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A straight fence is to be constructed from posts 6 inches wi

by varun289 » Wed Apr 24, 2013 12:25 am
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
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by Anju@Gurome » Wed Apr 24, 2013 12:41 am
varun289 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?
As the fence begins and ends with a post, the number of posts in the fence will be one more than number of chains in the fence.

Let us assume number of chains in the fence = N
So, number of posts in the fence = N + 1

Also assume the length of the fence in feet is L.

So, L = (total length of (N + 1) posts in feet) + (total length of N chains in feet)
= (N + 1)/2 + 5N
= [(N + 1) + 10N]/2
= (11N + 1)/2

So, (2L - 1) = 11N = multiple of 11 as n must be integer

Plug the answer choices as the value of L.
The correct option should be the one for which (2L - 1) is not a multiple of 11.
  • A. L = 17 ---> (2L - 1) = (34 - 1) = 33 ---> NO
    B. L = 28 ---> (2L - 1) = (56 - 1) = 55 ---> NO
    C. L = 35 ---> (2L - 1) = (70 - 1) = 69 ---> YES
As there will be only one correct option, no need to check the rest.

The correct answer is C.
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by Anju@Gurome » Wed Apr 24, 2013 12:50 am
After getting L = (11N + 1)/2, we can approach as follows too.
Now, if N is even, (11N + 1) will be odd and L cannot be an integer.
But all the options are integer. So, N must be an odd integer.

Possible values of L are as follows...
  • For N = 1 ---> L = (11 + 1)/2 = 6
    For N = 3 ---> L = (33 + 1)/2 = 17
    For N = 5 ---> L = (55 + 1)/2 = 28
    For N = 7 ---> L = (77 + 1)/2 = 39
As the values of L will only increase after this and we have skipped 35, l cannot be 35.

The correct answer is C.
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by GMATGuruNY » Wed Apr 24, 2013 2:53 am
varun289 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
The components of the fence ALTERNATE:
...post + chain + post...
The structure must BEGIN and END with a post.
Post = 1/2 foot and chain = 5 feet.

The smallest option among the answer choices is 17 feet, implying three lengths of 5:
1/2 + 5 + 1/2 + 5 + 1/2 + 5 + 1/2 = 4(1/2) + 3*5 = 17.
Every time we add chain + post, the total length increases by 5 + 1/2 = 5.5 feet.
The answer choices are all integers.
Possible integer lengths greater than 17:
17 + 2(5.5) = 28.
28 + 2(5.5) = 39.
No way to get a total length of 35.

The correct answer is C.
Last edited by GMATGuruNY on Wed Apr 24, 2013 3:25 am, edited 1 time in total.
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by Anju@Gurome » Wed Apr 24, 2013 3:09 am
GMATGuruNY wrote:... Post = 6 and chain = 5.

Possible total lengths:
6+5+6 = 17.
6+5+6+5+6 = 3*6 + 2*5 = 28.
6+5+6+5+6+5+6 = 4*6 = 3*5 = 39.
A small correction : length of a post is 6 inches = 1/2 feet not 6 feet.
And the possible lengths will change accordingly.
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by btgsnt » Wed Apr 24, 2013 8:04 am
Hi Anju@Gurome,

Could you provide the posts and chain in a graph, so that it will help us in understand the question in easy way.

Thanks in advance.
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by Anju@Gurome » Wed Apr 24, 2013 8:17 am
btgsnt wrote:Could you provide the posts and chain in a graph, so that it will help us in understand the question in easy way.
Refer to the diagram below,
Image
The vertical black lines are posts and the horizontal blue ones are chains...
1st : 2 posts and 1 chain
2nd : 3 posts and 2 chains
3rd : 4 posts and 3 chains
4th : 5 posts and 4 chains
and so on...
In general, there will always be one more post than the chains.

Hope that helps.
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