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

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".

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

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.

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.

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).

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.

Hi Bunnel

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.

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

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

oh yes..

Reckless reading. Thank you for your reply.

Regards
Megha

Hello Friends,
i did this directly as shown:

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.