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What is the length of the line AD? (1) AC = 10, BD=15 (2) AB/BC=BC/CD

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Math Expert
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V
Joined: 02 Sep 2009
Posts: 58458
What is the length of the line AD? (1) AC = 10, BD=15 (2) AB/BC=BC/CD  [#permalink]

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New post 17 Oct 2018, 00:38
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (01:43) correct 41% (01:46) wrong based on 66 sessions

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NUS School Moderator
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V
Joined: 18 Jul 2018
Posts: 1019
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
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Re: What is the length of the line AD? (1) AC = 10, BD=15 (2) AB/BC=BC/CD  [#permalink]

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New post 17 Oct 2018, 19:16
From statement 1:

AC = AB+BC = 10
BD = BC+CD = 15

AD = AB+BC+CD. Since BC is unknown. We cant determine the length of AD.
Insufficient.

From statement 2:

\(\frac{AB}{BC}\) = \(\frac{BC}{CD}\) Cross multiplying gives \(BC^2\) = AB*CD.
Clearly Insufficient.

Combining both From 1:
AB = 10-BC
CD = 15-BC
From 2 \(BC^2\) = AB*CD = (10-BC)(15-BC)
Solving gives BC as 6.

Hence AD becomes 19.
Sufficient.

C is the aswer.
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Re: What is the length of the line AD? (1) AC = 10, BD=15 (2) AB/BC=BC/CD   [#permalink] 17 Oct 2018, 19:16
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What is the length of the line AD? (1) AC = 10, BD=15 (2) AB/BC=BC/CD

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