A hunting lodge has enough fuel to keep 20 rooms heated for fourteen

Question

A hunting lodge has enough fuel to keep 20 rooms heated for fourteen days. If the lodge decides to save fuel by turning off the heat in 5 unoccupied rooms, and each room requires the same amount of fuel to heat it, how many extra FULL days will the fuel supply last?

(A) 3
(B) 4
(C) 5
(D) 18
(E) 19

(A) 3
(B) 4
(C) 5
(D) 18
(E) 19

bunny12345 · Accepted Answer

Option B.
Easy way is to do it as work rate problems.
As per the formula M1*D1 = M2*D2
20*14 = 15*D2
D2 = 18.67

Question asks how many extra FULL days will the fuel last.

So, Full days are only 18. So, 18-14 = 4

EgmatQuantExpert · Answer

Solution

Given:  
• Enough fuel is present to keep 20 rooms heated for 14 days
• Each room requires the same amount of fuel

To find:  
• Number of extra full days the fuel supply will last if the heat in the 5 unoccupied rooms is turned off

Approach and Working:   
• Let’s assume the fuel required by each room per day = f
 o Therefore, originally the total amount of fuel = f * 20 * 14 
• As the heat in the 5 unoccupied rooms is turned off, let’s assume the total days the fuel will last is D
 o Therefore, f * 20 * 14 = f * 15 * D 
 Or, D =  \frac{280}{15}  = 18.67 
• As the question is asking for FULL extra days, it will be (18 – 14) days = 4 days

Hence, the correct answer is option B.

Answer: B

chieri2 · Answer

EgmatQuantExpert 
Thank you for your solution very helpful.

Could you let me know why below solution is wrong ?
Basically, I thought if I get days per room and then multiply by 5 rooms I could get the answer.

14/20 =7/10 -> days per room
7/10 × 5 = 3.5 days

Thank you in advance.

selale · Answer

The original scheme had 20 X 14 fuel days, divide that by 15 and subtract 14 days.

Other option is to see it visually. 2D array of 20 X 14 with 15 black dots and 5 hollow dots for each day.
15 hollow dots account for 1 day, accounting for a total of 5 X 14. divide that by 15.

effatara · Answer

BASIC UNITARY METHOD

20 rooms can be heated for 14 days
15 rooms (since heat is turned off in 5 rooms) can be heated for 14*(20/15)=18.67 days
Number of full extra days: 18-14=4. Ans: B

aliakberza · Answer

Solved it in the following manner, please tell me if I am right or just got lucky?

So basically we have 25% fewer rooms so fuel will last 25% longer. So we calculate    times 14 to get 3.5 days ~= 4 days?

ScottTargetTestPrep · Answer

Let’s assume there are 280 gallons of fuel for the 20 rooms to be heated for 14 days. So each day (if all 20 rooms use fuel), the lodge uses 280/14 = 20 gallons of fuel, and each room will use 1 gallon of fuel. Since now only 15 rooms use fuel, the 280 gallons of fuel will last 280/15 = 18 ⅔ days, which is 4 ⅔ days more than the 14 days, or an extra 4 FULL days more than the 14 days.

Answer: B

Fdambro294 · Answer

Read the Question, Read the Question, Read the Question.....if I make that mistake 1 more time!

"How many EXTRA FULL Days will the Fuel Supply Last"

Enough Fuel to run 20 rooms --------------------------> 14 Days

Given a Constant Supply of Fuel, the Amount of Fuel we use is INVERSELY Proportional to the Number of Days we can run the facility

Run 20 Rooms ---------------------------> 14 Days

Run 15 Rooms -----------------------------> D Days

The Amount of Fuel Used has DECREASED by (1/4) ------- this means the Number of Days we can run the facility will INCREASE by (1/3)

D = 14 + (1/3) * 14

D = 18 and 2/3 days

Q- How many EXTRA FULL Days can they run the facility?

Prior = 14 Days

NOW = 18 FULL Days

4 Extra Days

-B-

miquelperezn · Answer

Bunuel  could you please explain why is this incorrect? I'm having the same issue

Thanks!

bumpbot · Answer

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A hunting lodge has enough fuel to keep 20 rooms heated for fourteen

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A hunting lodge has enough fuel to keep 20 rooms heated for fourteen

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