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Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of

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Bunuel
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Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of [#permalink] New post   22 Jan 2020, 02:21
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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
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A
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BrentGMATPrepNow
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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of [#permalink] New post   22 Jan 2020, 07:34
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Bunuel wrote:
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


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

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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of [#permalink] New post   04 Mar 2020, 06:23
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Bunuel wrote:
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


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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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of [#permalink] New post   19 Jul 2021, 06:17
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Let say there are 30 homes on Gotham Street:

=> \(\frac{1}{3}\) are termite-ridden: \(\frac{1}{3} * 30 = 10\)

=> \(\frac{3}{5}\) of these are collapsing: \(\frac{3}{5}\) * 10 = 6

Termite ridden NOT collapsing of all homes: 10 - 6 = \(\frac{4 }{ 30} = \frac{2}{15}\)

Answer A
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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of [#permalink] New post   16 Sep 2023, 23:46
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?

The total fraction of homes = 1
The fraction of homes that are termite-ridden = 1/3
The fraction of homes that are termite-ridden & collapsing = (3/5)*(1/3) = 1/5
Therefore, The fraction of homes that are termite-ridden but not collapsing = (1/3) - (1/5) = 2/15

Hence A
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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of [#permalink]
16 Sep 2023, 23:46
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