Problem Solving

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

OA is A

grandh01 wrote:In Township K,
1/5 of the housing
units are equipped with cable
television. If 1/10 of the housing units,
including 1/2 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

Sum of all fractions = 1.

Cable = 1/5
Video = 1/10
Both = 1/3 * 1/5 = 1/15 (1/3 of cable ones also have video)
Now:
1 = Cable + Video - Both + Neither
1 = 1/5 +1/10 -1/15 + Neither
30/30 = 6/30 + 3/30 -2/30 + Neither
Neither = 23/30.

A is correct

sorry about that I made a mistake, I edited the post.

grandh01 wrote:sorry about that I made a mistake, I edited the post.

And I've edited mine