The airplane with the most fuel efficient per passenger

GRE Quant Problem Solving
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Km/L = efficiency (E)
E/(# of passengers) = X

The less X, the more efficient per passenger its correspondent airplane. Agreed?

@gregmat, would you please explain your solution one more time? Thank you!

P.S. I posted this question here in case others would like to benefit as well.

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Not quite. If the fuel economy of a plane is (say) 0.1 km/L, and 100 passengers are in the plane, the fuel economy of each passenger is 0.1 \times 100 = 10 km/L. Maximise that instead.

Intuitively, this is why it’s good to have planes that are fully loaded.

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When you are MULTIPLYING that efficiency by the #of passengers, you are NOT calculating the efficiency PER PASSENGER. Your solution is giving you the measurement of a different quality.

See, that efficiency (KM/L) gives us how many KM can an airplane go PER LITRE.

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But we are?

Correct. When you load (for example) 100 passengers on the plane, these 100 passengers are collectively resulting in the plane having (say) 0.1 km/L. Hence, we need to multiply to get the fuel efficiency per passenger. Indeed, this makes sense, because (say) if we add one more passenger, assuming the weight does not change, the plane can carry more passengers on the same amount of fuel, which means that the fuel efficiency per passenger increases.

Does this make sense?

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I get what you are saying here. I paste my entire argument around the phrase “per passenger”. I 100% agree with you that when multiplying, COLLECTIVELY that airplane will have the greater efficiency. However, regarding "per passenger"i doubt about it. It wouldnt be “per passenger”. Instead, would be sth like the most fuel efficient airplane “with” passengers.

Thank you for your help. I appreciate that.

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That wouldn’t work. There are two distinct measures we need to look at:

  • the fuel economy of the plane as it is - how much fuel is the plane consuming by itself? The problem with this metric is that larger planes will naturally consume more fuel and hence have a poorer fuel economy under this metric, while they could actually be doing better since they are carrying more load when doing so.
  • the fuel economy of the plane per passenger - this one resolves the issue described above as we are accounting for the fact that a larger plane that consumes more fuel could be better if it carries more passengers when doing so. (Note that we should be looking at weight actually, but for this question we sidestepped that aspect for simplicity)

I can understand why the “per passenger” sounds counterintuitive (and as you saw above, confused even Greg at first), but I think that’s the right wording to use. Also see Fuel economy in aircraft - Wikipedia - they also use the “per passenger” terminology:

In 2016, over the transpacific routes, the average fuel consumption was 31 pax-km per L (3.23 L/100 km [73 mpg‑US] per passenger).

That being said, we’re open to suggestions that would further improve this question, if you have one.

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