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.

amitarya · Answer

Sajjad1994   Bunuel ... pls help for the solution..

GMATCoachBen · Answer

amitarya  Thanks for posting, interesting question!

I believe "efficient see" is a typo; if you have a chance, could you please edit it to "efficiency"?

Also, I'm curious, which exam number is this from?

amitarya · Answer

GMATCoachBen .. yes corrected..
Thanks a lot for solution.

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.

GMATCoachBen · Answer

Above, I was asking which exam this was from; I just noticed it on Focus Exam #3.

There's also a similar variation in the OG DI Review, posted above by  Iwillget770

OmerKor · Answer

Hi chetan2u and GMATCoachBen , Excellent explanation! thank you for your help in solving these kind of wierd questions

. I was surprised to see how simple it could be with this great algebra you did. One small thing I didn't fully understand, Where does it say that the cost is equal? You made a comparison of the 2 equations that they are equal but I can't find proof of that in the text. thank you!

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"

sayan640 · Answer

Thank you for confirming. Hence the official explanation , as shared by  Iwillget770  is not just complicated , it is also incorrect.

Posted from my mobile device

av722 · Answer

OmerKor 
This part was a bit confusing to me as well, but at the end of the second paragraph, it says "select... values... for which the fuel cost per BTU of usable heat energy... would be  approximately the same for each fuel burned alone ." which is just a complicated way of saying fuel cost per BTU is equal for both natural gas and propane.

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

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

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

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