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Fence

by knight247 » Fri Sep 09, 2011 2:27 pm
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

OA is C. Detailed explanations would be appreciated.
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by force5 » Fri Sep 09, 2011 2:50 pm
2 post 1 chain will give you 6*2+5 = 17
3 post and 2 chains = 18+10= 28
4 post and 3 chains= 24+15=39
5 posts and 4 chains = 30+20=50

hence only 35 is not possible

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by pemdas » Fri Sep 09, 2011 3:25 pm
p is # of posts, c is # of chains, p=c+1 and p/2+5c=A (answer choices)
(c+1)/2+5c=A <> 11c+1=2A
by testing below and allowing c to be only integer values
a) 17*2=11c+1, c=3 OK
b) 28*2=11c+1, c=5 OK
c) 35*2=11c+1, c=69/11 ? (correct choice)
d) 39*2=11c+1, c=7 OK
e) 50*2=11c+1, c=9 OK

c
knight247 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

OA is C. Detailed explanations would be appreciated.
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by pemdas » Fri Sep 09, 2011 3:30 pm
this do-try method turns out to be mistake c=5 feet and p=1/2 foot
50 feet is not equal to 5 posts (5*1/2=2.5) and 4 chains (4*5=20)
...
:(
force5 wrote:2 post 1 chain will give you 6*2+5 = 17
3 post and 2 chains = 18+10= 28
4 post and 3 chains= 24+15=39
5 posts and 4 chains = 30+20=50

hence only 35 is not possible

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by Whitney Garner » Fri Sep 09, 2011 4:31 pm
knight247 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

OA is C. Detailed explanations would be appreciated.
Notice that to have a fence, we need at least 2 posts and 1 chain. If we measure this in feet (because that is the measure for the answer):

[.5]-------5--------[.5]

The minimum length is 6 feet. Now, to increase the length of the fence, we would have to add an additional chain+post, or 5.5 feet. But take a look at the answers, they are all in whole numbers! That means that we will need to add enough fence each time to cancel out the 0.5 inch posts - so that means we need to add 2 chains and 2 posts each time: 5+0.5+5+0.5 = 11 feet.

Now we can just list out the possible numbers starting with 6 and increasing in 11 foot increments.

6, 17, 28, 39....

But wait - we just skipped over 35, choice C.

Hope this helps!
:)
Whit
Whitney Garner
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www.whitneygarner.com

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