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A straight fence is to be constructed from posts 6 inches
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04 Feb 2018, 01:37
04 Feb 2018, 01:37
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Question Stats:
57% (01:40) correct
42% (02:15) wrong based on 42 sessions
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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 be the length of the fence in feet? (12 inches = 1 foot)
Indicate ALL such answers
A) 17
B) 28
C) 35
D) 39
E) 50
Indicate ALL such answers
A) 17
B) 28
C) 35
D) 39
E) 50
ShowHide Answer
Official Answer
A,B,D,E
Re: A straight fence is to be constructed from posts 6 inches
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04 Feb 2018, 11:19
04 Feb 2018, 11:19
1
the fence goes like this:
| |___| |___| |_ .... _ | |
so you start with 1/2 foot and end up with 1/2 foot
(1/2+5)k represent the pair of wood+chain add 1/2 to it for the last unpaired piece of wood to get the total
(5+1/2)k+1/2=total
test answers, plug in total and make sure k is an integer.
All work except C:
(5+1/2)k+1/2= 11k/2+1/2=(11k+1)/2=total
2*35=11k+1
70-1=11k
69/11=/ not an integer
| |___| |___| |_ .... _ | |
so you start with 1/2 foot and end up with 1/2 foot
(1/2+5)k represent the pair of wood+chain add 1/2 to it for the last unpaired piece of wood to get the total
(5+1/2)k+1/2=total
test answers, plug in total and make sure k is an integer.
All work except C:
(5+1/2)k+1/2= 11k/2+1/2=(11k+1)/2=total
2*35=11k+1
70-1=11k
69/11=/ not an integer
Re: A straight fence is to be constructed from posts 6 inches
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02 Jul 2020, 22:54
02 Jul 2020, 22:54
If the fence starts and ends with a post:
For a fence with 1 chain we'll have 2 posts
For a fence with 2 chains we'll have 3 posts
For a fence with 3 chains we'll have 4 posts
And so on.
So if the number of chains is n, the number of posts will be n+1.
As a result the length of the fence will be:
l= (length of chain x n)+(length of post(in feet)x(n+1))
l= (5n)+(0.5x(n+1))
l= 5.5n+0.5
Now, if we want to analyze the options, we will work with "l".
n= (l-0.5)/5.5
And n should be an integer
Advice: We should always try to avoid decimal's use.Makes problem solving slower.
In this equation is possible to multiply it by 10.
Thus,
n= (10xl-5)/55
As we can see, the only way n can be an integer is to be a multiple of 55. That means multiple of 5 and 11 at the same time.
In this last equation, its obvious that any integer multiplyied by 10 and substracted by 5 is a multiple of 5.
So we need (10xl-5) to be multiple of 11.
Divisibility rules says that to be a multiple of 11 we must substract the last digit to the number made by the first to digits and the result should be a multiple of 11.
Analyzing the options:
17--->170-5=165--->16-5=11 - Right
28--->280-5=275--->27-5=22 - Right
35--->350-5=345--->34-5=29 - Not Right
39--->390-5=385--->38-5=33 - Right
50--->500-5=495--->49-5=44 - Right
Answer: A,B,D,E
For a fence with 1 chain we'll have 2 posts
For a fence with 2 chains we'll have 3 posts
For a fence with 3 chains we'll have 4 posts
And so on.
So if the number of chains is n, the number of posts will be n+1.
As a result the length of the fence will be:
l= (length of chain x n)+(length of post(in feet)x(n+1))
l= (5n)+(0.5x(n+1))
l= 5.5n+0.5
Now, if we want to analyze the options, we will work with "l".
n= (l-0.5)/5.5
And n should be an integer
Advice: We should always try to avoid decimal's use.Makes problem solving slower.
In this equation is possible to multiply it by 10.
Thus,
n= (10xl-5)/55
As we can see, the only way n can be an integer is to be a multiple of 55. That means multiple of 5 and 11 at the same time.
In this last equation, its obvious that any integer multiplyied by 10 and substracted by 5 is a multiple of 5.
So we need (10xl-5) to be multiple of 11.
Divisibility rules says that to be a multiple of 11 we must substract the last digit to the number made by the first to digits and the result should be a multiple of 11.
Analyzing the options:
17--->170-5=165--->16-5=11 - Right
28--->280-5=275--->27-5=22 - Right
35--->350-5=345--->34-5=29 - Not Right
39--->390-5=385--->38-5=33 - Right
50--->500-5=495--->49-5=44 - Right
Answer: A,B,D,E
