davo45 wrote:In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with vidieocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ?
(A)23/30
(B)11/15
(C)7/10
(D)1/6
(E)2/15
Total = Group 1 + Group 2 - Both + Neither.
The big idea with overlapping groups is to SUBTRACT THE OVERLAP. When we count all of the housing units with cable (Group 1) and all of the housing units with VCRs (Group 2), the overlap -- the number of households with BOTH cable and VCRS -- gets counted twice. So we need to subtract the overlap so that these households are not double-counted.
Let total households = 30.
Group 1 = households with cable = (1/5)*30 = 6.
Group 2 = households with VCRs = (1/10)*30 = 3.
Both = 1/3 of the households with cable = (1/3)*6 = 2.
Plugging these values into the formula:
30 = 6 + 3 - 2 + N
N = 23.
Neither/Total = 23/30.
The correct answer is
A.
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