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

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

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New post 08 Nov 2014, 09:20
2
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A
B
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D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:17) correct 19% (01:12) wrong based on 74 sessions

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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

Please provide explanation. Thanks!
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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of  [#permalink]

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New post 08 Nov 2014, 09:40
1
Blackbox 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

Please provide explanation. Thanks!


let total homes be 15
termite ridden= 1/3(15)= 5
termite ridden and collapsing = 3/5(5)=3
thus homes that are termite ridden, but not collapsing = 5-3=2
thus required ratio = 2/15
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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of  [#permalink]

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New post 08 Nov 2014, 19:16
The best way to pick a magic number is to look for a multiple of 3 and 5. I shall try to remember that. Thanks for the answer!
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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of  [#permalink]

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New post 08 Nov 2014, 20:52
1
Blackbox 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

Please provide explanation. Thanks!



Take smart Numbers to solve the problem.

LCM of 3 and 5 = 15
So let, total no. of houses = 15

1/3 of the total are termite ridden = (1/3)*15 = 5
3/5 of termite ridden homes are Collapsing = (3/5)*5 = 3

Therefore,
Homes that are termite ridden but not collapsing = Homes that are termite Ridden - Homes that are termite ridden and collapsing

= 5-3 = 2

Therefore Fraction of homes that are termite ridden but not collapsing = 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]

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New post 12 Aug 2018, 07:22
Let the total homes be "x"
No. of termite ridden homes=x/3
No of termite-ridden homes those are collapsing=x/3*3/5=3x/15
So, no of termite-ridden homes those are not collapsing=x/3-3x/15=2x/15

Answer(A)
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Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of &nbs [#permalink] 12 Aug 2018, 07:22
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