Natural gas, when burned as fuel for heat, produces about 1,000 BTU of

Question

Natural gas, when burned as fuel for heat, produces about 1,000 BTU of heat per cubic foot of gas when fully burned. Propane, another gas used as fuel, produces about 2,500 BTU per cubic foot of gas when fully burned.

Furnaces burning either fuel burn at various efficiencies, according to the proportion of heat energy available from the fuel that actually contributes to the heating of the building to be heated (as opposed, for example, to escaping up a chimney in the form of dissipated heat or unburned fuel).

Kgomotso is shopping for a furnace that will produce about 50,000 BTU per hour of usable heat. None of the available furnaces burns both propane and natural gas. Also, no two of them operate at the same efficiency. In the table, identify, if possible, a price per cubic foot of  Propane  and a price per cubic foot of  Natural gas , such that the fuel-cost per BTU of usable heat is the same using either fuel. If this determination is impossible with the given information, then choose “Undeterminable” in each column. Make only two selections, one in each column.

ID: 700155

egmat · Accepted Answer

It is not very often that you get a question in which both the answers are actually ‘indeterminable’. This is one of those few questions.

Watch this video solution with the intention of building your DI skill set. Here is how this solution will facilitate the same:
 
 See how we translate the dense dataset in this question. The key to arriving at the answer ‘indeterminable’ is in understanding what ‘usable heat’ means and how that links with the ‘efficiency’ of the furnance. 
 Utilize the alternate solution using mathematical expressions to expand your understanding of how you could arrive at an answer if certain specific information were presented in the dataset.

https://www.youtube.com/watch?v=qp7wmFkBvpE

KarishmaB · Answer

N produces 1,000 BTU of heat per cubic foot of gas when fully burned.
P produces 2,500 BTU per cubic foot of gas when fully burned.

This means that if everything else is the same, a price ratio is 2:5 will ensure that fuel-cost per BTU of usable heat is the same using either fuel.
Say if N is for $2 per cubic foot and P is for $5 per cubic foot, you will get 500 BTU of heat from each dollar you spend. Hence, you would look for a ratio of 2:5 in the pricing. But, the argument tells us that everything is not the same. 
Furnaces burning either fuel burn at various efficiencies - so a furnace for N could burn only 50% of a cubic foot of N to give half the BTUs expected while a furnace for P could burn 75% of a cubic foot of P efefctively to give 75% of expected BTU's. Then the pricing goes for a toss. We need to know the furnace efficiencies before we can decide on equivalent pricing.

Answer: Undeterminable

Elite097 · Answer

KarishmaB   GMATCoachBen   ChiranjeevSingh  please explain. I am getting B and D respectively. 
50000/2500=20 cubic feet per hour vs 50000/1000=50 cubic feet per hour
Fuel cost of a/50000=Fuel cost of b/50000
20a=50b-------- a=2.5b

Oppenheimer1945 · Answer

1cc of NG =1000Joules of heat is dissipated
1cc of P=2500Joules of heat is dissipated

Furnace with NG=eff1*1000 Joules of useful heat
Furnace with Propane=eff2*2500 Joules of useful heat

Lets say we run both furnaces for 1 hr. Total heat required=50,000 Joules
 NG price per cc=a, P price per cc=b
eff of NG when used in Furnace=eff1, eff of Propane when used in Furnace=eff2

volume of NG required in Furnace= (eff1*1000 Joules/cc)/50,000 Joules
volume of Propane required in Furnace= (eff2*2500 Joules/cc)/50,000 Joules

Fuel cost for NG in Furnace=a*(eff1*1000 Joules/cc)/50,000 Joules
Fuel cost for Propane in Furnace= b*(eff2*1000 Joules/cc)/50,000 Joules

tanishqgirotra · Answer

crazy question

manasp35 · Answer

Elite097  50,000 is usable heat 
2500 is referring to total heat.

50,000/ 2500 = 50,000 BTU of usable heat / 2500 BTU of total heat per cubic foot

Before this step, we need to convert total heat into usable heat with the help of efficiency. Let say propane efficiency is P %

P% of 2500 = P*2500/100= 25P BTU of usable heat per cubic foot.

So now,

50,000/25P =  50,000 BTU of usable heat / 25P BTU of usable heat per cubic foot = total cubic foot required.

Similarly for Natural gas :  50,000/10N = total cubic foot of Gas required

Now we can calculate prices and equate them.
price of natural per cubic foot / price of propane per cubic foot = 10N / 25P

But since we don't know about the respective efficiencies N and P, we can't determine individual prices despite the options.

shwetasood · Answer

there was no price factor given along with the efficiencies to measure or even estimate the price so i selected "Undeterminable", is this approach wrong??

KarishmaB · Answer

The approach is correct. Since we don't have the efficiencies, it is Undeterminable.
Furnaces burning either fuel burn at various efficiencies - so a furnace for N could burn only 50% of a cubic foot of N to give half the BTUs expected while a furnace for P could burn 75% of a cubic foot of P effectively to give 75% of expected BTU's. Then the pricing goes for a toss. We need to know the furnace efficiencies before we can decide on equivalent pricing.

