Fence

knight247 wrote:A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 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)

A. 17
B. 28
C. 35
D. 39
E. 50

OA is C. Detailed explanations would be appreciated.

Notice that to have a fence, we need at least 2 posts and 1 chain. If we measure this in feet (because that is the measure for the answer):

[.5]-------5--------[.5]

The minimum length is 6 feet. Now, to increase the length of the fence, we would have to add an additional chain+post, or 5.5 feet. But take a look at the answers, they are all in whole numbers! That means that we will need to add enough fence each time to cancel out the 0.5 inch posts - so that means we need to add 2 chains and 2 posts each time: 5+0.5+5+0.5 = 11 feet.

Now we can just list out the possible numbers starting with 6 and increasing in 11 foot increments.

6, 17, 28, 39....

But wait - we just skipped over 35, choice C.

Hope this helps!

Whit