Hospital bed

[GmatKiss]

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

[kullayappayenugula]

hi,

Assume that the capacity of the old tower is x.

=>new total capacity = 3x => the new tower capacity is 2x

now 1/3 of first tower is occupied => (1/3)x
also 1/5 of second tower is occupied => (1/5)x

now the total beds occupied = (1/3)x+(1/5)x = (11/15)x

therefore the total beds that are empty in tower 2 is given by 2x-(11/15)x => (19/15)x

The fraction of the beds in the new tower will be unoccupied once the transfer is complete

(19/15)x/(2x) => [spoiler]19/30[/spoiler]






[spoiler][/spoiler]

[GMATGuruNY]

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

To make the math easy, plug in the LCM of the denominators of 1/3 and 1/5.

Let the pre-tower number of beds = 15.
Then the current number of beds = 3*15 = 45, implying that the number of beds in the new tower = 45-15 = 30.
Occupied beds = (1/3)15 + (1/5)30 = 11.
Non-occupied beds in the new tower = 30-11 = 19.
Fraction not occupied in the new tower = 19/30.

The correct answer is D.