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11 Oct 2016, 01:58
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
71% (02:39) correct
29%
(02:45)
wrong
based on 867
sessions
History
Date
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Result
Not Attempted Yet
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 videocassette 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
(A) 23/30
(B) 11/15
(C) 7/10
(D) 1/6
(E) 2/15
11 Oct 2016, 02:57
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Bunuel
One is taking some value for number of housing units...
Choices have 6, 10, 15 & 30, all factors of 30..... so let's take the number as 30
Houses with CT.... 1/5th so \(\frac{1}{5}*30=6\)..
Houses with VCR 1/10th so \(\frac{1}{10}*30=3\)..
But houses having both= \(\frac{1}{3}*\frac{1}{5}*30=2\)....
\(Total=6+3-2=7\).....
So Houses with neither = 30-7=23..
Fraction=\(\frac{23}{30}\)
Another way...
Ans =\(1-( CT+VCR-BOTH)=1-( \frac{1}{5}+\frac{1}{10}-\frac{1}{3}*\frac{1}{5})=1-(\frac{3}{10}-\frac{1}{15})=1-\frac{7}{30}=\frac{23}{30}\)..
General Discussion
11 Oct 2016, 02:29
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Bunuel
Let total Housing Units = 5x.
As per question, Equipped with Cable TV = x
Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6.
So, Cable TV + VCR = x + x/6 = 7x/6
No Cable TV and VCR = 5x - 7x/6 = 23x/6.
Fraction = 23x/(6 * 5x) = 23/30. Hence, A.
