When fully burned, natural gas produces approximately 1,000 BTU of hea

Question

When fully burned, natural gas produces approximately 1,000 BTU of heat per cubic foot of fuel, and propane produces about 2,500 BTU of heat per cubic foot of fuel. For a furnace in which either natural gas or propane may be burned as fuel, the efficiency of a given fuel is the usable heat energy produced when the fuel is burned in the furnace, expressed as a percentage of the total heat energy produced when the fuel is burned.

Kaiser will purchase a furnace whose efficiency with respect to either natural gas burned alone or propane burned alone is 90%. In the table select for natural gas cost per cubic foot and for propane cost per cubic foot the values that are jointly consistent with the information given for which the fuel cost per BTU of usable heat energy produced by this furnace would be approximately the same for each fuel burned alone. Make only two selections, one in each column.

GMATCoachBen · Accepted Answer

amitarya  I made a video solution for you here:

https://www.youtube.com/watch?v=s3jRiLHxHAQ

The key is that our calculation is much less complicated than it might appear at first — the efficiency is the same for both natural gas and propane, so we don't need to take that into account. The only numbers we need are in the 1st sentence.

Therefore, since the cost per BTU must be the same for both, the costs must be in the same ratio as the BTU numbers in the 1st sentence.

So, using the answer choices, we guess and check to find numbers that are in a 1000:2500 (1 : 2.5) ratio:

70*2.5 = 175, so our answers are B and D.

egmat · Answer

Here is a  detailed video solution  for this interesting question. 
See how this question can be solved in the test environment using " Owning the Dataset " approach.

https://www.youtube.com/watch?v=s8IMvLF2YsY

Let us know if you have any questions.

Runjhun26 · Answer

Hey  GMATCoachBen , Can you please clarify my doubt- shouldn't the answer values be D & B. because the cost of natural gas will be greater as 1000 < 2500.
So, to get the same answer -> 
HeatN*CostN=HeatP*CostP
1000*175/2500 = CostP = 70

GMATCoachBen · Answer

Runjhun26 , the problem in your formula above is  multiplying instead of dividing  (colored red above): It should be CostN / HeatN = CostP / HeatP.

We do this because the question says that the "fuel cost per BTU" is the same for each, and "per" translates to division.

chetan2u · Answer

As  GMATCoachBen  has also mentioned above that too much of information given while the useful part is very less.

Natural gas:
Let cost per cubic foot = n
Heat produced= 1000BTU per cuft 
Efficiency Kaiser wants is = 90% or the useful heat = 0.9*1000
Cost per useful BTU =  \frac{n}{0.9*1000}

Propane gas:
Let cost per cubic foot = p
Heat produced= 2500BTU per cuft 
Efficiency Kaiser wants is = 90% or the useful heat = 0.9*2500
Cost per useful BTU =  \frac{p}{0.9*2500}

Since cost is same => Cost per useful BTU =  \frac{n}{0.9*1000} =  \frac{p}{0.9*2500} 
 2.5n=p 
So, look for value where p is 2.5 times of n. 
Start with the smallest for value of n. 
 n=70 gives p=175

Iwillget770 · Answer

Hello Experts,
 GMATCoachBen 
 chetan2u

I came across a similar question in OG of DI.
But the wordings of the question are a bit different, but the options are all same.
( I am wondering whether there is any substantial difference b/w both the questions?)

I selected the same answer , but my answer is wrong.

Also, I am not able to understand the Official Explaination. Please guide.

Regards

chetan2u · Answer

Hi

The two questions are different apart from the initial paragraph.

The first question gives you what usable heat is produced or what the efficiency is.

However, in their question, they just mention that efficiency of each furnace is different. But what these different efficiencies are is not known. Without knowing the values, we cannot find the answer.

GMATCoachBen · Answer

@ Iwillget770  Interesting variation, thanks for posting!

As  chetan2u  correctly mentioned, the key difference is that we DO know the efficiencies in the 1st version of the problem, but in this 2nd version that you posted, we DON'T know the efficiencies, which are necessary to make the calculation.

MartyMurray · Answer

Here's the information we have:

When fully burned,

natural gas produces approximately 1,000 BTU of heat per cubic foot of fuel

propane produces about 2,500 BTU of heat per cubic foot of fuel

So, the ratio of the amount of heat produced by a cubic foot of natural gas to the amount of heat produced by a cubic foot of propane is 1000/2500 = 1/2.5.

Then the second paragraph says the following:

Kaiser will purchase a furnace whose efficiency with respect to either natural gas burned alone or propane burned alone is 90%.

This information does not change the ratio we already have since (0.9 × 1000)/(0.9 × 2500) = 1000/2500 = 1/2.5.

In the table select for natural gas cost per cubic foot and for propane cost per cubic foot the values that are jointly consistent with the information given for which the fuel cost per BTU of usable heat energy produced by this furnace would be approximately the same for each fuel burned alone. Make only two selections, one in each column.

Since the two fuels produce heat in the ratio of 1/2.5 per unit, to make the fuel cost per unit the same, we can simply find two prices such that the ratio of prices for natural gas and propane is also in the ratio of 1/2.5.

0.0035

0.0070

0.0110

0.0175

0.0350

The only two prices that are in the ratio of 1/2.5 are 0.0070 and 0.0175.

For  Natural gas cost per cubic foot , select  0.0070 .

