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In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC =

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V
Joined: 02 Sep 2009
Posts: 52296
In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC =  [#permalink]

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New post 25 Dec 2018, 01:46
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

91% (01:43) correct 9% (02:40) wrong based on 35 sessions

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In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC =


A. 6
B. 4
C. 3
D. 2
E. 1

Attachment:
2018-12-25_1345.png
2018-12-25_1345.png [ 3.97 KiB | Viewed 237 times ]

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Re: In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC =  [#permalink]

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New post 25 Dec 2018, 02:44
1
Solution:
Let the distance between AB, BC, CD, & DE be a, b, c, and d units respectively.
Given that, AD = BE
=> a + b + c = b + c + d
=> a = d, i.e. AB = DE
Again AD = BE = 6
AD = a + b + c = 6
And AE = 8
a + b + c + d = 8
Therefore, d = 2 (Since a + b + c = 6)
a = d = 2
Again consider a + b + c + d = 8
Given that CD = 3(BC), i.e. c = 3b
a + b + 3b + d = 8
2 + 4B + 2 = 8 (Since a = d = 2)
4b = 4
b = 1, i.e. BC = 1

Hence, the correct answer is option E. 1
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In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC =  [#permalink]

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New post 25 Dec 2018, 07:45
Bunuel wrote:
Image
In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC =


A. 6
B. 4
C. 3
D. 2
E. 1

Attachment:
2018-12-25_1345.png



let bc = x so cd= 3x

AB= 6-4x
and we can say
6-4x+4x+6-4x=8

solve for x we get =1
IMO E
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In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC = &nbs [#permalink] 25 Dec 2018, 07:45
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In the diagram above, AD = BE = 6 and CD = 3(BC). If AE = 8, then BC =

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