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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]

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New post 20 Dec 2011, 08:05
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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]

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New post 05 Jan 2012, 11:09
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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.

Is D the correct answer?
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Re: Algebraic Translations  [#permalink]

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New post 20 Dec 2011, 12:01
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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]

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New post 05 Jan 2012, 07:49
Could someone please show the complete solution to this problem? I am getting an answer that is not listed in the answer choices. Please help. TIA.
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Re: Algebraic Translations  [#permalink]

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New post 05 Jan 2012, 14:45
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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]

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New post 05 Jan 2012, 21:24
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]

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New post 11 Feb 2012, 16:39
D as correct answer.
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]

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New post 07 Apr 2014, 00:30
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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 \(= \frac{19x}{15}* \frac{1}{2} = \frac{19x}{30}\)

Answer = D
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Re: A new tower has just been built at the Verbico military  [#permalink]

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New post 17 Jul 2015, 23:58
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olivite wrote:
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


Check the working in figure.

Answer: Option D
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A new tower has just been built at the Verbico military  [#permalink]

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New post 18 Dec 2015, 16:41
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olivite wrote:
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


Forget variables and formulas, try to pick some smart numbers:
Before new tower: 15
After new tower: 15*3=45 (OVERALL ! means new tower + old wing)

New tower: 30 and 20% are occupied = 6
Old wing: 15 (as before renovation) and \(\frac{1}{3}\)are occupied = 5 and then this amount is transfered to the new tower -> 6+5=11 as of now there are 11 beds occupied in the new tower and 30-11=19 beds free, what brings us to our solution\(\frac{19}{30}\) are unoccupied
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A new tower has just been built at the Verbico military  [#permalink]

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New post 30 Jan 2017, 10:55
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

let x=original beds
2x=new tower beds
(x/3)+(2x/5)=11x/15 occupied beds in new tower after transfer
2x-(11x/15)=19/15*x unoccupied beds in new tower after transfer
(19/15*x)/2x=19/30
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Re: A new tower has just been built at the Verbico military  [#permalink]

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New post 04 Mar 2018, 16:16
Hi All,

I'm a big fan of TESTing Values (BrainLab's explanation), but this question can also be solved with algebra….

We're told that adding a new tower to an existing hospital allows fore 3 times the number of available beds that were there before the tower was built:

Just the hospital = X beds
Hospital + new tower = 3X beds

Just the tower = 3X - X = 2X beds

We're told that 1/3 of the original hospital beds and 1/5 of the tower beds are occupied:

1/3 of X beds + 1/5 of 2X beds = X/3 + 2X/5 = 5X/15 + 6X/15 = 11X/15 occupied beds

Next, we're told that all of the patients in the original hospital must be transferred to the tower. Since the tower has 2X beds in it, the tower is now…..

[11X/15]/2X full = 11/30 full

The question asks for the fraction of the beds in the tower that are UNOCCUPIED:

30/30 - 11/30 = 19/30 UNOCCUPIED

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Re: A new tower has just been built at the Verbico military  [#permalink]

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New post 21 Aug 2018, 18:36
olivite wrote:
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


Let total number of beds in the hospital before the new tower =\(x\)
Now , the total number of beds available after the new tower was built = \(3x\)
therefore the total number of beds in the new tower = \(3x - x = 2x\)

now total number of occupied beds from the original beds(Before the new tower was built)
= \(\frac{1}{3}x\)

now total number of occupied beds from the new tower
= \(\frac{1}{5}2x\)

number of beds unoccupied from the new tower
= \(2x\)- \(\frac{2}{5}x\) = \(\frac{8}{5}x\)


now, numbers of beds left unoccupied in new tower after we shift the patients from old building to new tower
= \(\frac{8}{5}x\) -\(\frac{1}{3}x\)
= \(\frac{19}{15}x\)

Now, we have total number of unoccupied beds in the new tower(\(\frac{19}{15}x\)), as well as the total number of beds(occupied and unoccupied) in the new tower(\(2x)\)


therefore the answer is = \(\frac{19x}{15 *2x}\) = \(\frac{19}{30}\)
Option D
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Re: A new tower has just been built at the Verbico military  [#permalink]

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New post 30 Jan 2019, 19:11
olivite wrote:
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


We can assume there are 30 beds available in the original hospital wing, and thus there are 60 beds available in the new tower (notice that the total number of beds in the two locations is 90, which is 3 times the number of beds in the original hospital wing). We know that 1/3 x 30 = 10 beds in the original wing and 1/5 x 60 = 12 beds in the new tower are occupied, and the 10 patients from the original wingr are transferred to the new tower. So the new tower now has 12 + 10 = 22 patients, and thus the number of unoccupied beds is 60 - 22 = 38. Therefore, the fraction of the beds in the new tower that are unoccupied after the transfer is 38/60 = 19/30.

Answer: D .
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A new tower has just been built at the Verbico military  [#permalink]

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New post 14 Sep 2019, 23:19
olivite wrote:
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


Given:
1. 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.
2. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied.
3. 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.

Asked: 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?

Let the number of beds originally be x
Number of beds after a new tower is built = 3x
Number of beds in new tower = 3x-x = 2x

Occupied beds: -
x/3 original beds
2x/5 beds in new tower
Since all patients in original beds are transferred to new tower
Occupied beds in new tower will become = x/3 + 2x/5 = 11x/15
Fraction of beds occupied in new tower = 11x/15 / 2x = 11/30
Fraction of beds unoccupied in new tower = 1 - 11/30 = 19/30

IMO D
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A new tower has just been built at the Verbico military   [#permalink] 14 Sep 2019, 23:19
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