A probably medium question, pls help to explain the middle. : GMAT Problem Solving (PS)
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A probably medium question, pls help to explain the middle.

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A probably medium question, pls help to explain the middle. [#permalink]

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New post 24 Jul 2011, 02:45
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40% (02:21) correct 60% (00:21) wrong based on 5 sessions

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In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?

a)23/30
b)11/15
c)7/10
d)1/6
e)2/15

I calculate at the middle that 1/10*1/3= 1/30. but the answer is 1/15, why is that? I made the mistake at this point, pls instruct me. thank u~
[Reveal] Spoiler: OA
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Re: A probably medium question, pls help to explain the middle. [#permalink]

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New post 24 Jul 2011, 05:12
tracyyahoo wrote:
In Township K, 1/5 of the housing units are equiped with cable Tv. If 1/10 of the housing units, including 1/3 of those that are equiped with cable tv, are equipped with videocassette recorders, what fraction of the housing units have neither cable tv nor videocassette recorders?

a)23/30
b)11/15
c)7/10
d)1/6
e)2/15

I calculate at the middle that 1/10*1/3= 1/30. but the answer is 1/15, why is that? I made the mistake at this point, pls instruct me. thank u~


1/5 -- cable TV (This includes some data from video cassette recorder)
1/10 -- video cassette recorder including 1/3(equiped with cable tv) i.e. 1/3(1/5) = 1/15

therefore only video cassette recorder = 1/10 - 1/15 = 1/30
Total = 1/5+1/30+neither cable tv nor videocassette recorders
1 = 7/30 + neither cable tv nor videocassette recorders
therefore neither cable tv nor videocassette recorders = 1-7/30 = 23/30

Hence A.
Re: A probably medium question, pls help to explain the middle.   [#permalink] 24 Jul 2011, 05:12
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A probably medium question, pls help to explain the middle.

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