## A farmer constructs a fence along the northern edg

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### A farmer constructs a fence along the northern edg

by alanforde800Maximus » Mon Oct 03, 2016 5:23 am
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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by Brent@GMATPrepNow » Mon Oct 03, 2016 6:33 am
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

RELATED VIDEO
- Growth tables: https://www.gmatprepnow.com/module/gmat ... /video/929

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by [email protected] » Mon Oct 03, 2016 9:34 am
Hi alanforde800Maximus,

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

GMAT assassins aren't born, they're made,
Rich

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by Poisson » Fri Nov 25, 2016 3:23 pm
Brent@GMATPrepNow wrote:
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

RELATED VIDEO
- Growth tables: https://www.gmatprepnow.com/module/gmat ... /video/929
Thank you. I'm working on a similar problem. I'm trying to uncover the pattern involved.

A farmer plans to build a fence next to a stretch of driveway. Each post will be one foot wide and there will be three feet of space between each post. If the driveway is 65 feet long and the fence will be on only one side of the driveway, how many posts will the farmer need to complete the fence?

A.16
B.17
C.18
D.19
E.20

The pattern I'm seeing is:

(#) posts + 3x feet = # of feet

(1) post + 3(0) = 1 feet
(2) posts + 3(1) = 5 feet
(3) posts + 3(2) = 9 feet
(4) posts + 3(3) = 13 feet
.
.
.
.
(17) posts + 3(16) = 65 feet

Is there another pattern that I'm not seeing in this problem? I understand the quick way to get the answer is 65/4, but I want to make sure I understand the pattern. Thanks so much.

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by Brent@GMATPrepNow » Fri Nov 25, 2016 3:44 pm
Poisson wrote: Thank you. I'm working on a similar problem. I'm trying to uncover the pattern involved.

A farmer plans to build a fence next to a stretch of driveway. Each post will be one foot wide and there will be three feet of space between each post. If the driveway is 65 feet long and the fence will be on only one side of the driveway, how many posts will the farmer need to complete the fence?

A.16
B.17
C.18
D.19
E.20

The pattern I'm seeing is:

(#) posts + 3x feet = # of feet

(1) post + 3(0) = 1 feet
(2) posts + 3(1) = 5 feet
(3) posts + 3(2) = 9 feet
(4) posts + 3(3) = 13 feet
.
.
.
.
(17) posts + 3(16) = 65 feet

Is there another pattern that I'm not seeing in this problem? I understand the quick way to get the answer is 65/4, but I want to make sure I understand the pattern. Thanks so much.
Looks good to me.
So, algebraically speaking, if n = # of posts, then the length of the fence (including posts) = n + 3(n-1)
= n + 3n - 3
= 4n - 3

So, for a 65-foot fence, we set the equation to 65....
4n - 3 = 65
Solve to get n = 17

Cheers,
Brent

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