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# A new tower has just been built at the Verbico military

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A new tower has just been built at the Verbico military [#permalink]  20 Dec 2011, 07:05
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A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 3 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?

A. 11/30
B. 29/60
C. 17/30
D. 19/30
E. 11/15

I don't understand how can you infer from the sentence "the number of beds available for patients at the hospital is now 3 times the number available before the new tower was built" that the "The new tower is not itself three times the size of the old wing; the problem states that the capacity of the entire hospital is three times its original value, so the new tower has twice as many beds as the old wing"
I keep re-reading the sentece and still see that the new hospital is 3 times bigger than the old one.
HELP
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Re: Algebraic Translations [#permalink]  20 Dec 2011, 11:01
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The wording is definitely tricky!

So think of it this way: If the hospital currently has 10 beds and it is to triple the number of beds, there will now be 30 total beds: 10 for the original tower and 20 for the new tower. The number of beds in the new tower will therefore be double that of the old tower.

Had the new tower contained three times (e.g. 10 x 3 = 30 + 10 = 40) then there would be four times as many beds.

I think you may have conflated the term “new tower” with new hospital. “New hospital,” which is never explicitly stated, is a combination of the new tower and the old hospital.

Hope that resolves any ambiguity!
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Re: Algebraic Translations [#permalink]  05 Jan 2012, 06:49
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Re: Algebraic Translations [#permalink]  05 Jan 2012, 10:09
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I think D - 19/30 is the correct answer.

Here goes:

Lets assume originally the number of beds = x

After the new tower, the total combined no of beds = 3x

So old = x, New = 2x

Now 1/3 of x are occupied and 1/5 of 2x are occupied which simplifies to (2/5)x

We are shifting 1/3 of x to the new ward so there will now be:

1/3 of x plus 2/5 of x occupied in the new ward. Add them up to get 11/15 of x

There are 2x beds in New Tower so ratio is:

(11/15)x / 2x = 11/30 of x

Subtract that from 30/30 of x and you get the number of un-occupied beds to total capacity of New Tower.

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Re: Algebraic Translations [#permalink]  05 Jan 2012, 13:45
Let logically split this problem.

Old: number of beds = x. x/3 occupied
New: number of beds = 2x (overall 3x). 2x/5 occupied. So, 8x/5 unoccupied.

x/3 now moved from old to new -> unoccupied beds in new will be = 8x/5 - x/3 = 19x/15

So, fraction of unoccupied in new -> # of unoccupied / total in new = (19x/15) / 2x = 19/30 -> D
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Re: Algebraic Translations [#permalink]  05 Jan 2012, 20:24
Ans is D

let x be the no of beds in the original hospital
so 2x is the no of beds in the new hospital

now x/3 and 2x/5 are occupied. so total is 11x/15

so no of unoccupied beds = 2x-11x/15 = 19x/15

so the fraction is 19x/15/2 = 19x/30

definitely a wordy question.
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Re: Algebraic Translations [#permalink]  11 Feb 2012, 15:39
remember that the now the in total it can hold 3times as many people including the old building. Then set your own number of beds for simplicity 15 (old) 30 (new)
1/3 of 15 is 5 and 1/5 of 30 is 6.... 5+6 / 30 is your fraction of beds filled... you must subtract 11 from 30 to get the answer of how many are not filled. 19/30.
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Re: A new tower has just been built at the Verbico military [#permalink]  29 Nov 2013, 02:16
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Re: A new tower has just been built at the Verbico military [#permalink]  06 Apr 2014, 23:30
Old Hospital = x

New Hospital = 2x (After addition of new hospital, capacity = 3x which is thrice of the old hospital)

Old Hospital Occupancy $$= \frac{x}{3}$$

New Hospital Occupancy$$= \frac{2x}{5}$$

After transfer from old to new hospital,

New Hospital Occupancy$$= \frac{2x}{5} + \frac{x}{3} = \frac{11x}{15}$$

Vacancy in New Hospital $$= 2x - \frac{11x}{15} = \frac{19x}{15}$$

Fraction $$= \frac{19x}{15}* \frac{1}{2} = \frac{19x}{30}$$

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Re: A new tower has just been built at the Verbico military   [#permalink] 06 Apr 2014, 23:30
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