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Military hospital beds

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by gmattesttaker2 » Sat Oct 12, 2013 9:42 pm
Hello,

Can you plesae assist with this:

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?

11/30
29/60
17/30
19/30
11/15

OA: [spoiler]19/30[/spoiler]


Thanks for your help - Sri
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by theCodeToGMAT » Sat Oct 12, 2013 9:59 pm
Before Tower = x

New Tower = 3x

Currently, Occupied: x/3 & 2x/5

x/3 patients need to be transferred to New Tower
So, occupancy in New Tower = x/3 + 2x/5
Unoccupied Fraction= [2x - (x/3 + 2x/5)]/2x
=[2 - (5+6/15)]/2
=[30-11]/30
19/30

Answer [spoiler]{D}[/spoiler]
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by sanju09 » Sat Oct 12, 2013 10:40 pm
gmattesttaker2 wrote:Hello,

Can you plesae assist with this:

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?

11/30
29/60
17/30
19/30
11/15

OA: [spoiler]19/30[/spoiler]


Thanks for your help - Sri
A wordy question on GMAT merely tests our reading patience. We should read it piece by piece and draw the conclusions out step by step.

If there were 15 beds in the hospital before the new tower was built, then there must be 30 beds in the new wing as per the question. So, currently 1/3 of the original 15 or 5 beds, and 1/5 of the 30 new beds, i.e. 6 beds in the new tower, are occupied, or a total of [spoiler]11[/spoiler] beds are occupied. If all the 11 patients are made to occupy the new wing of 30 beds, then [spoiler]19[/spoiler] of the beds there would remain unoccupied, which constitutes [spoiler]19/30[/spoiler] of the total beds there.

[spoiler]Pick D[/spoiler]
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by GMATGuruNY » Sun Oct 13, 2013 3:56 am
gmattesttaker2 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?

11/30
29/60
17/30
19/30
11/15
TOTAL BEDS:
Let the ORIGINAL number of beds = the LCM of the denominators in the problem = 3*5 = 15.
Since there are now 3 times as many beds available, the CURRENT number of beds = 3*15 = 45.
Thus, the number of NEW TOWER BEDS = 45-15 = 30.

OCCUPIED BEDS:
Since 1/3 of the original beds and 1/5 of the new tower beds are occupied, the total number of occupied beds = (1/3)15 + (1/5)30 = 11.

UNOCCUPIED BEDS:
When all 11 patients are in the new tower, the number of unoccupied beds in the new tower = 30-11 = 19.
Thus, the fraction unoccupied in the new tower = unoccupied/total = 19/30.

The correct answer is D.
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