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A farmer constructs a fence along the northern edge of his property

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Nanobotstv
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A farmer constructs a fence along the northern edge of his property [#permalink] New post   03 Oct 2016, 06:27
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A farmer constructs a fence along the northern edge of his property, using materials such that he places a post every 7 meters. if he uses 100 posts, how many meters will the fence span?

A. 686
B. 693
C. 700
D. 707
E. 770
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B
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BrentGMATPrepNow
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A farmer constructs a fence along the northern edge of his property [#permalink] New post   Updated on: 20 Jan 2020, 08:21
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alanforde800Maximus wrote:
A farmer constructs a fence along the northern edge of his property, using materials such
that he places a post every 7 meters. if he uses 100 posts, how many meters will the fence span?

a)686
b)693
c)700
d)707
e)770

Please assist with above problem.


Let's look for a pattern...

1 post: fence span = 0 meters
2 posts: fence span = 7 meters
3 posts: fence span = 7 + 7 = 14 meters
4 posts: fence span = 7 + 7 + 7 = 21 meters
5 posts: fence span = 7 + 7 + 7 + 7 = 28 meters
.
.
.
We can see that, for n posts, we add 7 n-1 times
.
.
.
100 posts: fence span = sum of 99 sevens = (99)(7) = 693 meters
Answer:
Show Spoiler
B

Originally posted by BrentGMATPrepNow on 03 Oct 2016, 07:32.
Last edited by BrentGMATPrepNow on 20 Jan 2020, 08:21, edited 1 time in total.
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Re: A farmer constructs a fence along the northern edge of his property [#permalink] New post   03 Oct 2016, 07:26
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Between two post there is one length of fencing material, between three post there are two lengths, thus between 100 posts there are 99 lengths..
99 x 7 = 693

[url=https://gmatclub.com/forum/gmat-toolkit-iphone-ipod-application-82830.html][img]https://gmatclub.com/static/posted_from.png[/img][/url] [size=85][i][color=#666666]Posted from[/color] [b][url=https://gmatclub.com/forum/gmat-toolkit-iphone-ipod-application-82830.html][color=#459926]GMAT ToolKit[/color][/url][/b][/i][/size]
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Re: A farmer constructs a fence along the northern edge of his property [#permalink] New post   01 Jul 2017, 15:59
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|--7mts--|--7mts--|..............

He places a fence after each post. I.e he builds 99 fences before putting down the 100th post.
99*7
Units digit is 3. No need to calculate. Answer is B
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Re: A farmer constructs a fence along the northern edge of his property [#permalink] New post   02 Jul 2017, 16:23
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alanforde800Maximus wrote:
A farmer constructs a fence along the northern edge of his property, using materials such
that he places a post every 7 meters. if he uses 100 posts, how many meters will the fence span?

a)686
b)693
c)700
d)707
e)770

Please assist with above problem.

I like the solutions above. I literally drew a picture.

For any specific range with "marked off" beginning and end values, there will always be one more tick than interval.

Wasn't sure I remembered that rule correctly, so I drew 10 posts, and wrote 7 in between:

|7|7|7|7|7|7|7|7|7|

Then I counted. 10 fence posts, but only 9 lengths of 7 in between. So 100 fence posts = 99 intervals of 7 meters.

99*7 = 693. Answer B
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Re: A farmer constructs a fence along the northern edge of his property [#permalink] New post   23 Jan 2018, 14:23
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Hi All,

This is an example of a 'fence post' problem (literally and figuratively). The 'key' to these types of questions is to remember that there's a 'first post' that you have to include in your total. Here's a much simpler example of this type of math - if you read pages 2 through 5 (inclusive) of a book, then how many pages did you read? It's 4 pages (not 3), since you read pages 2, 3, 4 and 5.

Thus, we have the first post, then another post every 7 meters. That means that we're 99(7) meters away from the first post once we plant the last post.

(99)(7) = 693

Final Answer:
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B


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A farmer constructs a fence along the northern edge of his property [#permalink] New post   28 Jun 2019, 15:11
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We can also use the formula for arithmetic progression!

\(ntn = a + d (n -1)\)

nth = The value we are looking for.

a = 0 mts
d = 7 mts (every 7 meters)
n = 100 posts

\(nth = 0 + 7 (100 -1)\)

\(nth = 693\)
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Re: A farmer constructs a fence along the northern edge of his property [#permalink] New post   18 Feb 2020, 14:12
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A farmer constructs a fence along the northern edge of his property [#permalink] New post   21 Jul 2020, 10:31
Nanobotstv wrote:
A farmer constructs a fence along the northern edge of his property, using materials such that he places a post every 7 meters. if he uses 100 posts, how many meters will the fence span?

A. 686
B. 693
C. 700
D. 707
E. 770


Alternately, we can also use the formula to find the \(n^{th}\) term of an arithmetic progression i.e. first term + (n - 1) * common difference

Here, the posts are separated with a fixed distance of \(7\) meters hence common difference is \(7\) meters. The first post is at \(0\) meters hence we need find the location of the \(100^{th}\) post

\(0 + (100 - 1) * 7 = 99 * 7 = 693\)

Ans. B
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Re: A farmer constructs a fence along the northern edge of his property [#permalink] New post   22 Feb 2022, 18:51
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Re: A farmer constructs a fence along the northern edge of his property [#permalink]
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