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An irregular plot of land is surrounded by four straight segments

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An irregular plot of land is surrounded by four straight segments [#permalink]

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New post 07 Aug 2017, 23:37
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Difficulty:

  75% (hard)

Question Stats:

47% (01:39) correct 53% (02:31) wrong based on 38 sessions

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An irregular plot of land is surrounded by four straight segments of fence of meter lengths (5x + 5), (5x + 5), (3x + 10) and 2x. Is the total length of fence greater than 70 meters?

A. The average (arithmetic mean) fence segment length is less than 25 meters.

B. The largest fence segment is three times the length of the smallest fence segment.
[Reveal] Spoiler: OA

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Re: An irregular plot of land is surrounded by four straight segments [#permalink]

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New post 07 Aug 2017, 23:56
An irregular plot of land is surrounded by four straight segments of fence of meter lengths (5x + 5), (5x + 5), (3x + 10) and 2x. Is the total length of fence greater than 70 meters?

A. The average (arithmetic mean) fence segment length is less than 25 meters.

B. The largest fence segment is three times the length of the smallest fence segment.

perimeter = length of the fence = 15x + 15 > 70 or 3( x + 1) > 14 or x + 1 > 14/3 or x > (14 - 3)/3 > 11/3 > 3.6

[1] : average is = (15x + 15 )/ 4 < 25 or x + 1 < 100/15 or x < 85/15 or x < 5.6 : not sufficient

[2] : we do not know which length is lengthiest

so let's assume 3x + 10 = 3( 5x + 5) ==> 3x + 10 = 15x + 15 ==> can't be possible as x is coming out to be negative
so now let's assume 5x + 5 = 6x so x = 5 ==> possible
let's see further 3x + 10 = 6x so 2x = 10 ==> x = 5

hence x = 5 : sufficient to answer the question hence B
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Re: An irregular plot of land is surrounded by four straight segments [#permalink]

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New post 08 Aug 2017, 10:00
Leo8 wrote:
An irregular plot of land is surrounded by four straight segments of fence of meter lengths (5x + 5), (5x + 5), (3x + 10) and 2x. Is the total length of fence greater than 70 meters?

A. The average (arithmetic mean) fence segment length is less than 25 meters.

B. The largest fence segment is three times the length of the smallest fence segment.

perimeter = length of the fence = 15x + 15 > 70 or 3( x + 1) > 14 or x + 1 > 14/3 or x > (14 - 3)/3 > 11/3 > 3.6

[1] : average is = (15x + 15 )/ 4 < 25 or x + 1 < 100/15 or x < 85/15 or x < 5.6 : not sufficient

[2] : we do not know which length is lengthiest

so let's assume 3x + 10 = 3( 5x + 5) ==> 3x + 10 = 15x + 15 ==> can't be possible as x is coming out to be negative
so now let's assume 5x + 5 = 6x so x = 5 ==> possible
let's see further 3x + 10 = 6x so 2x = 10 ==> x = 5

hence x = 5 : sufficient to answer the question hence B


Refer to the red text in your post.

6x-3x =10 => x=10/3 => x=3.33

so ideally x >11/3 , but we are getting 10/3 and 5 as two options.
Can't be sure.
I think that the answer should be E.

Please provide OE. :)
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Re: An irregular plot of land is surrounded by four straight segments [#permalink]

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New post 08 Aug 2017, 10:38
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godot53 wrote:
An irregular plot of land is surrounded by four straight segments of fence of meter lengths (5x + 5), (5x + 5), (3x + 10) and 2x. Is the total length of fence greater than 70 meters?

15x + 20 > 70
=> x > \(\frac{10}{3}\) ?


Quote:
A. The average (arithmetic mean) fence segment length is less than 25 meters.

1) 15x + 20 < 100
=> x < \(\frac{16}{3}\)
Insufficient.


Quote:
B. The largest fence segment is three times the length of the smallest fence segment.

Smallest side has to be 2x regardless of the value of x, as x > 0.

2 scenarios
Greatest side is 5x + 5
5x + 5 = 6x
=> x = 5
5x + 5 > 3x + 10. Looks good.

Greatest side is 3x + 10
3x + 10 = 6x
=> x = \(\frac{10}{3}\)
Let's insert this value back into the equation to check, if it matches with our assumption.
3x + 10 < 5x + 5 ---> This breaks the statement, so we cannot use this value.

x = 5. Unique value. Sufficient. B is the answer.
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Re: An irregular plot of land is surrounded by four straight segments   [#permalink] 08 Aug 2017, 10:38
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