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

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Manager
Joined: 13 Sep 2016
Posts: 115
GMAT 1: 800 Q51 V51
A farmer constructs a fence along the northern edge of his property  [#permalink]

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03 Oct 2016, 06:27
2
14
00:00

Difficulty:

35% (medium)

Question Stats:

62% (01:13) correct 38% (01:16) wrong based on 286 sessions

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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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Joined: 20 Sep 2016
Posts: 2
Re: A farmer constructs a fence along the northern edge of his property  [#permalink]

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03 Oct 2016, 07:26
1
2
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

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Re: A farmer constructs a fence along the northern edge of his property  [#permalink]

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03 Oct 2016, 07:32
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Top Contributor
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

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

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Re: A farmer constructs a fence along the northern edge of his property  [#permalink]

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01 Jul 2017, 15:59
1
|--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]

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02 Jul 2017, 16:23
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

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.

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Re: A farmer constructs a fence along the northern edge of his property  [#permalink]

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23 Jan 2018, 14:23
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

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A farmer constructs a fence along the northern edge of his property  [#permalink]

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28 Jun 2019, 15:11
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

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

$$nth = 693$$
A farmer constructs a fence along the northern edge of his property   [#permalink] 28 Jun 2019, 15:11
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