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Equation problem

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by diegocuenca » Thu Aug 04, 2011 12:24 pm
A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length of the fence including the fence posts on each end?

A. mn
B. m(n + x)
C. m(n + x) + x
D. m(n + x) + 2x
E. 2mn

The correct is C, why is it not D?
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by pinchharmonic » Thu Aug 04, 2011 5:20 pm
this is where m = 2

|x|--n--|x|--n--|x|

taking care of the lengths of fence you have m * n.
now you have to take care of the posts. The posts are always between each length of fence as well as at the beginning and after. As the picture shows, that is always 1 more than the number of fence pieces. You can see in the picture, 3 posts for 2 fence pieces.

(m+1)x thus gives you the total length of the posts.

m * n + (m+1)x

then factor

m*n + mx + x
m(n + x) + x
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by gmatboost » Thu Aug 04, 2011 7:24 pm
One way to think about counting the number of posts correctly:

Think of the posts as being attached to every length of fence on the left side of the length.

So it goes: PL-PL-PL....
equal number of posts and lengths ...
until the very end, when we will need 1 post on the right to close it off:
...PL-PL-PL-P

That means the number of posts is equal to the number of lengths, plus 1.
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