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Of all the homes on Gotham Street, 1/3 are termite-ridden,

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by BTGModeratorVI » Sun Feb 23, 2020 6:52 am
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Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?

A. 2/15
B. 3/15
C. 4/5
D. 2/5
E. 1/5

Answer: A
Source: Manhattan Prep
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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden,

by Brent@GMATPrepNow » Wed Feb 26, 2020 7:01 am
BTGModeratorVI wrote: ↑
Sun Feb 23, 2020 6:52 am
 Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?

A. 2/15
B. 3/15
C. 4/5
D. 2/5
E. 1/5

Answer: A
Source: Manhattan Prep
Given: 1/3 of the homes are termite-ridden
Given: 3/5 of the termite-ridden homes are collapsing.
So, 2/5 of the termite-ridden homes are NOT collapsing.

So, the the fraction of the homes are termite-ridden, but NOT collapsing = (1/3)(2/5)
= 2/15

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden,

by Scott@TargetTestPrep » Sun Mar 01, 2020 12:55 pm
BTGModeratorVI wrote: ↑
Sun Feb 23, 2020 6:52 am
 Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?

A. 2/15
B. 3/15
C. 4/5
D. 2/5
E. 1/5

Answer: A
Source: Manhattan Prep
Solution:

If there are 60 homes, 60 x 1/3 = 20 are termite-ridden, and of those 20 homes, 20 x 3/5 = 12 are collapsing. Thus, 8 homes are termite-ridden but not collapsing, and they account for 8/60 = 2/15 of all the homes.

Alternate solution:

Since 1/3 of all homes are termite-ridden and 3/5 of them are collapsing, 2/5 of them are not collapsing. Therefore, 2/5 of 1/3 of all homes are termite-ridden but not collapsing. That is, 2/5 x 1/3 = 2/15 of all homes are termite-ridden but not collapsing.

Answer: A

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