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

Question

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

BrentGMATPrepNow · Accepted Answer

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:  B

winkherehere · Answer

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

sasyaharry · Answer

|--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

generis · Answer

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

EMPOWERgmatRichC · Answer

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:  B

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

jfranciscocuencag · Answer

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

Pritishd · Answer

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

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

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