A certain renewable energy company is planning to construct a wind farm at Site S. Some of the most important...

GMAT Multi Source Reasoning : (MSR) Questions

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Turbine Characteristics

Turbine Models

Wind Speeds

A certain renewable energy company is planning to construct a wind farm at Site S. Some of the most important characteristics of the wind turbines they researched for the site are described below.

The cut-in speed is the least wind speed required to turn the blades of the turbine and generate power. The turbine will not generate power at speeds less than the cut-in speed.
The rated output speed is the wind speed at which the turbine generates the greatest amount of power. The turbine will generate no additional power at speeds exceeding the rated output speed.
The cut-out speed is the wind speed at which there is risk of damaging the turbine should the blades continue to rotate. At speeds exceeding the cut-out speed, a braking system automatically stops the blades from rotating, and no power is generated.
The amount of power P, in watts, generated by a turbine operating at any wind speed from its cut-in speed to its rated output speed is given by:

\(\mathrm{P = kl^2v^3}\)

where k is an efficiency coefficient that varies for different models of turbines, l is the turbine blade length in meters (m), and v is the wind speed in meters per second (m/s).

Ques. 1/3

According to the information provided, which one of the following is nearest to the amount of power one Model M turbine would have generated at the average wind speed for Site S last year?

0,023,000 watts

0,065,000 watts

0,150,000 watts

0,800,000 watts

1,300,000 watts

Solution

Owning the Dataset

Understanding Source A: Text - Turbine Characteristics

Information from Dataset	Analysis
""The cut-in speed is the least wind speed required to turn the blades of the turbine and generate power. The turbine will not generate power at speeds less than the cut-in speed.""	Turbines need a minimum wind speed to start working Below cut-in speed = zero power generation Inference: Different turbine models likely have different cut-in speeds
""The rated output speed is the wind speed at which the turbine generates the greatest amount of power. The turbine will generate no additional power at speeds exceeding the rated output speed.""	Turbines reach maximum power at a specific wind speed Higher winds beyond this point don't increase power Inference: Power output plateaus after reaching rated output speed
""The cut-out speed is the wind speed at which there is risk of damaging the turbine...a braking system automatically stops the blades from rotating, and no power is generated.""	Safety mechanism prevents turbine damage in extreme winds Turbines shut down completely above cut-out speed Inference: No power generation occurs when winds are too strong
""(mathrm{P = kl^2v^3})"" where (mathrm{k}) = efficiency coefficient, (mathrm{l}) = blade length (m), (mathrm{v}) = wind speed (m/s)	Power depends on three factors: efficiency, blade length, and wind speed Power increases with the cube of wind speed (very sensitive to speed changes) Power increases with the square of blade length Inference: Formula only applies between cut-in and rated output speeds
""A certain renewable energy company is planning to construct a wind farm at Site S""	This is a company planning document for wind farm at Site S Inference: The turbine characteristics will be evaluated for this specific site

Key Finding: Turbines operate within specific wind speed ranges
Power generation starts at cut-in speed
Power maximizes at rated output speed
Turbines stop at cut-out speed for safety

Understanding Source B: Table - Turbine Models

Information from Dataset	Analysis
Cut-in speeds: Model M (1.9 m/s) to Model Q (4.8 m/s)	Model M starts generating power at the lowest wind speeds Model Q needs much higher winds to begin operation Inference: Nearly 3 m/s difference between most and least sensitive models Connection to Source A: These are the specific cut-in speeds defined
Rated output speeds: Model P (12.7 m/s) to Model Q (16.1 m/s)	Model P reaches maximum power at lowest wind speed All models max out between 12-17 m/s Connection to Source A: These are the rated output speeds where power plateaus
Cut-out speeds: Model P (20.3 m/s) to Model N (34.2 m/s)	Model P has lowest tolerance for high winds Model N can operate in the strongest winds Inference: Safety thresholds vary significantly across models Connection to Source A: These are the safety shutdown speeds described
Efficiency coefficients: Model O (0.38) to Model Q (0.46)	Model Q is most efficient at converting wind to power About 20% variation in efficiency across models Connection to Source A: These are the 'k' values for the power formula
Blade lengths: Model N (22m) to Model Q (58m)	Model Q has longest blades (over 2.5x Model N) Inference: Significant size variation across models Connection to Source A: These are the 'l' values that get squared in the power formula

Key Finding: The five turbine models show substantial variation in all characteristics
Trade-offs exist between low cut-in speeds (Model M) and high efficiency/blade length (Model Q)

