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

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Bunuel
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A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   01 May 2018, 05:31
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58% (02:12) correct 42% (02:15) wrong based on 183 sessions
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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
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B
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EgmatQuantExpert
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Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   01 May 2018, 06:44
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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
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Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   01 May 2018, 08:36
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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
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Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   31 May 2019, 02:24
EgmatQuantExpert wrote:

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


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.
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selale
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Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   31 May 2019, 03:02
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.
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Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   04 Jun 2019, 08:16
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
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Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   07 Jun 2019, 13:09
Bunuel wrote:
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


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 [1][/4] times 14 to get 3.5 days ~= 4 days?
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Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   09 Jun 2019, 19:11
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Bunuel wrote:
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


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
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Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   07 Nov 2020, 23:51
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-
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Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink] A hunting lodge has enough fuel to keep 20 rooms heated for fourteen   03 May 2024, 03:52
Bunuel could you please explain why is this incorrect? I'm having the same issue

Thanks!

chieri2 wrote:
EgmatQuantExpert wrote:

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


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.

­
gmatclubot
Re: A hunting lodge has enough fuel to keep 20 rooms heated for fourteen [#permalink]
03 May 2024, 03:52
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Bunuel
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