MartyMurray · Answer

Natural gas, when burned as fuel for heat, produces about 1,000 BTU of heat per cubic foot of gas when fully burned. Propane, another gas used as fuel, produces about 2,500 BTU per cubic foot of gas when fully burned.Furnaces burning either fuel burn at various efficiencies, according to the proportion of heat energy available from the fuel that actually contributes to the heating of the building to be heated (as opposed, for example, to escaping up a chimney in the form of dissipated heat or unburned fuel).

Kgomotso is shopping for a furnace that will produce about 50,000 BTU per hour of usable heat. None of the available furnaces burns both propane and natural gas. Also, no two of them operate at the same efficiency. In the table, identify, if possible, a price per cubic foot of Propane and a price per cubic foot of Natural gas, such that the fuel-cost per BTU of usable heat is the same using either fuel. If this determination is impossible with the given information, then choose “Undeterminable” in each column. Make only two selections, one in each column.

We see the ratio of the amount of heat produced through burning a cubic foot of natural gas to the amount of heat produced through burning a cubic foot of propane is 1000:2500, or 1:2.5.

So, if the two types of fuel were burned at the same efficiency, then the prices per unit of gas such that the fuel-cost per BTU of usable heat is the same using either fuel would also be in the ratio of 1:2.5.

However, the passage says the following:

None of the available furnaces burns both propane and natural gas. Also, no two of them operate at the same efficiency.

Since we are not told the efficiency at which the gases will be burned by the available furnaces, we have no way of determining how much usable heat per cubic foot of either gas will be produced through burning. Thus, we have no way of determining the prices per prices per unit of gas such that the fuel-cost per BTU of usable heat is the same using either fuel.

So, the correct answer for each column is Undeterminable.

Correct answer:   Undeterminable ,  Undeterminable

Gemmie · Answer

Let:
 
 P_n be the price per cubic foot of natural gas 
 P_p be the price per cubic foot of propane  
 Cost per BTU of usable heat for natural gas:   \frac{Price }{ BTU-output-per-cubic-foot} * (Furnace-efficiency) = \frac{P_n }{ 1000 BTU} * (furnace-efficiency)

Cost per BTU of usable heat for propane:   \frac{Price }{ BTU-output-per-cubic-foot} * (Furnace-efficiency) = \frac{P_p }{ 2500 BTU} * (furnace-efficiency)

Since we want the cost per BTU to be the same for both fuels, we can set these equations equal to each other:

\frac{P_n }{ 1000 BTU} =\frac{ P_p }{ 2500 BTU}

Solving (Undeterminable)

Unfortunately, with the given information, we cannot solve for specific prices ( P_n  and  P_p ). This is because the equation only relates the prices of natural gas and propane, but the unknown furnace efficiency term remains on both sides. Without knowing the efficiency, we cannot determine the exact prices that would make the cost per BTU equal.

Therefore, the answer for both Propane price per cubic foot and Natural gas price per cubic foot is  Undeterminable .

Elite097 · Answer

KarishmaB   MartyMurray   egmat  the point is that if the efficiencies were given and no prices were given in the stimulus, then would it not still be undeterminable because we would merely have price ratios and not the price and the question explicitly asks us to find the actual price and not the ratio?

And if you will say that we are allowed to use the ratios and determine the ans choices that suit that ratio, then what in the stimulus tells us that we are expected to apply the ratio to answer choices?

cheshire · Answer

Yes, we can validly use the ratio to select from answer choices.
 Even if the stimulus gives no prices, as long as the efficiency-adjusted energy yields are known, we can:
 
 Compute the cost-per-BTU ratio for propane vs natural gas. 
 Apply that ratio to the answer choices to find a matching pair. 
 Choose the price pair from the options that satisfies the ratio.  
The question only required us to identify, "if possible," a price per cubic foot of each fuel such that their cost per usable BTU is the same.
 So finding prices from the list that satisfy the ratio is 100% within scope.

Coming back to the actual question. Even if we had efficiencies, we:
 
 Still don’t know which furnaces are being used 
 Know that no two operate at the same efficiency 
 Don't know which efficiency goes with which fuel  
So we cannot assign the BTU-per-dollar values, even via ratio.
 Undeterminable is correct in this case.

Pr4n · Answer

price factor is indeed mentioned, that at what value fuel cost is equal that is something you need to look for in the stem. But yes as efficiency is not given hence we can't determine it.

kayarat600 · Answer

Consider writing the fuel efficiency for b9th equation s as different variables or else it looks doale

Propane	Natural Gas
		$0.0035
		$0.0070
		$0.0110
		$0.0175
		$0.0350
		Undeterminable

Natural gas, when burned as fuel for heat, produces about 1,000 BTU of

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Natural gas, when burned as fuel for heat, produces about 1,000 BTU of

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