A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 7 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot) Choose the correct answer.
A) 18
B) 23
C) 38
D) 53
E) 68
There is one post for each length of chain, plus one final post at the end.   The length of the fence in feet is 7.5x + 0.5, where each is the number of chain lengths.   The length of the fence is an integer when x = 1,3,5,7,...   The length of the fence could be 8, 23, 38, 53, 68,...   The answer is 18.
<result>A</result>
A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 7 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)