I29-193

Question

A metropolitan transit authority is considering two plans (Plans A and B) for a new public transportation route. Both plans would provide the same passenger capacity annually. Plan A would use two subway trains, while Plan B would use five buses.
 
Subway trains consume less fuel per passenger transported but generate construction debris that is costly to dispose of. Buses create no such debris.
 
In terms of emissions, trains release about twice as much nitrogen exhaust and more than twice as much particulate matter per passenger as buses.
 
Finally, the two vehicle types differ in noise: each subway train is louder than each bus.Noise is measured in decibels (dB).
 
• Each subway train produces, on average, 90 dB of noise.
 
• Each bus produces, on average, 75 dB of noise.
 
To evaluate overall exposure for the community, the transit authority defines a Noise Exposure Index as:
 
Noise Exposure Index = (average noise per vehicle) × (number of vehicles in the plan)The following table shows the average annual emissions per passenger transported, by vehicle type.
      Vehicle Type   Nitrogen Exhaust (g/passenger)   Particulate Matter (g/passenger)       Train   12   9       Bus   6   4      
Because nitrogen exhaust and particulate matter affect health and the environment in different ways, the transit authority defines two measures:
 
• Pollution Index (PI) = (2 × Nitrogen Exhaust) + (3 × Particulate Matter)
 
• Health Cost Index (HCI) = (0.5 × Nitrogen Exhaust) + (1 × Particulate Matter)
 
To compare overall environmental impact, the authority also defines an Overall Index (OI) as:
 
• Overall Index = (PI + HCI) ÷ 2

Bunuel · Answer

Official Solution:

Plan A: 
 PI = 2×12 + 3×9 = 51,
 HCI = 0.5×12 + 9 = 15,
 OI = (51 + 15)/2 = 33
 
 Plan B: 
 PI = 2×6 + 3×4 = 24,
 HCI = 0.5×6 + 4 = 7,
 OI = (24 + 7)/2 = 15.5
 
 • The Pollution Index for Plan A is more than twice that for Plan B. 
 51 > 2×24 →  Yes 
 
 • The Health Cost Index for Plan B is less than half that for Plan A. 
 7 < 0.5×15 →  Yes 
 
 • The Overall Index for Plan A is more than double that for Plan B. 
 33 > 2×15.5 →  Yes

Correct answer:

The Pollution Index for Plan A is more than twice that for Plan B.  "Yes"

The Health Cost Index for Plan B is less than half that for Plan A.  "Yes"

The Overall Index for Plan A is more than double that for Plan B.  "Yes"

ishan15tech · Answer

In above solution, shouldn't we multiply the pollution index with the total number of trains and buses for plan A and plan B respectively. As we are given the above formula for a train and a bus. If we do that, the answer will be totally opposite.

Bunuel · Answer

No, we should not multiply the Pollution Index by the number of trains or buses. The emissions table gives emissions per passenger transported, and both plans provide the same annual passenger capacity. The number of vehicles is relevant for the Noise Exposure Index, but not for these per-passenger emissions indices.

I29-193

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