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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

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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

The OA is D

Source: Manhattan Prep

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swerve 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
Let the PRE-TOWER number of beds = the LCM of the denominators in the problem = 3*5 = 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.

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Hi j_shreyans,

I'm a big fan of TESTing Values (Mitch'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

Final Answer: D

GMAT assassins aren't born, they're mad,
Rich

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Contact Rich at Rich.C@empowergmat.com

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swerve 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

The OA is D

Source: Manhattan Prep
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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scott@targettestprep.com



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