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In a hostel, the number of students decreased by 8% and the [#permalink]

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01 May 2012, 21:22

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In a hostel, the number of students decreased by 8% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?

In a hostel, the number of students decreased by 8% and the [#permalink]

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01 May 2012, 23:23

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Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)

Originally, C = FNP

When number of students decrease by 8%, and the price of food increases by 20%, C = F(new) * (0.92N) * (1.2P) => F(new) = F/(0.92*1.2) => F(new) = 0.906F

Therefore the new cost of food must be 90.6% of the old cost, or the cost of food must decrease by 9.4% (option E) _________________

Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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20 Aug 2014, 10:58

I cannot see this being a GMAT problem - how is one supposed to calculate 1- [1/(.92*1.2)] without a calculator? Even with using fractions I get 13/138 which is also not easily solved.

Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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21 Aug 2014, 00:08

speedilly wrote:

I cannot see this being a GMAT problem - how is one supposed to calculate 1- [1/(.92*1.2)] without a calculator? Even with using fractions I get 13/138 which is also not easily solved.

Agree.. this calculation goes tough. Any simpler way to avoid that 92 & 12 factor? _________________

Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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21 Aug 2014, 01:04

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PareshGmat wrote:

speedilly wrote:

I cannot see this being a GMAT problem - how is one supposed to calculate 1- [1/(.92*1.2)] without a calculator? Even with using fractions I get 13/138 which is also not easily solved.

Agree.. this calculation goes tough. Any simpler way to avoid that 92 & 12 factor?

Hello

My approach is

Name: S = number of students P = Price Q = Quantity of food consumption. C = total cost

==> C = S*P*Q

One way to solve this kind of question is plug in numbers. Assume: before we have 100 students, P = $10 ==> C = 100*10*Q = 1000*Q After: we have 92 students, P = $12 ==> C' = 92*12*Q' = 1104*Q'

The red part is the decrease of food consumption. We can guess 104/1104 ~ 9.4% (The ONLY option < 10%) --> E is answer.

Hope it helps. _________________

Please +1 KUDO if my post helps. Thank you.

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Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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13 Feb 2016, 02:37

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a hostel, the number of students decreased by 8% and the [#permalink]

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14 Apr 2016, 03:51

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stonecold wrote:

Vyshak Any Shortcuts here ? took me 8 minutes to solve i solved twice actually thrice

regards Stone Cold

Yes bro possible

IMHO that we need to take three factors ( No of Students , Consumption per student and Cost of Food ) and create a table as below -

Attachment:

1.PNG [ 4.07 KiB | Viewed 186 times ]

Where Total Cost = No of Students * Consumption per student * Cost of Food

So, from the above table find the new value of Consumption per student

Consumption per student = Total Cost / ( No of Students * Cost of Food ) =>Consumption per student = 10000 / 92 * 12 =>New Consumption per student = 9.06

Now find the last part -

Quote:

By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?

Reduction in consumption required is 10 - 9.06 = 0.94

So, Percentage consumption of food be cut short by every student = 0.94/10 * 100 = 9.40% _________________

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