For  Propane cost per cubic foot , select  0.0175 .

sayan640 · Answer

GMATCoachBen   chetan2u   KarishmaB  Kindly check the offcial explanation provided by  Iwillget770 .

Dont you think it should be ,

2500 * p/100 BTU costs P $
1 BTU cost P/(2500 * p/100 ) as price per BTU instead of what is derived in the solution (  i.e P * 2500p /100 ; looks like it is wrong )

KarishmaB · Answer

The official explanation given for that question is way too complicated for my liking. The logic is extremely simple and I have discussed it on this link where that question variation is posted: https://gmatclub.com/forum/natural-gas- ... l#p3359850 The answer for this variation (posted by the OP in this thread) is the first part of that explanation: 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. Since here everything else is the same (efficiency is 90% for both), it means that cost should be in the ratio 2:5 and that is why 0.0070 and 0.0175 work. ANSWER: 0.0070 and 0.0175

sayan640 · Answer

I understand that  KarishmaB  . But here is my question :-

If 2500 * p/100 BTU costs P $
1 BTU costs   P/(2500 * p/100 )  as price per BTU instead of what is derived in the official solution (  i.e   P * 2500p /100  ; looks like it is wrong in the official picture shared by  Iwillget770  )

Your comment on this is requested.  KarishmaB   chetan2u

KarishmaB · Answer

Yes, you are right there. It should be P (dollars per cubic foot) divided by "BTU per cubic foot" (which is p% of 2500) to get "dollars per BTU"

GMATinsight · Answer

A very hard question explained beautifully and simply. Please check the video 
  https://www.youtube.com/watch?v=gJZdKPbiDBI

MartyMurray · Answer

When fully burned, natural gas produces approximately 1,000 BTU of heat per cubic foot of fuel, and propane produces about 2,500 BTU of heat per cubic foot of fuel. For a furnace in which either natural gas or propane may be burned as fuel, the efficiency of a given fuel is the usable heat energy produced when the fuel is burned in the furnace, expressed as a percentage of the total heat energy produced when the fuel is burned.

Kaiser will purchase a furnace whose efficiency with respect to either natural gas burned alone or propane burned alone is 90%. In the table select for natural gas cost per cubic foot and for propane cost per cubic foot the values that are jointly consistent with the information given for which the fuel cost per BTU of usable heat energy produced by this furnace would be approximately the same for each fuel burned alone. Make only two selections, one in each column.

Find the Relationship Between the Two Costs Per Cubic Foot

Kaiser will purchase a furnace whose efficiency with respect to either natural gas burned alone or propane burned alone is 90%. So, the efficiency is THE SAME for natural gas as it is for propane.

So, we can ignore the information about the efficiency and consider only the amounts of heat produced by the two types of fuel.

BTU Per Cubic Foot of Natural Gas: 1,000

BTU Per Cubic Foot of Propane: 2,500

So, a cubic foot of propane produces 2,500/1,000 = 2.5 times the amount of heat produced by a cubic foot of natural gas.

Thus, to keep the cost per BTU the same, the cost per cubic foot of propane must be 2.5 times the cost of a cubic foot of natural gas.

2.5N = P

Find Two Values in the List That Fit the Relationship

0.0035

0.0070

0.0110

0.0175

0.0350

Since 2.5N = P, the N value cannot have 5 in the ten thousandths place since 0.0005/2 = 0.00025 and no value has 5 in the hundred thousandths place.

So, N must end in 0.

Try 0.0070 for N.

2.5(0.0070) = 0.0175

Correct answer:   0.0070 ,  0.0175

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83591 Many of these questions are easily solvable by paying attention to units and thinking for a bit about how to arrive at what is asked, from what is given at a unit level. --- Harsha GMAT-Club-Forum-gkavxjqy.png

MercedesF1 · Answer

KarishmaB   GMATCoachBen  - If the energy produced is in the ratio of 2:5 then shouldn't price be in the ratio of 5:2 as the question stem mentions " BTU of usable heat energy produced by this furnace would be approximately the same for  each  fuel burned alone"

KarishmaB · Answer

BTUs of energy produced is in the ratio 2 : 5 BTUs per cubic foot.

BTUs of usable heat energy produced will be in the ratio 0.9*2 : 0.9*5 (Efficiency of the furnace is 90% for both fuels)
This ratio is still 2:5. Say natural gas produces 2 BTU of usable energy per cubic foot and propane produces 5 BTU of usable energy per cubic foot

Usable heat energy is based on the efficiency of the burner. It has nothing to do with pricing. When heat is produced how much of it can be used effectively and how much dissipates in the furnace - that decides the efficiency of the furnace. Here 90% of the heat is used. Hence usable energy is simply 90% of energy produced.

If FUEL COST per BTU of usable energy should be same, fuel cost should be in the ratio 2:5. 
One possibility is fuel cost for natural gas could be $2 (for 2 BTU of usable energy) per cubic foot and for propane $5 (for 5 BTU of usable energy) per cubic foot. 
In this case cost per BTU of usable energy for both fuels is the same $1/BTU of usable energy.

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When fully burned, natural gas produces approximately 1,000 BTU of hea

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Natural gas cost per cubic foot	Propane cost per cubic foot
		0.0035
		0.0070
		0.0110
		0.0175
		0.0350

GMAT Two-part Analysis (TPA) Questions

When fully burned, natural gas produces approximately 1,000 BTU of hea

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