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On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC

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On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC  [#permalink]

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New post 04 Oct 2018, 02:02
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (02:57) correct 33% (03:13) wrong based on 89 sessions

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Math Expert
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Joined: 02 Aug 2009
Posts: 8324
Re: On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC  [#permalink]

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New post 04 Oct 2018, 20:57
1
Bunuel wrote:
On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC = 24, then AD =
Image

(A) 24
(B) 48
(C) 72
(D) 96
(E) 120


Attachment:
2018-10-04_1300.png


AB+BC+CD=AD
NOW CD=2AB and
2BD=3AC....2(BC+CD)=3(AB+BC).....2CD=3AB+BC
But CD=2AB, so 2*(2AB)=3*AB+24.....AB=24
CD=2*24=48
Therefore AD=24+24+48=96

D
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Re: On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC  [#permalink]

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New post 05 Oct 2018, 07:19
2
Top Contributor
1
Bunuel wrote:
On the line segment AD shown below, AB = (1/2)(CD) and BD = (3/2)(AC). If BC = 24, then AD =
Image

(A) 24
(B) 48
(C) 72
(D) 96
(E) 120

Attachment:
2018-10-04_1300.png


GIVEN: BC = 24. Add this to the diagram.
Also, let x = the length of CD
Image

GIVEN: AB = (1/2)(CD)
Since CD has length x, we know that 0.5x = the length of AB
Image

GIVEN: BD = (3/2)(AC)
BD has length 24 + x
AC has length 24 + 0.5x
So, we can write: 24 + x = (3/2)(24 + 0.5x)
Expand right side to get: 24 + x = 36 + 0.75x
Subtract 0.75x from both sides to get: 24 + 0.25x = 36
Subtract 24 from both sides to get: 0.25x = 12
Solve: x = 48
If x = 48, then 0.5x = 24

Add this information to the diagram:
Image

Length of AD = 24 + 24 + 48
= 96

Answer: D

Cheers,
Brent
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Re: On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC  [#permalink]

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New post 23 Oct 2019, 11:40
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Re: On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC   [#permalink] 23 Oct 2019, 11:40
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