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

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Manager
Joined: 30 May 2012
Posts: 198
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of  [#permalink]

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08 Nov 2014, 10:20
2
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:17) correct 24% (01:07) wrong based on 88 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

Senior Manager
Joined: 13 Jun 2013
Posts: 266
Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of  [#permalink]

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08 Nov 2014, 10:40
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

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
Manager
Joined: 30 May 2012
Posts: 198
Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of  [#permalink]

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08 Nov 2014, 20:16
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!
Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 108
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of  [#permalink]

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08 Nov 2014, 21:52
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

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

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Intern
Joined: 16 May 2017
Posts: 48
GPA: 3.8
WE: Medicine and Health (Health Care)
Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of  [#permalink]

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12 Aug 2018, 08:22
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

Re: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of   [#permalink] 12 Aug 2018, 08:22
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