Understanding Source C: Graph with Text - Wind Speeds at Site S

Information from Dataset	Analysis
""The average wind speed last year was 6.8 m/s""	Site S has moderate average wind conditions Connection to Sources A and B: This is well above all cut-in speeds but below all rated output speeds All turbine models would be generating power at this average speed
""The maximum wind speed was 23.7 m/s""	Site experiences high wind events up to 23.7 m/s Connection to Source B: This exceeds Model P's cut-out speed (20.3 m/s) but is below all other models' cut-out speeds
Peak frequency at 5-7 m/s range (11.6% at 5-6 m/s, 11.5% at 6-7 m/s)	Most common winds cluster near the average Site experiences these speeds about 23% of the time Connection to Source B: All models would be operating during these most frequent conditions
Winds below 3 m/s occur about 8.1% of time (1.4% + 2.5% + 5.2%)	Calm conditions are relatively uncommon Connection to Source B: Model M (cut-in 1.9 m/s) could generate power even during most calm periods, while Model Q (cut-in 4.8 m/s) would be idle
Winds above 15 m/s occur less than 5% of time	High wind events are infrequent Inference: Most operational time will be at moderate speeds Connection to Source B: Turbines rarely operate at their rated output speeds or higher

Key Finding: Site S has consistent moderate winds averaging 6.8 m/s
Favors turbines with low cut-in speeds like Model M
Model P's low cut-out speed would cause shutdowns during peak winds

Overall Analysis

Site S experiences moderate, consistent winds that would allow all five turbine models to generate power during typical conditions
Model M advantage: Low cut-in speed (1.9 m/s) maximizes operational time by capturing power even during calm periods
Model P limitation: Would shut down during the site's strongest winds (23.7 m/s)
Since winds strong enough for maximum power generation occur less than 5% of the time, models with lower cut-in speeds offer more total operational hours than models optimized for high-wind conditions like Model Q

Source Analysis

Source A - Turbine Characteristics

Provides the power generation formula (mathrm{P = kl^2v^3}), where:
- P = power in watts
- k = efficiency coefficient
- l = blade length in meters
- v = wind speed in m/s
Defines operational ranges:
- Cut-in speed: minimum for power generation
- Rated output speed: maximum power
- Cut-out speed: safety shutdown

Source B - Turbine Models

Model M turbine specifications:
- Cut-in speed: 1.9 m/s
- Rated output speed: 14.0 m/s
- Cut-out speed: 28.9 m/s
- Efficiency coefficient (k): 0.40
- Blade length (l): 35 meters

Source C - Wind Speeds

Average wind speed at Site S last year: 6.8 m/s

Information Integration

The average wind speed (6.8 m/s) falls within Model M's operational range since (mathrm{1.9 leq 6.8 leq 14.0}) m/s
This means the turbine would generate power according to the formula (mathrm{P = kl^2v^3})

Statement Evaluations

Statement 1 Analysis

""0,023,000 watts""

Analysis: This value of 23,000 watts is significantly lower than the calculated power output
Evidence Available: Using the power formula P = kl²v³ with k=0.40, l=35m, v=6.8m/s gives approximately 154,032 watts
Conclusion: NOT SUPPORTED - The calculated value is about 6.7 times higher than this option

Statement 2 Analysis

""0,065,000 watts""

Analysis: This value of 65,000 watts is substantially lower than the calculated power output
Evidence Available: The step-by-step calculation yields P = 0.40 × 1,225 × 314.432 = 154,031.68 watts
Conclusion: NOT SUPPORTED - The calculated value is approximately 2.4 times higher than this option

Statement 3 Analysis

""0,150,000 watts""

Analysis: This value of 150,000 watts is the closest to the calculated power output of approximately 154,032 watts
Evidence Available: Step-by-step calculation shows: l² = 35² = 1,225; v³ = 6.8³ = 314.432; P = 0.40 × 1,225 × 314.432 = 154,031.68 watts
Conclusion: SUPPORTED - This option represents the nearest value to the calculated result among all given choices

Statement 4 Analysis

""0,800,000 watts""

Analysis: This value of 800,000 watts is significantly higher than the calculated power output
Evidence Available: The calculated power of approximately 154,032 watts is much lower than this option
Conclusion: NOT SUPPORTED - This value is about 5.2 times higher than the calculated result

Statement 5 Analysis

""1,300,000 watts""

Analysis: This value of 1,300,000 watts is extremely high compared to the calculated power output
Evidence Available: The power formula calculation gives approximately 154,032 watts, which is far below this option
Conclusion: NOT SUPPORTED - This value is approximately 8.4 times higher than the calculated result

Answer Selection

The calculated power of approximately 154,032 watts is nearest to 150,000 watts among the given options
The other options (23,000, 65,000, 800,000, and 1,300,000 watts) are significantly different from our calculated value

150,000 watts

Answer Choices Explained

0,023,000 watts

0,065,000 watts

0,150,000 watts

0,800,000 watts

1,300,000 watts

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