A metropolitan transit authority is considering exactly two plans

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 · Accepted Answer

Solution to Question 1

• Reducing fuel consumption per passenger:  Yes .

Tab 1: subway trains consume less fuel per passenger transported compared with buses. 
 This supports a preference for Plan A.

• Avoiding the disposal of construction debris:  No .
 
 Tab 1: trains generate costly construction debris, whereas buses do not. 
 Choosing Plan A does not avoid debris.

• Minimizing nitrogen exhaust per passenger:  No .

Tab 3: trains emit 12 g/passenger, buses emit 6 g/passenger. 
 Trains produce twice as much nitrogen exhaust, so Plan A would not help minimize it.

I29-189

Bunuel · Answer

Solution to Question 2

Noise Exposure Index = (average noise per vehicle) × (number of vehicles in the plan).

• Plan A (2 trains): 90 × 2 = 180

• Plan B (5 buses): 75 × 5 = 375

• Ratio = 375/180 = 2.08... ≈ 2

I29-192

Bunuel · Answer

Solution to Question 3

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

I29-193

svsivakrishna · Answer

Hi  Bunuel

Please clarify on the answer for question 2:  The ratio of the Noise Exposure Index for Plan B (buses) to that for Plan A (subway trains) is approximately:

As per the given data:

Each subway train produces, on average, 90 dB of noise.

Each bus produces, on average, 75 dB of noise

Therefore, the ratio is 75:90, ie., 5:6

however, the correct answer is shown as 2:1,

Where did I go wrong? or Am i missing something?

Bunuel · Answer

The question read:

The ratio of the  Noise Exposure Index  for Plan B (buses) to that for Plan A (subway trains) is approximately:

So, we need the Noise Exposure Index ratio not just the noise ratio.

svsivakrishna · Answer

Oh!, Got it.

The index is noise level x numbers
Therefore
ratio for buses to train is (75*5): (90*2) = 375:180 , approximately 2:1.
Thanks

Bunuel · Answer

Yes, that's correct!

fugaquasi · Answer

Bunuel  Im slightly confused about q3

Since the question asks for the index values of Plan a and plan b instead of for 1 train and 1 bus, why shoud'nt we multiply each index by 2 and 5 respectively to account for the number of vehicles in each plan? Why is the index independent of the number of vehicles or am I missing something else important here?

Bunuel · Answer

Because  the emissions are already given per passenger.

fugaquasi · Answer

AH, okay. Thank you very much!

AryamanMalik · Answer

hi  Bunuel  in question 3, we were asked to compare plans not individual passenger. 
First, for plan A 
P.I.= 2  =102.
HCI= 2 =30
overall Index = 102+30=132
For plan B 
P.I. = 5 =120.
HCI=5 =35
Overall Index= 155
Thus, resulting in Answer NO to all questions in 3rd.

Bunuel · Answer

No. We are told that " Both plans would provide the same passenger capacity annually ", so we can calculate per passenger and it still would get the same results when comparing.

AryamanMalik · Answer

thank you for your assistance.

	1:2
	5:6
	6:5
	3:2
	2:1

A metropolitan transit authority is considering exactly two plans

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Yes	No
		Reducing fuel consumption per passenger
		Avoiding the disposal of construction debris
		Minimizing nitrogen exhaust per passenger

Yes	No
		The Pollution Index for Plan A is more than twice that for Plan B.
		The Health Cost Index for Plan B is less than half that for Plan A.
		The Overall Index for Plan A is more than double that for Plan B.

GMAT Multi-Source Reasoning (MSR) Questions

A metropolitan transit authority is considering exactly two plans

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