x=340    x=854x + 5(60) = 640 \implies 4x = 340 \implies x = 85.
Using substitution resolves the two-variable system to find the standard rates.
5
Calculate the target quantities requested in the prompt.
Standard rate of Type B =y=60 kg/hr= y = 60\text{ kg/hr}.
High-efficiency rate of Type A =1.20x=1.20×85=102 kg/hr= 1.20x = 1.20 \times 85 = 102\text{ kg/hr}.
The question specifically asks for Type A's high-efficiency rate and Type B's standard rate.

Anahtar Kavram

Formulating and solving simultaneous multi-variable linear systems derived from work rate scenarios with non-standard modifiers.

Alternatif Yöntem

Clear the hourly rates immediately: Equation 1 gives combined rate 4x+5y=6404x + 5y = 640. Equation 2 gives 3.6x+6.8y=7143.6x + 6.8y = 714. Multiply Equation 1 by 0.90.9 to align xx-coefficients (3.6x+4.5y=5763.6x + 4.5y = 576), then subtract from Equation 2: 2.3y=138    y=602.3y = 138 \implies y = 60.
Tahmini Süre:2m 30s
ÖncekiSayfa 105 / 110Sonraki
Tüm alıştırma soruları — GMAT | Examkin