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A fence consists of m lengths of fence that are each n feet [#permalink]

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09 Dec 2012, 11:53

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C

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E

Difficulty:

45% (medium)

Question Stats:

55% (02:38) correct
45% (01:15) wrong based on 83 sessions

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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

Re: A fence consists of m lengths of fence that are each n feet [#permalink]

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10 Dec 2012, 00:44

Expert's post

akshayb2 wrote:

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

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.

Re: A fence consists of m lengths of fence that are each n feet [#permalink]

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11 Dec 2012, 12:37

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

Re: A fence consists of m lengths of fence that are each n feet [#permalink]

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12 Dec 2012, 02:30

Expert's post

Ousmane wrote:

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

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". _________________

Re: A fence consists of m lengths of fence that are each n feet [#permalink]

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14 Dec 2012, 02:55

1

This post received KUDOS

Bunuel wrote:

akshayb2 wrote:

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

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.

Re: A fence consists of m lengths of fence that are each n feet [#permalink]

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14 Dec 2012, 03:02

Expert's post

mtripathy wrote:

Bunuel wrote:

akshayb2 wrote:

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

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.

Re: A fence consists of m lengths of fence that are each n feet [#permalink]

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14 Dec 2012, 03:17

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). _________________

Re: A fence consists of m lengths of fence that are each n feet [#permalink]

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17 Dec 2012, 00:15

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.

Re: A fence consists of m lengths of fence that are each n feet [#permalink]

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09 Feb 2014, 02:22

Bunuel wrote:

akshayb2 wrote:

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

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.

Re: A fence consists of m lengths of fence that are each n feet [#permalink]

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09 Feb 2014, 02:40

Expert's post

Qoofi wrote:

Bunuel wrote:

akshayb2 wrote:

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

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.

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

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. _________________

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