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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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Carcass
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On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC [#permalink] New post   08 Apr 2021, 01:52
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On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC = 24, then AD =
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(A) 24
(B) 48
(C) 72
(D) 96
(E) 120

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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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] New post   08 Apr 2021, 04:27
1
let ab=x and bc=y
then cd=2x and bd=y+2x and ac=x+y

Putting this information in bd=3/2*ac and bc=24
->y=24 and (y+2x)=3/2*(x+y)
Solving for x-> x=24

We need to find ad
-> ad=ab+bc+cd
-> ad=x+y+2x=3x+y=96

Correct answer is 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] New post   08 Apr 2021, 04:59
1
AB = 0.5 CD
2 AB = CD

BD = 1.5 AC
BC + CD = 1.5 (AB + BC)
24 + 2AB = 1.5 AB + 36
0.5 AB = 12
AB = 24
and CD = 24 * 2 = 48

So, AD = AB + BC + CD = 24 + 24 + 48 = 96 (Ans 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] New post   08 Apr 2021, 05:24
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Carcass 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

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


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] New post   08 Apr 2021, 15:44
A B C D

unknown, 24, unknown


\(\frac{3}{2}\)*(\(\frac{x}{2}\) + 24) = 24 + x

x = 48
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Re: On the line segment AD shown below, AB = 1/2*CD and BD = 3/2*AC. If BC [#permalink] New post   04 Jun 2023, 21:26
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