A fence consists of m lengths of fence that are each n feet

Question

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

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

Bunuel · Answer

Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (m+1)x. The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x. Answer: C. Hope it's clear. P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rules #2 and 3. Thank you.

akshayb2 · Answer

Hey Bunuel, thanks for the quick reply. I was bit confused with the wordings. Its clear now

Ousmane · Answer

Bunnuel I don't agree with you.
For me if there are n = 2 fences, then according to the requirement of there being a post to seperate them, there ought to be n-1 post. So mn + (n-1)x
But if the fence got to start and finish with a post, then yes you are right. But this is not what the stem says. I am getting things wrong? Please help.
Brother Karamazov

Bunuel · Answer

I think, this is exactly what the stem is saying:
"A fence post separates  each length  of fence..."
"What is the total length of the fence including  the fence posts  on each end  ".

Ousmane · Answer

Bunnuel, you are so kind. You should at times go angry. But don't mind me. I struggle with English some times
Thanks anyway
Brother Karamazov

mtripathy · Answer

Notice that since a fence post separates each length of fence, then there will be n+1 posts, for example if there are n=2 fences, then there will be 3 posts: PFPFP. Thus the total length of the posts is (n+1)x.

The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (n+1)x+mn= nx+x+mn=m(n+x)+x.

Answer: C.

Hope it's clear.

Hi, could you please recheck the highlighted portion. I think there is a mistake.

Bunuel · Answer

There was a typo: n instead of m (a-fence-consists-of-m-lengths-of-fence-that-are-each-n-feet-143845.html#p1152801) Thus it should be (m+1)x+mn=mx+x+mn=m(n+x)+x. Thank you for pointing that out. +1.

priyamne · Answer

Ans:

the total length of fence without the posts would be mn, now if there are 2 fences there would be 3 posts because PFPFP, so total posts= (n+1). Length of posts=(n+1)x. Total length of fence= nx+x+mn, therefore the answer is (C).

maddyboiler · Answer

Firstly the term just "fence" is not clear. Now a "fence" can be a  closed fence  or it can be an  open fence . If this kind of wording was given then it would have been more clear because..

Things we know for sure
1. A "post" separates the "fence lengths" 
2. m = #of fence lengths, 1lenght = n feet long, total length of the fence alone = mn
3. z = # of posts, length of 1 post = x feet long, total length of all the posts alone = zx
4. Total length of fence and posts = mn + zx

The crucial factor here is z. we have to determine what z is.

Now i stress more on the wording here in the question is because
1. Closed fence (the ends are joined)
When a fence is closed then the #of posts = #of fence lengths. Diagram it, it looks something like PFPF
m = z . Therefore Total = mn + mx

2. Open Fence (the ends are not joined)
What if the Fence starts wit a post
Case 1 - PFPFP here x = m + 1. Total length = mn + x(m + 1)
Case 2 - PFPFPF here x = m, Total Length = mn + mx

What if The fence starts with a Fence length
Case 1 - FPFPF here x = m -1, Total length = mn + (m-1)x
Case 2 - FPFP here x = m, Total Lenght = mn + mx

We have here three different kinds of answers and all of them are correct. The question is not specific.

Qoofi · Answer

Hi Bunnel

Can you make a pictorial representation of your explanation? I'm not able to get it. 
Apologies for the pain.

Bunuel · Answer

It's already given. If m=2 fences there will be 3 posts: {Post}{Fence}{Post}{Fence}{Post}. Each fence is n feet and each post is x feet.

megha_2709 · Answer

How can we assume there is a post at the beginning . It could be the case : fence post fence post , in that case no of fences = no of posts.

Please help.

Regards
Megha

abhimahna · Answer

It is given in the question "including the fence posts on  each end ". Hence, we need to consider fence post-fence-fence post -.. order.

megha_2709 · Answer

oh yes.. Reckless reading. Thank you for your reply.

Regards Megha

manishtank1988 · Answer

Hello Friends, 
i did this directly as shown:

JeffTargetTestPrep · Answer

The total length of the fence only (without the posts) is mn feet long. Since each post is x feet long and there is a post at each end of the fence in addition to the posts separating each length of the fence, there must be (m + 1) posts along the fence. Thus the total length of the posts is x(m + 1), and the total length of the fence, including the posts, is:

mn + x(m + 1)

mn + xm + x

m(n + x) + x

Alternate Solution:

Let’s suppose that there were m = 3 lengths of fence that are n = 2 feet long and the posts separating the fences were x = 1 foot. Under these assumptions, the total length is 1 + 2 + 1 + 2 + 1 + 2 + 1 = 10 feet. Let us see which answer choice(s) give us 10 when m = 3, n = 2 and x = 1:

Answer Choice A:

mn = 3(2) = 6

Eliminate answer choice A.

Answer Choice B:

m(n + x) = 3(2 + 1) = 9

Eliminate answer choice B.

Answer Choice C:

m(n + x) + x = 3(2 + 1) + 1 = 10

C is a possible choice.

Answer Choice D:

m(n + x) + 2x = 3(2 + 1) + 2 = 11

Eliminate answer choice D.

Answer Choice E:

2mn = 2(3)(2) = 12

Eliminate answer choice E.

The only possible answer choice is C.

Answer: C

bumpbot · Answer

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A fence consists of m lengths of fence that are each n feet

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A fence consists of m lengths of fence that are each n feet

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